A BAYESIAN SPATIAL AND TEMPORAL MODELING APPROACH TO MAPPING GEOGRAPHIC VARIATION IN MORTALITY RATES FOR SUBNATIONAL AREAS WITH R-INLA.

PubMed

Khana, Diba; Rossen, Lauren M; Hedegaard, Holly; Warner, Margaret

2018-01-01

Hierarchical Bayes models have been used in disease mapping to examine small scale geographic variation. State level geographic variation for less common causes of mortality outcomes have been reported however county level variation is rarely examined. Due to concerns about statistical reliability and confidentiality, county-level mortality rates based on fewer than 20 deaths are suppressed based on Division of Vital Statistics, National Center for Health Statistics (NCHS) statistical reliability criteria, precluding an examination of spatio-temporal variation in less common causes of mortality outcomes such as suicide rates (SRs) at the county level using direct estimates. Existing Bayesian spatio-temporal modeling strategies can be applied via Integrated Nested Laplace Approximation (INLA) in R to a large number of rare causes of mortality outcomes to enable examination of spatio-temporal variations on smaller geographic scales such as counties. This method allows examination of spatiotemporal variation across the entire U.S., even where the data are sparse. We used mortality data from 2005-2015 to explore spatiotemporal variation in SRs, as one particular application of the Bayesian spatio-temporal modeling strategy in R-INLA to predict year and county-specific SRs. Specifically, hierarchical Bayesian spatio-temporal models were implemented with spatially structured and unstructured random effects, correlated time effects, time varying confounders and space-time interaction terms in the software R-INLA, borrowing strength across both counties and years to produce smoothed county level SRs. Model-based estimates of SRs were mapped to explore geographic variation.

NASA's Human Mission to a Near-Earth Asteroid: Landing on a Moving Target

NASA Technical Reports Server (NTRS)

Smith, Jeffrey H.; Lincoln, William P.; Weisbin, Charles R.

2011-01-01

This paper describes a Bayesian approach for comparing the productivity and cost-risk tradeoffs of sending versus not sending one or more robotic surveyor missions prior to a human mission to land on an asteroid. The expected value of sample information based on productivity combined with parametric variations in the prior probability an asteroid might be found suitable for landing were used to assess the optimal number of spacecraft and asteroids to survey. The analysis supports the value of surveyor missions to asteroids and indicates one launch with two spacecraft going simultaneously to two independent asteroids appears optimal.

A Spatial Poisson Hurdle Model for Exploring Geographic Variation in Emergency Department Visits

PubMed Central

Neelon, Brian; Ghosh, Pulak; Loebs, Patrick F.

2012-01-01

Summary We develop a spatial Poisson hurdle model to explore geographic variation in emergency department (ED) visits while accounting for zero inflation. The model consists of two components: a Bernoulli component that models the probability of any ED use (i.e., at least one ED visit per year), and a truncated Poisson component that models the number of ED visits given use. Together, these components address both the abundance of zeros and the right-skewed nature of the nonzero counts. The model has a hierarchical structure that incorporates patient- and area-level covariates, as well as spatially correlated random effects for each areal unit. Because regions with high rates of ED use are likely to have high expected counts among users, we model the spatial random effects via a bivariate conditionally autoregressive (CAR) prior, which introduces dependence between the components and provides spatial smoothing and sharing of information across neighboring regions. Using a simulation study, we show that modeling the between-component correlation reduces bias in parameter estimates. We adopt a Bayesian estimation approach, and the model can be fit using standard Bayesian software. We apply the model to a study of patient and neighborhood factors influencing emergency department use in Durham County, North Carolina. PMID:23543242

Estimation for coefficient of variation of an extension of the exponential distribution under type-II censoring scheme

NASA Astrophysics Data System (ADS)

Bakoban, Rana A.

2017-08-01

The coefficient of variation [CV] has several applications in applied statistics. So in this paper, we adopt Bayesian and non-Bayesian approaches for the estimation of CV under type-II censored data from extension exponential distribution [EED]. The point and interval estimate of the CV are obtained for each of the maximum likelihood and parametric bootstrap techniques. Also the Bayesian approach with the help of MCMC method is presented. A real data set is presented and analyzed, hence the obtained results are used to assess the obtained theoretical results.

Understanding the Scalability of Bayesian Network Inference Using Clique Tree Growth Curves

NASA Technical Reports Server (NTRS)

Mengshoel, Ole J.

2010-01-01

One of the main approaches to performing computation in Bayesian networks (BNs) is clique tree clustering and propagation. The clique tree approach consists of propagation in a clique tree compiled from a Bayesian network, and while it was introduced in the 1980s, there is still a lack of understanding of how clique tree computation time depends on variations in BN size and structure. In this article, we improve this understanding by developing an approach to characterizing clique tree growth as a function of parameters that can be computed in polynomial time from BNs, specifically: (i) the ratio of the number of a BN s non-root nodes to the number of root nodes, and (ii) the expected number of moral edges in their moral graphs. Analytically, we partition the set of cliques in a clique tree into different sets, and introduce a growth curve for the total size of each set. For the special case of bipartite BNs, there are two sets and two growth curves, a mixed clique growth curve and a root clique growth curve. In experiments, where random bipartite BNs generated using the BPART algorithm are studied, we systematically increase the out-degree of the root nodes in bipartite Bayesian networks, by increasing the number of leaf nodes. Surprisingly, root clique growth is well-approximated by Gompertz growth curves, an S-shaped family of curves that has previously been used to describe growth processes in biology, medicine, and neuroscience. We believe that this research improves the understanding of the scaling behavior of clique tree clustering for a certain class of Bayesian networks; presents an aid for trade-off studies of clique tree clustering using growth curves; and ultimately provides a foundation for benchmarking and developing improved BN inference and machine learning algorithms.

Comparing spatially varying coefficient models: a case study examining violent crime rates and their relationships to alcohol outlets and illegal drug arrests

NASA Astrophysics Data System (ADS)

Wheeler, David C.; Waller, Lance A.

2009-03-01

In this paper, we compare and contrast a Bayesian spatially varying coefficient process (SVCP) model with a geographically weighted regression (GWR) model for the estimation of the potentially spatially varying regression effects of alcohol outlets and illegal drug activity on violent crime in Houston, Texas. In addition, we focus on the inherent coefficient shrinkage properties of the Bayesian SVCP model as a way to address increased coefficient variance that follows from collinearity in GWR models. We outline the advantages of the Bayesian model in terms of reducing inflated coefficient variance, enhanced model flexibility, and more formal measuring of model uncertainty for prediction. We find spatially varying effects for alcohol outlets and drug violations, but the amount of variation depends on the type of model used. For the Bayesian model, this variation is controllable through the amount of prior influence placed on the variance of the coefficients. For example, the spatial pattern of coefficients is similar for the GWR and Bayesian models when a relatively large prior variance is used in the Bayesian model.

Mean Field Variational Bayesian Data Assimilation

NASA Astrophysics Data System (ADS)

Vrettas, M.; Cornford, D.; Opper, M.

2012-04-01

Current data assimilation schemes propose a range of approximate solutions to the classical data assimilation problem, particularly state estimation. Broadly there are three main active research areas: ensemble Kalman filter methods which rely on statistical linearization of the model evolution equations, particle filters which provide a discrete point representation of the posterior filtering or smoothing distribution and 4DVAR methods which seek the most likely posterior smoothing solution. In this paper we present a recent extension to our variational Bayesian algorithm which seeks the most probably posterior distribution over the states, within the family of non-stationary Gaussian processes. Our original work on variational Bayesian approaches to data assimilation sought the best approximating time varying Gaussian process to the posterior smoothing distribution for stochastic dynamical systems. This approach was based on minimising the Kullback-Leibler divergence between the true posterior over paths, and our Gaussian process approximation. So long as the observation density was sufficiently high to bring the posterior smoothing density close to Gaussian the algorithm proved very effective, on lower dimensional systems. However for higher dimensional systems, the algorithm was computationally very demanding. We have been developing a mean field version of the algorithm which treats the state variables at a given time as being independent in the posterior approximation, but still accounts for their relationships between each other in the mean solution arising from the original dynamical system. In this work we present the new mean field variational Bayesian approach, illustrating its performance on a range of classical data assimilation problems. We discuss the potential and limitations of the new approach. We emphasise that the variational Bayesian approach we adopt, in contrast to other variational approaches, provides a bound on the marginal likelihood of the observations given parameters in the model which also allows inference of parameters such as observation errors, and parameters in the model and model error representation, particularly if this is written as a deterministic form with small additive noise. We stress that our approach can address very long time window and weak constraint settings. However like traditional variational approaches our Bayesian variational method has the benefit of being posed as an optimisation problem. We finish with a sketch of the future directions for our approach.

The Dopaminergic Midbrain Encodes the Expected Certainty about Desired Outcomes.

PubMed

Schwartenbeck, Philipp; FitzGerald, Thomas H B; Mathys, Christoph; Dolan, Ray; Friston, Karl

2015-10-01

Dopamine plays a key role in learning; however, its exact function in decision making and choice remains unclear. Recently, we proposed a generic model based on active (Bayesian) inference wherein dopamine encodes the precision of beliefs about optimal policies. Put simply, dopamine discharges reflect the confidence that a chosen policy will lead to desired outcomes. We designed a novel task to test this hypothesis, where subjects played a "limited offer" game in a functional magnetic resonance imaging experiment. Subjects had to decide how long to wait for a high offer before accepting a low offer, with the risk of losing everything if they waited too long. Bayesian model comparison showed that behavior strongly supported active inference, based on surprise minimization, over classical utility maximization schemes. Furthermore, midbrain activity, encompassing dopamine projection neurons, was accurately predicted by trial-by-trial variations in model-based estimates of precision. Our findings demonstrate that human subjects infer both optimal policies and the precision of those inferences, and thus support the notion that humans perform hierarchical probabilistic Bayesian inference. In other words, subjects have to infer both what they should do as well as how confident they are in their choices, where confidence may be encoded by dopaminergic firing. © The Author 2014. Published by Oxford University Press.

The Dopaminergic Midbrain Encodes the Expected Certainty about Desired Outcomes

PubMed Central

Schwartenbeck, Philipp; FitzGerald, Thomas H. B.; Mathys, Christoph; Dolan, Ray; Friston, Karl

2015-01-01

Dopamine plays a key role in learning; however, its exact function in decision making and choice remains unclear. Recently, we proposed a generic model based on active (Bayesian) inference wherein dopamine encodes the precision of beliefs about optimal policies. Put simply, dopamine discharges reflect the confidence that a chosen policy will lead to desired outcomes. We designed a novel task to test this hypothesis, where subjects played a “limited offer” game in a functional magnetic resonance imaging experiment. Subjects had to decide how long to wait for a high offer before accepting a low offer, with the risk of losing everything if they waited too long. Bayesian model comparison showed that behavior strongly supported active inference, based on surprise minimization, over classical utility maximization schemes. Furthermore, midbrain activity, encompassing dopamine projection neurons, was accurately predicted by trial-by-trial variations in model-based estimates of precision. Our findings demonstrate that human subjects infer both optimal policies and the precision of those inferences, and thus support the notion that humans perform hierarchical probabilistic Bayesian inference. In other words, subjects have to infer both what they should do as well as how confident they are in their choices, where confidence may be encoded by dopaminergic firing. PMID:25056572

Universal Darwinism As a Process of Bayesian Inference.

PubMed

Campbell, John O

2016-01-01

Many of the mathematical frameworks describing natural selection are equivalent to Bayes' Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus, natural selection serves as a counter example to a widely-held interpretation that restricts Bayesian Inference to human mental processes (including the endeavors of statisticians). As Bayesian inference can always be cast in terms of (variational) free energy minimization, natural selection can be viewed as comprising two components: a generative model of an "experiment" in the external world environment, and the results of that "experiment" or the "surprise" entailed by predicted and actual outcomes of the "experiment." Minimization of free energy implies that the implicit measure of "surprise" experienced serves to update the generative model in a Bayesian manner. This description closely accords with the mechanisms of generalized Darwinian process proposed both by Dawkins, in terms of replicators and vehicles, and Campbell, in terms of inferential systems. Bayesian inference is an algorithm for the accumulation of evidence-based knowledge. This algorithm is now seen to operate over a wide range of evolutionary processes, including natural selection, the evolution of mental models and cultural evolutionary processes, notably including science itself. The variational principle of free energy minimization may thus serve as a unifying mathematical framework for universal Darwinism, the study of evolutionary processes operating throughout nature.

Universal Darwinism As a Process of Bayesian Inference

PubMed Central

Campbell, John O.

2016-01-01

Many of the mathematical frameworks describing natural selection are equivalent to Bayes' Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus, natural selection serves as a counter example to a widely-held interpretation that restricts Bayesian Inference to human mental processes (including the endeavors of statisticians). As Bayesian inference can always be cast in terms of (variational) free energy minimization, natural selection can be viewed as comprising two components: a generative model of an “experiment” in the external world environment, and the results of that “experiment” or the “surprise” entailed by predicted and actual outcomes of the “experiment.” Minimization of free energy implies that the implicit measure of “surprise” experienced serves to update the generative model in a Bayesian manner. This description closely accords with the mechanisms of generalized Darwinian process proposed both by Dawkins, in terms of replicators and vehicles, and Campbell, in terms of inferential systems. Bayesian inference is an algorithm for the accumulation of evidence-based knowledge. This algorithm is now seen to operate over a wide range of evolutionary processes, including natural selection, the evolution of mental models and cultural evolutionary processes, notably including science itself. The variational principle of free energy minimization may thus serve as a unifying mathematical framework for universal Darwinism, the study of evolutionary processes operating throughout nature. PMID:27375438

Expectation propagation for large scale Bayesian inference of non-linear molecular networks from perturbation data.

PubMed

Narimani, Zahra; Beigy, Hamid; Ahmad, Ashar; Masoudi-Nejad, Ali; Fröhlich, Holger

2017-01-01

Inferring the structure of molecular networks from time series protein or gene expression data provides valuable information about the complex biological processes of the cell. Causal network structure inference has been approached using different methods in the past. Most causal network inference techniques, such as Dynamic Bayesian Networks and ordinary differential equations, are limited by their computational complexity and thus make large scale inference infeasible. This is specifically true if a Bayesian framework is applied in order to deal with the unavoidable uncertainty about the correct model. We devise a novel Bayesian network reverse engineering approach using ordinary differential equations with the ability to include non-linearity. Besides modeling arbitrary, possibly combinatorial and time dependent perturbations with unknown targets, one of our main contributions is the use of Expectation Propagation, an algorithm for approximate Bayesian inference over large scale network structures in short computation time. We further explore the possibility of integrating prior knowledge into network inference. We evaluate the proposed model on DREAM4 and DREAM8 data and find it competitive against several state-of-the-art existing network inference methods.

Numerical study on the sequential Bayesian approach for radioactive materials detection

NASA Astrophysics Data System (ADS)

Qingpei, Xiang; Dongfeng, Tian; Jianyu, Zhu; Fanhua, Hao; Ge, Ding; Jun, Zeng

2013-01-01

A new detection method, based on the sequential Bayesian approach proposed by Candy et al., offers new horizons for the research of radioactive detection. Compared with the commonly adopted detection methods incorporated with statistical theory, the sequential Bayesian approach offers the advantages of shorter verification time during the analysis of spectra that contain low total counts, especially in complex radionuclide components. In this paper, a simulation experiment platform implanted with the methodology of sequential Bayesian approach was developed. Events sequences of γ-rays associating with the true parameters of a LaBr3(Ce) detector were obtained based on an events sequence generator using Monte Carlo sampling theory to study the performance of the sequential Bayesian approach. The numerical experimental results are in accordance with those of Candy. Moreover, the relationship between the detection model and the event generator, respectively represented by the expected detection rate (Am) and the tested detection rate (Gm) parameters, is investigated. To achieve an optimal performance for this processor, the interval of the tested detection rate as a function of the expected detection rate is also presented.

Next Steps in Bayesian Structural Equation Models: Comments on, Variations of, and Extensions to Muthen and Asparouhov (2012)

ERIC Educational Resources Information Center

Rindskopf, David

2012-01-01

Muthen and Asparouhov (2012) made a strong case for the advantages of Bayesian methodology in factor analysis and structural equation models. I show additional extensions and adaptations of their methods and show how non-Bayesians can take advantage of many (though not all) of these advantages by using interval restrictions on parameters. By…

Modeling of Academic Achievement of Primary School Students in Ethiopia Using Bayesian Multilevel Approach

ERIC Educational Resources Information Center

Sebro, Negusse Yohannes; Goshu, Ayele Taye

2017-01-01

This study aims to explore Bayesian multilevel modeling to investigate variations of average academic achievement of grade eight school students. A sample of 636 students is randomly selected from 26 private and government schools by a two-stage stratified sampling design. Bayesian method is used to estimate the fixed and random effects. Input and…

Bayesian random-effect model for predicting outcome fraught with heterogeneity--an illustration with episodes of 44 patients with intractable epilepsy.

PubMed

Yen, A M-F; Liou, H-H; Lin, H-L; Chen, T H-H

2006-01-01

The study aimed to develop a predictive model to deal with data fraught with heterogeneity that cannot be explained by sampling variation or measured covariates. The random-effect Poisson regression model was first proposed to deal with over-dispersion for data fraught with heterogeneity after making allowance for measured covariates. Bayesian acyclic graphic model in conjunction with Markov Chain Monte Carlo (MCMC) technique was then applied to estimate the parameters of both relevant covariates and random effect. Predictive distribution was then generated to compare the predicted with the observed for the Bayesian model with and without random effect. Data from repeated measurement of episodes among 44 patients with intractable epilepsy were used as an illustration. The application of Poisson regression without taking heterogeneity into account to epilepsy data yielded a large value of heterogeneity (heterogeneity factor = 17.90, deviance = 1485, degree of freedom (df) = 83). After taking the random effect into account, the value of heterogeneity factor was greatly reduced (heterogeneity factor = 0.52, deviance = 42.5, df = 81). The Pearson chi2 for the comparison between the expected seizure frequencies and the observed ones at two and three months of the model with and without random effect were 34.27 (p = 1.00) and 1799.90 (p < 0.0001), respectively. The Bayesian acyclic model using the MCMC method was demonstrated to have great potential for disease prediction while data show over-dispersion attributed either to correlated property or to subject-to-subject variability.

Fully Bayesian tests of neutrality using genealogical summary statistics.

PubMed

Drummond, Alexei J; Suchard, Marc A

2008-10-31

Many data summary statistics have been developed to detect departures from neutral expectations of evolutionary models. However questions about the neutrality of the evolution of genetic loci within natural populations remain difficult to assess. One critical cause of this difficulty is that most methods for testing neutrality make simplifying assumptions simultaneously about the mutational model and the population size model. Consequentially, rejecting the null hypothesis of neutrality under these methods could result from violations of either or both assumptions, making interpretation troublesome. Here we harness posterior predictive simulation to exploit summary statistics of both the data and model parameters to test the goodness-of-fit of standard models of evolution. We apply the method to test the selective neutrality of molecular evolution in non-recombining gene genealogies and we demonstrate the utility of our method on four real data sets, identifying significant departures of neutrality in human influenza A virus, even after controlling for variation in population size. Importantly, by employing a full model-based Bayesian analysis, our method separates the effects of demography from the effects of selection. The method also allows multiple summary statistics to be used in concert, thus potentially increasing sensitivity. Furthermore, our method remains useful in situations where analytical expectations and variances of summary statistics are not available. This aspect has great potential for the analysis of temporally spaced data, an expanding area previously ignored for limited availability of theory and methods.

Active inference, evidence accumulation and the urn task

PubMed Central

FitzGerald, Thomas HB; Schwartenbeck, Philipp; Moutoussis, Michael; Dolan, Raymond J; Friston, Karl

2015-01-01

Deciding how much evidence to accumulate before making a decision is a problem we and other animals often face, but one which is not completely understood. This issue is particularly important because a tendency to sample less information (often known as reflection impulsivity) is a feature in several psychopathologies, such as psychosis. A formal understanding information sampling may therefore clarify the computational anatomy of psychopathology. In this theoretical paper, we consider evidence accumulation in terms of active (Bayesian) inference using a generic model of Markov decision processes. Here, agents are equipped with beliefs about their own behaviour – in this case, that they will make informed decisions. Normative decision-making is then modelled using variational Bayes to minimise surprise about choice outcomes. Under this scheme, different facets of belief updating map naturally onto the functional anatomy of the brain (at least at a heuristic level). Of particular interest is the key role played by the expected precision of beliefs about control, which we have previously suggested may be encoded by dopaminergic neurons in the midbrain. We show that manipulating expected precision strongly affects how much information an agent characteristically samples, and thus provides a possible link between impulsivity and dopaminergic dysfunction. Our study therefore represents a step towards understanding evidence accumulation in terms of neurobiologically plausible Bayesian inference, and may cast light on why this process is disordered in psychopathology. PMID:25514108

The anatomy of choice: active inference and agency.

PubMed

Friston, Karl; Schwartenbeck, Philipp; Fitzgerald, Thomas; Moutoussis, Michael; Behrens, Timothy; Dolan, Raymond J

2013-01-01

This paper considers agency in the setting of embodied or active inference. In brief, we associate a sense of agency with prior beliefs about action and ask what sorts of beliefs underlie optimal behavior. In particular, we consider prior beliefs that action minimizes the Kullback-Leibler (KL) divergence between desired states and attainable states in the future. This allows one to formulate bounded rationality as approximate Bayesian inference that optimizes a free energy bound on model evidence. We show that constructs like expected utility, exploration bonuses, softmax choice rules and optimism bias emerge as natural consequences of this formulation. Previous accounts of active inference have focused on predictive coding and Bayesian filtering schemes for minimizing free energy. Here, we consider variational Bayes as an alternative scheme that provides formal constraints on the computational anatomy of inference and action-constraints that are remarkably consistent with neuroanatomy. Furthermore, this scheme contextualizes optimal decision theory and economic (utilitarian) formulations as pure inference problems. For example, expected utility theory emerges as a special case of free energy minimization, where the sensitivity or inverse temperature (of softmax functions and quantal response equilibria) has a unique and Bayes-optimal solution-that minimizes free energy. This sensitivity corresponds to the precision of beliefs about behavior, such that attainable goals are afforded a higher precision or confidence. In turn, this means that optimal behavior entails a representation of confidence about outcomes that are under an agent's control.

Parameterization of aquatic ecosystem functioning and its natural variation: Hierarchical Bayesian modelling of plankton food web dynamics

NASA Astrophysics Data System (ADS)

Norros, Veera; Laine, Marko; Lignell, Risto; Thingstad, Frede

2017-10-01

Methods for extracting empirically and theoretically sound parameter values are urgently needed in aquatic ecosystem modelling to describe key flows and their variation in the system. Here, we compare three Bayesian formulations for mechanistic model parameterization that differ in their assumptions about the variation in parameter values between various datasets: 1) global analysis - no variation, 2) separate analysis - independent variation and 3) hierarchical analysis - variation arising from a shared distribution defined by hyperparameters. We tested these methods, using computer-generated and empirical data, coupled with simplified and reasonably realistic plankton food web models, respectively. While all methods were adequate, the simulated example demonstrated that a well-designed hierarchical analysis can result in the most accurate and precise parameter estimates and predictions, due to its ability to combine information across datasets. However, our results also highlighted sensitivity to hyperparameter prior distributions as an important caveat of hierarchical analysis. In the more complex empirical example, hierarchical analysis was able to combine precise identification of parameter values with reasonably good predictive performance, although the ranking of the methods was less straightforward. We conclude that hierarchical Bayesian analysis is a promising tool for identifying key ecosystem-functioning parameters and their variation from empirical datasets.

Effects of Mitochondrial DNA Rate Variation on Reconstruction of Pleistocene Demographic History in a Social Avian Species, Pomatostomus superciliosus

PubMed Central

Norman, Janette A.; Blackmore, Caroline J.; Rourke, Meaghan; Christidis, Les

2014-01-01

Mitochondrial sequence data is often used to reconstruct the demographic history of Pleistocene populations in an effort to understand how species have responded to past climate change events. However, departures from neutral equilibrium conditions can confound evolutionary inference in species with structured populations or those that have experienced periods of population expansion or decline. Selection can affect patterns of mitochondrial DNA variation and variable mutation rates among mitochondrial genes can compromise inferences drawn from single markers. We investigated the contribution of these factors to patterns of mitochondrial variation and estimates of time to most recent common ancestor (TMRCA) for two clades in a co-operatively breeding avian species, the white-browed babbler Pomatostomus superciliosus. Both the protein-coding ND3 gene and hypervariable domain I control region sequences showed departures from neutral expectations within the superciliosus clade, and a two-fold difference in TMRCA estimates. Bayesian phylogenetic analysis provided evidence of departure from a strict clock model of molecular evolution in domain I, leading to an over-estimation of TMRCA for the superciliosus clade at this marker. Our results suggest mitochondrial studies that attempt to reconstruct Pleistocene demographic histories should rigorously evaluate data for departures from neutral equilibrium expectations, including variation in evolutionary rates across multiple markers. Failure to do so can lead to serious errors in the estimation of evolutionary parameters and subsequent demographic inferences concerning the role of climate as a driver of evolutionary change. These effects may be especially pronounced in species with complex social structures occupying heterogeneous environments. We propose that environmentally driven differences in social structure may explain observed differences in evolutionary rate of domain I sequences, resulting from longer than expected retention times for matriarchal lineages in the superciliosus clade. PMID:25181547

Variations on Bayesian Prediction and Inference

DTIC Science & Technology

2016-05-09

inference 2.2.1 Background There are a number of statistical inference problems that are not generally formulated via a full probability model...problem of inference about an unknown parameter, the Bayesian approach requires a full probability 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...the problem of inference about an unknown parameter, the Bayesian approach requires a full probability model/likelihood which can be an obstacle

An economic growth model based on financial credits distribution to the government economy priority sectors of each regency in Indonesia using hierarchical Bayesian method

NASA Astrophysics Data System (ADS)

Yasmirullah, Septia Devi Prihastuti; Iriawan, Nur; Sipayung, Feronika Rosalinda

2017-11-01

The success of regional economic establishment could be measured by economic growth. Since the Act No. 32 of 2004 has been implemented, unbalance economic among the regency in Indonesia is increasing. This condition is contrary different with the government goal to build society welfare through the economic activity development in each region. This research aims to examine economic growth through the distribution of bank credits to each Indonesia's regency. The data analyzed in this research is hierarchically structured data which follow normal distribution in first level. Two modeling approaches are employed in this research, a global-one level Bayesian approach and two-level hierarchical Bayesian approach. The result shows that hierarchical Bayesian has succeeded to demonstrate a better estimation than a global-one level Bayesian. It proves that the different economic growth in each province is significantly influenced by the variations of micro level characteristics in each province. These variations are significantly affected by cities and province characteristics in second level.

Bayesian estimates of the incidence of rare cancers in Europe.

PubMed

Botta, Laura; Capocaccia, Riccardo; Trama, Annalisa; Herrmann, Christian; Salmerón, Diego; De Angelis, Roberta; Mallone, Sandra; Bidoli, Ettore; Marcos-Gragera, Rafael; Dudek-Godeau, Dorota; Gatta, Gemma; Cleries, Ramon

2018-04-21

The RARECAREnet project has updated the estimates of the burden of the 198 rare cancers in each European country. Suspecting that scant data could affect the reliability of statistical analysis, we employed a Bayesian approach to estimate the incidence of these cancers. We analyzed about 2,000,000 rare cancers diagnosed in 2000-2007 provided by 83 population-based cancer registries from 27 European countries. We considered European incidence rates (IRs), calculated over all the data available in RARECAREnet, as a valid a priori to merge with country-specific observed data. Therefore we provided (1) Bayesian estimates of IRs and the yearly numbers of cases of rare cancers in each country; (2) the expected time (T) in years needed to observe one new case; and (3) practical criteria to decide when to use the Bayesian approach. Bayesian and classical estimates did not differ much; substantial differences (>10%) ranged from 77 rare cancers in Iceland to 14 in England. The smaller the population the larger the number of rare cancers needing a Bayesian approach. Bayesian estimates were useful for cancers with fewer than 150 observed cases in a country during the study period; this occurred mostly when the population of the country is small. For the first time the Bayesian estimates of IRs and the yearly expected numbers of cases for each rare cancer in each individual European country were calculated. Moreover, the indicator T is useful to convey incidence estimates for exceptionally rare cancers and in small countries; it far exceeds the professional lifespan of a medical doctor. Copyright © 2018 Elsevier Ltd. All rights reserved.

On the uncertainty in single molecule fluorescent lifetime and energy emission measurements

NASA Technical Reports Server (NTRS)

Brown, Emery N.; Zhang, Zhenhua; Mccollom, Alex D.

1995-01-01

Time-correlated single photon counting has recently been combined with mode-locked picosecond pulsed excitation to measure the fluorescent lifetimes and energy emissions of single molecules in a flow stream. Maximum likelihood (ML) and least square methods agree and are optimal when the number of detected photons is large however, in single molecule fluorescence experiments the number of detected photons can be less than 20, 67% of those can be noise and the detection time is restricted to 10 nanoseconds. Under the assumption that the photon signal and background noise are two independent inhomogeneous poisson processes, we derive the exact joint arrival time probably density of the photons collected in a single counting experiment performed in the presence of background noise. The model obviates the need to bin experimental data for analysis, and makes it possible to analyze formally the effect of background noise on the photon detection experiment using both ML or Bayesian methods. For both methods we derive the joint and marginal probability densities of the fluorescent lifetime and fluorescent emission. the ML and Bayesian methods are compared in an analysis of simulated single molecule fluorescence experiments of Rhodamine 110 using different combinations of expected background nose and expected fluorescence emission. While both the ML or Bayesian procedures perform well for analyzing fluorescence emissions, the Bayesian methods provide more realistic measures of uncertainty in the fluorescent lifetimes. The Bayesian methods would be especially useful for measuring uncertainty in fluorescent lifetime estimates in current single molecule flow stream experiments where the expected fluorescence emission is low. Both the ML and Bayesian algorithms can be automated for applications in molecular biology.

On the Uncertainty in Single Molecule Fluorescent Lifetime and Energy Emission Measurements

NASA Technical Reports Server (NTRS)

Brown, Emery N.; Zhang, Zhenhua; McCollom, Alex D.

1996-01-01

Time-correlated single photon counting has recently been combined with mode-locked picosecond pulsed excitation to measure the fluorescent lifetimes and energy emissions of single molecules in a flow stream. Maximum likelihood (ML) and least squares methods agree and are optimal when the number of detected photons is large, however, in single molecule fluorescence experiments the number of detected photons can be less than 20, 67 percent of those can be noise, and the detection time is restricted to 10 nanoseconds. Under the assumption that the photon signal and background noise are two independent inhomogeneous Poisson processes, we derive the exact joint arrival time probability density of the photons collected in a single counting experiment performed in the presence of background noise. The model obviates the need to bin experimental data for analysis, and makes it possible to analyze formally the effect of background noise on the photon detection experiment using both ML or Bayesian methods. For both methods we derive the joint and marginal probability densities of the fluorescent lifetime and fluorescent emission. The ML and Bayesian methods are compared in an analysis of simulated single molecule fluorescence experiments of Rhodamine 110 using different combinations of expected background noise and expected fluorescence emission. While both the ML or Bayesian procedures perform well for analyzing fluorescence emissions, the Bayesian methods provide more realistic measures of uncertainty in the fluorescent lifetimes. The Bayesian methods would be especially useful for measuring uncertainty in fluorescent lifetime estimates in current single molecule flow stream experiments where the expected fluorescence emission is low. Both the ML and Bayesian algorithms can be automated for applications in molecular biology.

Superresolution radar imaging based on fast inverse-free sparse Bayesian learning for multiple measurement vectors

NASA Astrophysics Data System (ADS)

He, Xingyu; Tong, Ningning; Hu, Xiaowei

2018-01-01

Compressive sensing has been successfully applied to inverse synthetic aperture radar (ISAR) imaging of moving targets. By exploiting the block sparse structure of the target image, sparse solution for multiple measurement vectors (MMV) can be applied in ISAR imaging and a substantial performance improvement can be achieved. As an effective sparse recovery method, sparse Bayesian learning (SBL) for MMV involves a matrix inverse at each iteration. Its associated computational complexity grows significantly with the problem size. To address this problem, we develop a fast inverse-free (IF) SBL method for MMV. A relaxed evidence lower bound (ELBO), which is computationally more amiable than the traditional ELBO used by SBL, is obtained by invoking fundamental property for smooth functions. A variational expectation-maximization scheme is then employed to maximize the relaxed ELBO, and a computationally efficient IF-MSBL algorithm is proposed. Numerical results based on simulated and real data show that the proposed method can reconstruct row sparse signal accurately and obtain clear superresolution ISAR images. Moreover, the running time and computational complexity are reduced to a great extent compared with traditional SBL methods.

Genetic Structure and Diversity of the Endangered Fir Tree of Lebanon (Abies cilicica Carr.): Implications for Conservation

PubMed Central

Awad, Lara; Fady, Bruno; Khater, Carla; Roig, Anne; Cheddadi, Rachid

2014-01-01

The threatened conifer Abies cilicica currently persists in Lebanon in geographically isolated forest patches. The impact of demographic and evolutionary processes on population genetic diversity and structure were assessed using 10 nuclear microsatellite loci. All remnant 15 local populations revealed a low genetic variation but a high recent effective population size. FST-based measures of population genetic differentiation revealed a low spatial genetic structure, but Bayesian analysis of population structure identified a significant Northeast-Southwest population structure. Populations showed significant but weak isolation-by-distance, indicating non-equilibrium conditions between dispersal and genetic drift. Bayesian assignment tests detected an asymmetric Northeast-Southwest migration involving some long-distance dispersal events. We suggest that the persistence and Northeast-Southwest geographic structure of Abies cilicica in Lebanon is the result of at least two demographic processes during its recent evolutionary history: (1) recent migration to currently marginal populations and (2) local persistence through altitudinal shifts along a mountainous topography. These results might help us better understand the mechanisms involved in the species response to expected climate change. PMID:24587219

An introduction to using Bayesian linear regression with clinical data.

PubMed

Baldwin, Scott A; Larson, Michael J

2017-11-01

Statistical training psychology focuses on frequentist methods. Bayesian methods are an alternative to standard frequentist methods. This article provides researchers with an introduction to fundamental ideas in Bayesian modeling. We use data from an electroencephalogram (EEG) and anxiety study to illustrate Bayesian models. Specifically, the models examine the relationship between error-related negativity (ERN), a particular event-related potential, and trait anxiety. Methodological topics covered include: how to set up a regression model in a Bayesian framework, specifying priors, examining convergence of the model, visualizing and interpreting posterior distributions, interval estimates, expected and predicted values, and model comparison tools. We also discuss situations where Bayesian methods can outperform frequentist methods as well has how to specify more complicated regression models. Finally, we conclude with recommendations about reporting guidelines for those using Bayesian methods in their own research. We provide data and R code for replicating our analyses. Copyright © 2017 Elsevier Ltd. All rights reserved.

Geomagnetic field secular variation in Pacific Ocean: A Bayesian reference curve based on Holocene Hawaiian lava flows

NASA Astrophysics Data System (ADS)

Tema, E.; Herrero-Bervera, E.; Lanos, Ph.

2017-11-01

Hawaii is an ideal place for reconstructing the past variations of the Earth's magnetic field in the Pacific Ocean thanks to the almost continuous volcanic activity during the last 10 000 yrs. We present here an updated compilation of palaeomagnetic data from historic and radiocarbon dated Hawaiian lava flows available for the last ten millennia. A total of 278 directional and 66 intensity reference data have been used for the calculation of the first full geomagnetic field reference secular variation (SV) curves for central Pacific covering the last ten millennia. The obtained SV curves are calculated following recent advances on curve building based on the Bayesian statistics and are well constrained for the last five millennia while for older periods their error envelopes are wide due to the scarce number of reference data. The new Bayesian SV curves show three clear intensity maxima during the last 3000 yrs that are accompanied by sharp directional changes. Such short-term variations of the geomagnetic field could be interpreted as archaeomagnetic jerks and could be an interesting feature of the geomagnetic field variation in the Pacific Ocean that should be further explored by new data.

A Bayesian Approach to Interactive Retrieval

ERIC Educational Resources Information Center

Tague, Jean M.

1973-01-01

A probabilistic model for interactive retrieval is presented. Bayesian statistical decision theory principles are applied: use of prior and sample information about the relationship of document descriptions to query relevance; maximization of expected value of a utility function, to the problem of optimally restructuring search strategies in an…

A Bayesian-frequentist two-stage single-arm phase II clinical trial design.

PubMed

Dong, Gaohong; Shih, Weichung Joe; Moore, Dirk; Quan, Hui; Marcella, Stephen

2012-08-30

It is well-known that both frequentist and Bayesian clinical trial designs have their own advantages and disadvantages. To have better properties inherited from these two types of designs, we developed a Bayesian-frequentist two-stage single-arm phase II clinical trial design. This design allows both early acceptance and rejection of the null hypothesis ( H(0) ). The measures (for example probability of trial early termination, expected sample size, etc.) of the design properties under both frequentist and Bayesian settings are derived. Moreover, under the Bayesian setting, the upper and lower boundaries are determined with predictive probability of trial success outcome. Given a beta prior and a sample size for stage I, based on the marginal distribution of the responses at stage I, we derived Bayesian Type I and Type II error rates. By controlling both frequentist and Bayesian error rates, the Bayesian-frequentist two-stage design has special features compared with other two-stage designs. Copyright © 2012 John Wiley & Sons, Ltd.

Bayesian Inference for Source Term Estimation: Application to the International Monitoring System Radionuclide Network

DTIC Science & Technology

2014-10-01

de l’exactitude et de la précision), comparativement au modèle de mesure plus simple qui n’utilise pas de multiplicateurs. Importance pour la défense...3) Bayesian experimental design for receptor placement in order to maximize the expected information in the measured concen- tration data for...applications of the Bayesian inferential methodology for source recon- struction have used high-quality concentration data from well- designed atmospheric

A Bayesian connectivity-based approach to constructing probabilistic gene regulatory networks.

PubMed

Zhou, Xiaobo; Wang, Xiaodong; Pal, Ranadip; Ivanov, Ivan; Bittner, Michael; Dougherty, Edward R

2004-11-22

We have hypothesized that the construction of transcriptional regulatory networks using a method that optimizes connectivity would lead to regulation consistent with biological expectations. A key expectation is that the hypothetical networks should produce a few, very strong attractors, highly similar to the original observations, mimicking biological state stability and determinism. Another central expectation is that, since it is expected that the biological control is distributed and mutually reinforcing, interpretation of the observations should lead to a very small number of connection schemes. We propose a fully Bayesian approach to constructing probabilistic gene regulatory networks (PGRNs) that emphasizes network topology. The method computes the possible parent sets of each gene, the corresponding predictors and the associated probabilities based on a nonlinear perceptron model, using a reversible jump Markov chain Monte Carlo (MCMC) technique, and an MCMC method is employed to search the network configurations to find those with the highest Bayesian scores to construct the PGRN. The Bayesian method has been used to construct a PGRN based on the observed behavior of a set of genes whose expression patterns vary across a set of melanoma samples exhibiting two very different phenotypes with respect to cell motility and invasiveness. Key biological features have been faithfully reflected in the model. Its steady-state distribution contains attractors that are either identical or very similar to the states observed in the data, and many of the attractors are singletons, which mimics the biological propensity to stably occupy a given state. Most interestingly, the connectivity rules for the most optimal generated networks constituting the PGRN are remarkably similar, as would be expected for a network operating on a distributed basis, with strong interactions between the components.

The choice of sample size: a mixed Bayesian / frequentist approach.

PubMed

Pezeshk, Hamid; Nematollahi, Nader; Maroufy, Vahed; Gittins, John

2009-04-01

Sample size computations are largely based on frequentist or classical methods. In the Bayesian approach the prior information on the unknown parameters is taken into account. In this work we consider a fully Bayesian approach to the sample size determination problem which was introduced by Grundy et al. and developed by Lindley. This approach treats the problem as a decision problem and employs a utility function to find the optimal sample size of a trial. Furthermore, we assume that a regulatory authority, which is deciding on whether or not to grant a licence to a new treatment, uses a frequentist approach. We then find the optimal sample size for the trial by maximising the expected net benefit, which is the expected benefit of subsequent use of the new treatment minus the cost of the trial.

Approximate Bayesian Computation Reveals the Crucial Role of Oceanic Islands for the Assembly of Continental Biodiversity.

PubMed

Patiño, Jairo; Carine, Mark; Mardulyn, Patrick; Devos, Nicolas; Mateo, Rubén G; González-Mancebo, Juana M; Shaw, A Jonathan; Vanderpoorten, Alain

2015-07-01

The perceived low levels of genetic diversity, poor interspecific competitive and defensive ability, and loss of dispersal capacities of insular lineages have driven the view that oceanic islands are evolutionary dead ends. Focusing on the Atlantic bryophyte flora distributed across the archipelagos of the Azores, Madeira, the Canary Islands, Western Europe, and northwestern Africa, we used an integrative approach with species distribution modeling and population genetic analyses based on approximate Bayesian computation to determine whether this view applies to organisms with inherent high dispersal capacities. Genetic diversity was found to be higher in island than in continental populations, contributing to mounting evidence that, contrary to theoretical expectations, island populations are not necessarily genetically depauperate. Patterns of genetic variation among island and continental populations consistently fitted those simulated under a scenario of de novo foundation of continental populations from insular ancestors better than those expected if islands would represent a sink or a refugium of continental biodiversity. We, suggest that the northeastern Atlantic archipelagos have played a key role as a stepping stone for transoceanic migrants. Our results challenge the traditional notion that oceanic islands are the end of the colonization road and illustrate the significant role of oceanic islands as reservoirs of novel biodiversity for the assembly of continental floras. © The Author(s) 2015. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

The anatomy of choice: active inference and agency

PubMed Central

Friston, Karl; Schwartenbeck, Philipp; FitzGerald, Thomas; Moutoussis, Michael; Behrens, Timothy; Dolan, Raymond J.

2013-01-01

This paper considers agency in the setting of embodied or active inference. In brief, we associate a sense of agency with prior beliefs about action and ask what sorts of beliefs underlie optimal behavior. In particular, we consider prior beliefs that action minimizes the Kullback–Leibler (KL) divergence between desired states and attainable states in the future. This allows one to formulate bounded rationality as approximate Bayesian inference that optimizes a free energy bound on model evidence. We show that constructs like expected utility, exploration bonuses, softmax choice rules and optimism bias emerge as natural consequences of this formulation. Previous accounts of active inference have focused on predictive coding and Bayesian filtering schemes for minimizing free energy. Here, we consider variational Bayes as an alternative scheme that provides formal constraints on the computational anatomy of inference and action—constraints that are remarkably consistent with neuroanatomy. Furthermore, this scheme contextualizes optimal decision theory and economic (utilitarian) formulations as pure inference problems. For example, expected utility theory emerges as a special case of free energy minimization, where the sensitivity or inverse temperature (of softmax functions and quantal response equilibria) has a unique and Bayes-optimal solution—that minimizes free energy. This sensitivity corresponds to the precision of beliefs about behavior, such that attainable goals are afforded a higher precision or confidence. In turn, this means that optimal behavior entails a representation of confidence about outcomes that are under an agent's control. PMID:24093015

Choosing a design to fit the situation: how to improve specificity and positive predictive values using Bayesian lot quality assurance sampling.

PubMed

Olives, Casey; Pagano, Marcello

2013-02-01

Lot Quality Assurance Sampling (LQAS) is a provably useful tool for monitoring health programmes. Although LQAS ensures acceptable Producer and Consumer risks, the literature alleges that the method suffers from poor specificity and positive predictive values (PPVs). We suggest that poor LQAS performance is due, in part, to variation in the true underlying distribution. However, until now the role of the underlying distribution in expected performance has not been adequately examined. We present Bayesian-LQAS (B-LQAS), an approach to incorporating prior information into the choice of the LQAS sample size and decision rule, and explore its properties through a numerical study. Additionally, we analyse vaccination coverage data from UNICEF's State of the World's Children in 1968-1989 and 2008 to exemplify the performance of LQAS and B-LQAS. Results of our numerical study show that the choice of LQAS sample size and decision rule is sensitive to the distribution of prior information, as well as to individual beliefs about the importance of correct classification. Application of the B-LQAS approach to the UNICEF data improves specificity and PPV in both time periods (1968-1989 and 2008) with minimal reductions in sensitivity and negative predictive value. LQAS is shown to be a robust tool that is not necessarily prone to poor specificity and PPV as previously alleged. In situations where prior or historical data are available, B-LQAS can lead to improvements in expected performance.

A Bayesian observer replicates convexity context effects in figure-ground perception.

PubMed

Goldreich, Daniel; Peterson, Mary A

2012-01-01

Peterson and Salvagio (2008) demonstrated convexity context effects in figure-ground perception. Subjects shown displays consisting of unfamiliar alternating convex and concave regions identified the convex regions as foreground objects progressively more frequently as the number of regions increased; this occurred only when the concave regions were homogeneously colored. The origins of these effects have been unclear. Here, we present a two-free-parameter Bayesian observer that replicates convexity context effects. The Bayesian observer incorporates two plausible expectations regarding three-dimensional scenes: (1) objects tend to be convex rather than concave, and (2) backgrounds tend (more than foreground objects) to be homogeneously colored. The Bayesian observer estimates the probability that a depicted scene is three-dimensional, and that the convex regions are figures. It responds stochastically by sampling from its posterior distributions. Like human observers, the Bayesian observer shows convexity context effects only for images with homogeneously colored concave regions. With optimal parameter settings, it performs similarly to the average human subject on the four display types tested. We propose that object convexity and background color homogeneity are environmental regularities exploited by human visual perception; vision achieves figure-ground perception by interpreting ambiguous images in light of these and other expected regularities in natural scenes.

A Bayesian Belief Network Approach to Explore Alternative Decisions for Sediment Control and water Storage Capacity at Lago Lucchetti, Puerto Rico

EPA Science Inventory

A Bayesian belief network (BBN) was developed to characterize the effects of sediment accumulation on the water storage capacity of Lago Lucchetti (located in southwest Puerto Rico) and to forecast the life expectancy (usefulness) of the reservoir under different management scena...

Nonparametric Bayesian predictive distributions for future order statistics

Treesearch

Richard A. Johnson; James W. Evans; David W. Green

1999-01-01

We derive the predictive distribution for a specified order statistic, determined from a future random sample, under a Dirichlet process prior. Two variants of the approach are treated and some limiting cases studied. A practical application to monitoring the strength of lumber is discussed including choices of prior expectation and comparisons made to a Bayesian...

Contrasting support for alternative models of genomic variation based on microhabitat preference: species-specific effects of climate change in alpine sedges.

PubMed

Massatti, Rob; Knowles, L Lacey

2016-08-01

Deterministic processes may uniquely affect codistributed species' phylogeographic patterns such that discordant genetic variation among taxa is predicted. Yet, explicitly testing expectations of genomic discordance in a statistical framework remains challenging. Here, we construct spatially and temporally dynamic models to investigate the hypothesized effect of microhabitat preferences on the permeability of glaciated regions to gene flow in two closely related montane species. Utilizing environmental niche models from the Last Glacial Maximum and the present to inform demographic models of changes in habitat suitability over time, we evaluate the relative probabilities of two alternative models using approximate Bayesian computation (ABC) in which glaciated regions are either (i) permeable or (ii) a barrier to gene flow. Results based on the fit of the empirical data to data sets simulated using a spatially explicit coalescent under alternative models indicate that genomic data are consistent with predictions about the hypothesized role of microhabitat in generating discordant patterns of genetic variation among the taxa. Specifically, a model in which glaciated areas acted as a barrier was much more probable based on patterns of genomic variation in Carex nova, a wet-adapted species. However, in the dry-adapted Carex chalciolepis, the permeable model was more probable, although the difference in the support of the models was small. This work highlights how statistical inferences can be used to distinguish deterministic processes that are expected to result in discordant genomic patterns among species, including species-specific responses to climate change. © 2016 John Wiley & Sons Ltd.

How Recent History Affects Perception: The Normative Approach and Its Heuristic Approximation

PubMed Central

Raviv, Ofri; Ahissar, Merav; Loewenstein, Yonatan

2012-01-01

There is accumulating evidence that prior knowledge about expectations plays an important role in perception. The Bayesian framework is the standard computational approach to explain how prior knowledge about the distribution of expected stimuli is incorporated with noisy observations in order to improve performance. However, it is unclear what information about the prior distribution is acquired by the perceptual system over short periods of time and how this information is utilized in the process of perceptual decision making. Here we address this question using a simple two-tone discrimination task. We find that the “contraction bias”, in which small magnitudes are overestimated and large magnitudes are underestimated, dominates the pattern of responses of human participants. This contraction bias is consistent with the Bayesian hypothesis in which the true prior information is available to the decision-maker. However, a trial-by-trial analysis of the pattern of responses reveals that the contribution of most recent trials to performance is overweighted compared with the predictions of a standard Bayesian model. Moreover, we study participants' performance in a-typical distributions of stimuli and demonstrate substantial deviations from the ideal Bayesian detector, suggesting that the brain utilizes a heuristic approximation of the Bayesian inference. We propose a biologically plausible model, in which decision in the two-tone discrimination task is based on a comparison between the second tone and an exponentially-decaying average of the first tone and past tones. We show that this model accounts for both the contraction bias and the deviations from the ideal Bayesian detector hypothesis. These findings demonstrate the power of Bayesian-like heuristics in the brain, as well as their limitations in their failure to fully adapt to novel environments. PMID:23133343

Evaluation of Flagging Criteria of United States Kidney Transplant Center Performance: How to Best Define Outliers?

PubMed

Schold, Jesse D; Miller, Charles M; Henry, Mitchell L; Buccini, Laura D; Flechner, Stuart M; Goldfarb, David A; Poggio, Emilio D; Andreoni, Kenneth A

2017-06-01

Scientific Registry of Transplant Recipients report cards of US organ transplant center performance are publicly available and used for quality oversight. Low center performance (LP) evaluations are associated with changes in practice including reduced transplant rates and increased waitlist removals. In 2014, Scientific Registry of Transplant Recipients implemented new Bayesian methodology to evaluate performance which was not adopted by Center for Medicare and Medicaid Services (CMS). In May 2016, CMS altered their performance criteria, reducing the likelihood of LP evaluations. Our aims were to evaluate incidence, survival rates, and volume of LP centers with Bayesian, historical (old-CMS) and new-CMS criteria using 6 consecutive program-specific reports (PSR), January 2013 to July 2015 among adult kidney transplant centers. Bayesian, old-CMS and new-CMS criteria identified 13.4%, 8.3%, and 6.1% LP PSRs, respectively. Over the 3-year period, 31.9% (Bayesian), 23.4% (old-CMS), and 19.8% (new-CMS) of centers had 1 or more LP evaluation. For small centers (<83 transplants/PSR), there were 4-fold additional LP evaluations (52 vs 13 PSRs) for 1-year mortality with Bayesian versus new-CMS criteria. For large centers (>183 transplants/PSR), there were 3-fold additional LP evaluations for 1-year mortality with Bayesian versus new-CMS criteria with median differences in observed and expected patient survival of -1.6% and -2.2%, respectively. A significant proportion of kidney transplant centers are identified as low performing with relatively small survival differences compared with expected. Bayesian criteria have significantly higher flagging rates and new-CMS criteria modestly reduce flagging. Critical appraisal of performance criteria is needed to assess whether quality oversight is meeting intended goals and whether further modifications could reduce risk aversion, more efficiently allocate resources, and increase transplant opportunities.

The Bayesian reader: explaining word recognition as an optimal Bayesian decision process.

PubMed

Norris, Dennis

2006-04-01

This article presents a theory of visual word recognition that assumes that, in the tasks of word identification, lexical decision, and semantic categorization, human readers behave as optimal Bayesian decision makers. This leads to the development of a computational model of word recognition, the Bayesian reader. The Bayesian reader successfully simulates some of the most significant data on human reading. The model accounts for the nature of the function relating word frequency to reaction time and identification threshold, the effects of neighborhood density and its interaction with frequency, and the variation in the pattern of neighborhood density effects seen in different experimental tasks. Both the general behavior of the model and the way the model predicts different patterns of results in different tasks follow entirely from the assumption that human readers approximate optimal Bayesian decision makers. ((c) 2006 APA, all rights reserved).

Fast Low-Rank Bayesian Matrix Completion With Hierarchical Gaussian Prior Models

NASA Astrophysics Data System (ADS)

Yang, Linxiao; Fang, Jun; Duan, Huiping; Li, Hongbin; Zeng, Bing

2018-06-01

The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a Wishart distribution is specified as a hyperprior over the precision matrix. We show that such a hierarchical Gaussian prior has the potential to encourage a low-rank solution. Based on the proposed hierarchical prior model, a variational Bayesian method is developed for matrix completion, where the generalized approximate massage passing (GAMP) technique is embedded into the variational Bayesian inference in order to circumvent cumbersome matrix inverse operations. Simulation results show that our proposed method demonstrates superiority over existing state-of-the-art matrix completion methods.

Evidence of major genes affecting stress response in rainbow trout using Bayesian methods of complex segregation analysis

USDA-ARS?s Scientific Manuscript database

As a first step towards the genetic mapping of quantitative trait loci (QTL) affecting stress response variation in rainbow trout, we performed complex segregation analyses (CSA) fitting mixed inheritance models of plasma cortisol using Bayesian methods in large full-sib families of rainbow trout. ...

Bayesian models for comparative analysis integrating phylogenetic uncertainty.

PubMed

de Villemereuil, Pierre; Wells, Jessie A; Edwards, Robert D; Blomberg, Simon P

2012-06-28

Uncertainty in comparative analyses can come from at least two sources: a) phylogenetic uncertainty in the tree topology or branch lengths, and b) uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow) and inflated significance in hypothesis testing (e.g. p-values will be too small). Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable. We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses. We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS. Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible general purpose tool for phylogenetic comparative analyses, particularly for modelling in the face of phylogenetic uncertainty and accounting for measurement error or individual variation in explanatory variables. Code for all models is provided in the BUGS model description language.

Bayesian models for comparative analysis integrating phylogenetic uncertainty

PubMed Central

2012-01-01

Background Uncertainty in comparative analyses can come from at least two sources: a) phylogenetic uncertainty in the tree topology or branch lengths, and b) uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow) and inflated significance in hypothesis testing (e.g. p-values will be too small). Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable. Methods We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses. Results We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS. Conclusions Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible general purpose tool for phylogenetic comparative analyses, particularly for modelling in the face of phylogenetic uncertainty and accounting for measurement error or individual variation in explanatory variables. Code for all models is provided in the BUGS model description language. PMID:22741602

Bertrand Model Under Incomplete Information

NASA Astrophysics Data System (ADS)

Ferreira, Fernanda A.; Pinto, Alberto A.

2008-09-01

We consider a Bertrand duopoly model with unknown costs. The firms' aim is to choose the price of its product according to the well-known concept of Bayesian Nash equilibrium. The chooses are made simultaneously by both firms. In this paper, we suppose that each firm has two different technologies, and uses one of them according to a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We show that this game has exactly one Bayesian Nash equilibrium. We analyse the advantages, for firms and for consumers, of using the technology with highest production cost versus the one with cheapest production cost. We prove that the expected profit of each firm increases with the variance of its production costs. We also show that the expected price of each good increases with both expected production costs, being the effect of the expected production costs of the rival dominated by the effect of the own expected production costs.

Parameter estimation of multivariate multiple regression model using bayesian with non-informative Jeffreys’ prior distribution

NASA Astrophysics Data System (ADS)

Saputro, D. R. S.; Amalia, F.; Widyaningsih, P.; Affan, R. C.

2018-05-01

Bayesian method is a method that can be used to estimate the parameters of multivariate multiple regression model. Bayesian method has two distributions, there are prior and posterior distributions. Posterior distribution is influenced by the selection of prior distribution. Jeffreys’ prior distribution is a kind of Non-informative prior distribution. This prior is used when the information about parameter not available. Non-informative Jeffreys’ prior distribution is combined with the sample information resulting the posterior distribution. Posterior distribution is used to estimate the parameter. The purposes of this research is to estimate the parameters of multivariate regression model using Bayesian method with Non-informative Jeffreys’ prior distribution. Based on the results and discussion, parameter estimation of β and Σ which were obtained from expected value of random variable of marginal posterior distribution function. The marginal posterior distributions for β and Σ are multivariate normal and inverse Wishart. However, in calculation of the expected value involving integral of a function which difficult to determine the value. Therefore, approach is needed by generating of random samples according to the posterior distribution characteristics of each parameter using Markov chain Monte Carlo (MCMC) Gibbs sampling algorithm.

Evaluating Expectations about Negative Emotional States of Aggressive Boys Using Bayesian Model Selection

ERIC Educational Resources Information Center

van de Schoot, Rens; Hoijtink, Herbert; Mulder, Joris; Van Aken, Marcel A. G.; Orobio de Castro, Bram; Meeus, Wim; Romeijn, Jan-Willem

2011-01-01

Researchers often have expectations about the research outcomes in regard to inequality constraints between, e.g., group means. Consider the example of researchers who investigated the effects of inducing a negative emotional state in aggressive boys. It was expected that highly aggressive boys would, on average, score higher on aggressive…

Bayesian denoising in digital radiography: a comparison in the dental field.

PubMed

Frosio, I; Olivieri, C; Lucchese, M; Borghese, N A; Boccacci, P

2013-01-01

We compared two Bayesian denoising algorithms for digital radiographs, based on Total Variation regularization and wavelet decomposition. The comparison was performed on simulated radiographs with different photon counts and frequency content and on real dental radiographs. Four different quality indices were considered to quantify the quality of the filtered radiographs. The experimental results suggested that Total Variation is more suited to preserve fine anatomical details, whereas wavelets produce images of higher quality at global scale; they also highlighted the need for more reliable image quality indices. Copyright © 2012 Elsevier Ltd. All rights reserved.

Response Expectancy and the Placebo Effect.

PubMed

Kirsch, Irving

2018-01-01

In this chapter, I review basic tenets of response expectancy theory (Kirsch, 1985), beginning with the important distinction between response expectancies and stimulus expectancies. Although both can affect experience, the effects of response expectancies are stronger and more resistant to extinction than those of stimulus expectancies. Further, response expectancies are especially important to understanding placebo effects. The response expectancy framework is consistent with and has been amplified by the Bayesian model of predictive coding. Clinical implications of these phenomena are exemplified. © 2018 Elsevier Inc. All rights reserved.

In-situ resource utilization for the human exploration of Mars : a Bayesian approach to valuation of precursor missions

NASA Technical Reports Server (NTRS)

Smith, Jeffrey H.

2006-01-01

The need for sufficient quantities of oxygen, water, and fuel resources to support a crew on the surface of Mars presents a critical logistical issue of whether to transport such resources from Earth or manufacture them on Mars. An approach based on the classical Wildcat Drilling Problem of Bayesian decision theory was applied to the problem of finding water in order to compute the expected value of precursor mission sample information. An implicit (required) probability of finding water on Mars was derived from the value of sample information using the expected mass savings of alternative precursor missions.

Choosing a design to fit the situation: how to improve specificity and positive predictive values using Bayesian lot quality assurance sampling

PubMed Central

Olives, Casey; Pagano, Marcello

2013-01-01

Background Lot Quality Assurance Sampling (LQAS) is a provably useful tool for monitoring health programmes. Although LQAS ensures acceptable Producer and Consumer risks, the literature alleges that the method suffers from poor specificity and positive predictive values (PPVs). We suggest that poor LQAS performance is due, in part, to variation in the true underlying distribution. However, until now the role of the underlying distribution in expected performance has not been adequately examined. Methods We present Bayesian-LQAS (B-LQAS), an approach to incorporating prior information into the choice of the LQAS sample size and decision rule, and explore its properties through a numerical study. Additionally, we analyse vaccination coverage data from UNICEF’s State of the World’s Children in 1968–1989 and 2008 to exemplify the performance of LQAS and B-LQAS. Results Results of our numerical study show that the choice of LQAS sample size and decision rule is sensitive to the distribution of prior information, as well as to individual beliefs about the importance of correct classification. Application of the B-LQAS approach to the UNICEF data improves specificity and PPV in both time periods (1968–1989 and 2008) with minimal reductions in sensitivity and negative predictive value. Conclusions LQAS is shown to be a robust tool that is not necessarily prone to poor specificity and PPV as previously alleged. In situations where prior or historical data are available, B-LQAS can lead to improvements in expected performance. PMID:23378151

A Bayesian-Based Approach to Marine Spatial Planning: Evaluating Spatial and Temporal Variance in the Provision of Ecosystem Services Before and After the Establishment Oregon's Marine Protected Areas

NASA Astrophysics Data System (ADS)

Black, B.; Harte, M.; Goldfinger, C.

2017-12-01

Participating in a ten-year monitoring project to assess the ecological, social, and socioeconomic impacts of Oregon's Marine Protected Areas (MPAs), we have worked in partnership with the Oregon Department of Fish and Wildlife (ODFW) to develop a Bayesian geospatial method to evaluate the spatial and temporal variance in the provision of ecosystem services produced by Oregon's MPAs. Probabilistic (Bayesian) approaches to Marine Spatial Planning (MSP) show considerable potential for addressing issues such as uncertainty, cumulative effects, and the need to integrate stakeholder-held information and preferences into decision making processes. To that end, we have created a Bayesian-based geospatial approach to MSP capable of modelling the evolution of the provision of ecosystem services before and after the establishment of Oregon's MPAs. Our approach permits both planners and stakeholders to view expected impacts of differing policies, behaviors, or choices made concerning Oregon's MPAs and surrounding areas in a geospatial (map) format while simultaneously considering multiple parties' beliefs on the policies or uses in question. We quantify the influence of the MPAs as the shift in the spatial distribution of ecosystem services, both inside and outside the protected areas, over time. Once the MPAs' influence on the provision of coastal ecosystem services has been evaluated, it is possible to view these impacts through geovisualization techniques. As a specific example of model use and output, a user could investigate the effects of altering the habitat preferences of a rockfish species over a prescribed period of time (5, 10, 20 years post-harvesting restrictions, etc.) on the relative intensity of spillover from nearby reserves (please see submitted figure). Particular strengths of our Bayesian-based approach include its ability to integrate highly disparate input types (qualitative or quantitative), to accommodate data gaps, address uncertainty, and to investigate temporal and spatial variation. This approach conveys the modeled outcome of proposed policy changes and is also a vehicle through which stakeholders and planners can work together to compare and deliberate on the impacts of policy and management changes, a capacity of considerable utility for planners and stakeholders engaged in MSP.

Relationships between land cover and dissolved organic matter change along the river to lake transition

USGS Publications Warehouse

Larson, James H.; Frost, Paul C.; Xenopoulos, Marguerite A.; Williams, Clayton J.; Morales-Williams, Ana M.; Vallazza, Jonathan M.; Nelson, J. C.; Richardson, William B.

2014-01-01

Dissolved organic matter (DOM) influences the physical, chemical, and biological properties of aquatic ecosystems. We hypothesized that controls over spatial variation in DOM quantity and composition (measured with DOM optical properties) differ based on the source of DOM to aquatic ecosystems. DOM quantity and composition should be better predicted by land cover in aquatic habitats with allochthonous DOM and related more strongly to nutrients in aquatic habitats with autochthonous DOM. Three habitat types [rivers (R), rivermouths (RM), and the nearshore zone (L)] associated with 23 tributaries of the Laurentian Great Lakes were sampled to test this prediction. Evidence from optical indices suggests that DOM in these habitats generally ranged from allochthonous (R sites) to a mix of allochthonous-like and autochthonous-like (L sites). Contrary to expectations, DOM properties such as the fluorescence index, humification index, and spectral slope ratio were only weakly related to land cover or nutrient data (Bayesian R 2 values were indistinguishable from zero). Strongly supported models in all habitat types linked DOM quantity (that is, dissolved organic carbon concentration [DOC]) to both land cover and nutrients (Bayesian R2 values ranging from 0.55 to 0.72). Strongly supported models predicting DOC changed with habitat type: The most important predictor in R sites was wetlands whereas the most important predictor at L sites was croplands. These results suggest that as the DOM pool becomes more autochthonous-like, croplands become a more important driver of spatial variation in DOC and wetlands become less important.

Bayesian estimation inherent in a Mexican-hat-type neural network

NASA Astrophysics Data System (ADS)

Takiyama, Ken

2016-05-01

Brain functions, such as perception, motor control and learning, and decision making, have been explained based on a Bayesian framework, i.e., to decrease the effects of noise inherent in the human nervous system or external environment, our brain integrates sensory and a priori information in a Bayesian optimal manner. However, it remains unclear how Bayesian computations are implemented in the brain. Herein, I address this issue by analyzing a Mexican-hat-type neural network, which was used as a model of the visual cortex, motor cortex, and prefrontal cortex. I analytically demonstrate that the dynamics of an order parameter in the model corresponds exactly to a variational inference of a linear Gaussian state-space model, a Bayesian estimation, when the strength of recurrent synaptic connectivity is appropriately stronger than that of an external stimulus, a plausible condition in the brain. This exact correspondence can reveal the relationship between the parameters in the Bayesian estimation and those in the neural network, providing insight for understanding brain functions.

A Bayesian estimation of a stochastic predator-prey model of economic fluctuations

NASA Astrophysics Data System (ADS)

Dibeh, Ghassan; Luchinsky, Dmitry G.; Luchinskaya, Daria D.; Smelyanskiy, Vadim N.

2007-06-01

In this paper, we develop a Bayesian framework for the empirical estimation of the parameters of one of the best known nonlinear models of the business cycle: The Marx-inspired model of a growth cycle introduced by R. M. Goodwin. The model predicts a series of closed cycles representing the dynamics of labor's share and the employment rate in the capitalist economy. The Bayesian framework is used to empirically estimate a modified Goodwin model. The original model is extended in two ways. First, we allow for exogenous periodic variations of the otherwise steady growth rates of the labor force and productivity per worker. Second, we allow for stochastic variations of those parameters. The resultant modified Goodwin model is a stochastic predator-prey model with periodic forcing. The model is then estimated using a newly developed Bayesian estimation method on data sets representing growth cycles in France and Italy during the years 1960-2005. Results show that inference of the parameters of the stochastic Goodwin model can be achieved. The comparison of the dynamics of the Goodwin model with the inferred values of parameters demonstrates quantitative agreement with the growth cycle empirical data.

RAPD variation and population genetic structure of Physalaemus cuvieri (Anura: Leptodactylidae) in Central Brazil.

PubMed

Telles, Mariana Pires de Campos; Bastos, Rogério Pereira; Soares, Thannya Nascimento; Resende, Lucileide Vilela; Diniz-Filho, José Alexandre Felizola

2006-01-01

Studies about the organization of the genetic variability and population structure in natural populations are used either to understand microevolutionary processes or the effects of isolation by human-inducted landscape modifications. In this paper, we analyzed patterns of genetic population structure using 126 RAPD loci scored for 214 individuals of Physalaemus cuvieri, sampled from 18 local populations. Around 97% of these loci were polymorphic. The among-population variation component (Phi(ST)) obtained by AMOVA was equal to 0.101 and theta B obtained using a Bayesian approach for dominant markers was 0.103. Genetic divergence, analyzed by Mantel spatial correlogram, revealed only a short-distance significant correlation between genetic and geographic distances. This is expected if low levels of population differentiation, due to high abundance buffering the effect of stochastic processes, are combined with low spatially restricted gene flow. Although this may be consistent with the current knowledge of species' biology, the spatial distribution of local populations observed in this study also suggest that, at least in part, recent human occupation and habitat fragmentation may also explain part of the interpopulational component of the genetic variation.

Bayesian estimation of seasonal course of canopy leaf area index from hyperspectral satellite data

NASA Astrophysics Data System (ADS)

Varvia, Petri; Rautiainen, Miina; Seppänen, Aku

2018-03-01

In this paper, Bayesian inversion of a physically-based forest reflectance model is investigated to estimate of boreal forest canopy leaf area index (LAI) from EO-1 Hyperion hyperspectral data. The data consist of multiple forest stands with different species compositions and structures, imaged in three phases of the growing season. The Bayesian estimates of canopy LAI are compared to reference estimates based on a spectral vegetation index. The forest reflectance model contains also other unknown variables in addition to LAI, for example leaf single scattering albedo and understory reflectance. In the Bayesian approach, these variables are estimated simultaneously with LAI. The feasibility and seasonal variation of these estimates is also examined. Credible intervals for the estimates are also calculated and evaluated. The results show that the Bayesian inversion approach is significantly better than using a comparable spectral vegetation index regression.

Bayesian methods including nonrandomized study data increased the efficiency of postlaunch RCTs.

PubMed

Schmidt, Amand F; Klugkist, Irene; Klungel, Olaf H; Nielen, Mirjam; de Boer, Anthonius; Hoes, Arno W; Groenwold, Rolf H H

2015-04-01

Findings from nonrandomized studies on safety or efficacy of treatment in patient subgroups may trigger postlaunch randomized clinical trials (RCTs). In the analysis of such RCTs, results from nonrandomized studies are typically ignored. This study explores the trade-off between bias and power of Bayesian RCT analysis incorporating information from nonrandomized studies. A simulation study was conducted to compare frequentist with Bayesian analyses using noninformative and informative priors in their ability to detect interaction effects. In simulated subgroups, the effect of a hypothetical treatment differed between subgroups (odds ratio 1.00 vs. 2.33). Simulations varied in sample size, proportions of the subgroups, and specification of the priors. As expected, the results for the informative Bayesian analyses were more biased than those from the noninformative Bayesian analysis or frequentist analysis. However, because of a reduction in posterior variance, informative Bayesian analyses were generally more powerful to detect an effect. In scenarios where the informative priors were in the opposite direction of the RCT data, type 1 error rates could be 100% and power 0%. Bayesian methods incorporating data from nonrandomized studies can meaningfully increase power of interaction tests in postlaunch RCTs. Copyright © 2015 Elsevier Inc. All rights reserved.

Learning what to expect (in visual perception)

PubMed Central

Seriès, Peggy; Seitz, Aaron R.

2013-01-01

Expectations are known to greatly affect our experience of the world. A growing theory in computational neuroscience is that perception can be successfully described using Bayesian inference models and that the brain is “Bayes-optimal” under some constraints. In this context, expectations are particularly interesting, because they can be viewed as prior beliefs in the statistical inference process. A number of questions remain unsolved, however, for example: How fast do priors change over time? Are there limits in the complexity of the priors that can be learned? How do an individual’s priors compare to the true scene statistics? Can we unlearn priors that are thought to correspond to natural scene statistics? Where and what are the neural substrate of priors? Focusing on the perception of visual motion, we here review recent studies from our laboratories and others addressing these issues. We discuss how these data on motion perception fit within the broader literature on perceptual Bayesian priors, perceptual expectations, and statistical and perceptual learning and review the possible neural basis of priors. PMID:24187536

Testing students' e-learning via Facebook through Bayesian structural equation modeling.

PubMed

Salarzadeh Jenatabadi, Hashem; Moghavvemi, Sedigheh; Wan Mohamed Radzi, Che Wan Jasimah Bt; Babashamsi, Parastoo; Arashi, Mohammad

2017-01-01

Learning is an intentional activity, with several factors affecting students' intention to use new learning technology. Researchers have investigated technology acceptance in different contexts by developing various theories/models and testing them by a number of means. Although most theories/models developed have been examined through regression or structural equation modeling, Bayesian analysis offers more accurate data analysis results. To address this gap, the unified theory of acceptance and technology use in the context of e-learning via Facebook are re-examined in this study using Bayesian analysis. The data (S1 Data) were collected from 170 students enrolled in a business statistics course at University of Malaya, Malaysia, and tested with the maximum likelihood and Bayesian approaches. The difference between the two methods' results indicates that performance expectancy and hedonic motivation are the strongest factors influencing the intention to use e-learning via Facebook. The Bayesian estimation model exhibited better data fit than the maximum likelihood estimator model. The results of the Bayesian and maximum likelihood estimator approaches are compared and the reasons for the result discrepancy are deliberated.

Testing students’ e-learning via Facebook through Bayesian structural equation modeling

PubMed Central

Moghavvemi, Sedigheh; Wan Mohamed Radzi, Che Wan Jasimah Bt; Babashamsi, Parastoo; Arashi, Mohammad

2017-01-01

Learning is an intentional activity, with several factors affecting students’ intention to use new learning technology. Researchers have investigated technology acceptance in different contexts by developing various theories/models and testing them by a number of means. Although most theories/models developed have been examined through regression or structural equation modeling, Bayesian analysis offers more accurate data analysis results. To address this gap, the unified theory of acceptance and technology use in the context of e-learning via Facebook are re-examined in this study using Bayesian analysis. The data (S1 Data) were collected from 170 students enrolled in a business statistics course at University of Malaya, Malaysia, and tested with the maximum likelihood and Bayesian approaches. The difference between the two methods’ results indicates that performance expectancy and hedonic motivation are the strongest factors influencing the intention to use e-learning via Facebook. The Bayesian estimation model exhibited better data fit than the maximum likelihood estimator model. The results of the Bayesian and maximum likelihood estimator approaches are compared and the reasons for the result discrepancy are deliberated. PMID:28886019

Priors in perception: Top-down modulation, Bayesian perceptual learning rate, and prediction error minimization.

PubMed

Hohwy, Jakob

2017-01-01

I discuss top-down modulation of perception in terms of a variable Bayesian learning rate, revealing a wide range of prior hierarchical expectations that can modulate perception. I then switch to the prediction error minimization framework and seek to conceive cognitive penetration specifically as prediction error minimization deviations from a variable Bayesian learning rate. This approach retains cognitive penetration as a category somewhat distinct from other top-down effects, and carves a reasonable route between penetrability and impenetrability. It prevents rampant, relativistic cognitive penetration of perception and yet is consistent with the continuity of cognition and perception. Copyright © 2016 Elsevier Inc. All rights reserved.

Strategies to reduce the complexity of hydrologic data assimilation for high-dimensional models

NASA Astrophysics Data System (ADS)

Hernandez, F.; Liang, X.

2017-12-01

Probabilistic forecasts in the geosciences offer invaluable information by allowing to estimate the uncertainty of predicted conditions (including threats like floods and droughts). However, while forecast systems based on modern data assimilation algorithms are capable of producing multi-variate probability distributions of future conditions, the computational resources required to fully characterize the dependencies between the model's state variables render their applicability impractical for high-resolution cases. This occurs because of the quadratic space complexity of storing the covariance matrices that encode these dependencies and the cubic time complexity of performing inference operations with them. In this work we introduce two complementary strategies to reduce the size of the covariance matrices that are at the heart of Bayesian assimilation methods—like some variants of (ensemble) Kalman filters and of particle filters—and variational methods. The first strategy involves the optimized grouping of state variables by clustering individual cells of the model into "super-cells." A dynamic fuzzy clustering approach is used to take into account the states (e.g., soil moisture) and forcings (e.g., precipitation) of each cell at each time step. The second strategy consists in finding a compressed representation of the covariance matrix that still encodes the most relevant information but that can be more efficiently stored and processed. A learning and a belief-propagation inference algorithm are developed to take advantage of this modified low-rank representation. The two proposed strategies are incorporated into OPTIMISTS, a state-of-the-art hybrid Bayesian/variational data assimilation algorithm, and comparative streamflow forecasting tests are performed using two watersheds modeled with the Distributed Hydrology Soil Vegetation Model (DHSVM). Contrasts are made between the efficiency gains and forecast accuracy losses of each strategy used in isolation, and of those achieved through their coupling. We expect these developments to help catalyze improvements in the predictive accuracy of large-scale forecasting operations by lowering the costs of deploying advanced data assimilation techniques.

Bayesian predictive power: choice of prior and some recommendations for its use as probability of success in drug development.

PubMed

Rufibach, Kaspar; Burger, Hans Ulrich; Abt, Markus

2016-09-01

Bayesian predictive power, the expectation of the power function with respect to a prior distribution for the true underlying effect size, is routinely used in drug development to quantify the probability of success of a clinical trial. Choosing the prior is crucial for the properties and interpretability of Bayesian predictive power. We review recommendations on the choice of prior for Bayesian predictive power and explore its features as a function of the prior. The density of power values induced by a given prior is derived analytically and its shape characterized. We find that for a typical clinical trial scenario, this density has a u-shape very similar, but not equal, to a β-distribution. Alternative priors are discussed, and practical recommendations to assess the sensitivity of Bayesian predictive power to its input parameters are provided. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Statistical analysis of modal parameters of a suspension bridge based on Bayesian spectral density approach and SHM data

NASA Astrophysics Data System (ADS)

Li, Zhijun; Feng, Maria Q.; Luo, Longxi; Feng, Dongming; Xu, Xiuli

2018-01-01

Uncertainty of modal parameters estimation appear in structural health monitoring (SHM) practice of civil engineering to quite some significant extent due to environmental influences and modeling errors. Reasonable methodologies are needed for processing the uncertainty. Bayesian inference can provide a promising and feasible identification solution for the purpose of SHM. However, there are relatively few researches on the application of Bayesian spectral method in the modal identification using SHM data sets. To extract modal parameters from large data sets collected by SHM system, the Bayesian spectral density algorithm was applied to address the uncertainty of mode extraction from output-only response of a long-span suspension bridge. The posterior most possible values of modal parameters and their uncertainties were estimated through Bayesian inference. A long-term variation and statistical analysis was performed using the sensor data sets collected from the SHM system of the suspension bridge over a one-year period. The t location-scale distribution was shown to be a better candidate function for frequencies of lower modes. On the other hand, the burr distribution provided the best fitting to the higher modes which are sensitive to the temperature. In addition, wind-induced variation of modal parameters was also investigated. It was observed that both the damping ratios and modal forces increased during the period of typhoon excitations. Meanwhile, the modal damping ratios exhibit significant correlation with the spectral intensities of the corresponding modal forces.

Bayesian inference and decision theory - A framework for decision making in natural resource management

USGS Publications Warehouse

Dorazio, R.M.; Johnson, F.A.

2003-01-01

Bayesian inference and decision theory may be used in the solution of relatively complex problems of natural resource management, owing to recent advances in statistical theory and computing. In particular, Markov chain Monte Carlo algorithms provide a computational framework for fitting models of adequate complexity and for evaluating the expected consequences of alternative management actions. We illustrate these features using an example based on management of waterfowl habitat.

CytoBayesJ: software tools for Bayesian analysis of cytogenetic radiation dosimetry data.

PubMed

Ainsbury, Elizabeth A; Vinnikov, Volodymyr; Puig, Pedro; Maznyk, Nataliya; Rothkamm, Kai; Lloyd, David C

2013-08-30

A number of authors have suggested that a Bayesian approach may be most appropriate for analysis of cytogenetic radiation dosimetry data. In the Bayesian framework, probability of an event is described in terms of previous expectations and uncertainty. Previously existing, or prior, information is used in combination with experimental results to infer probabilities or the likelihood that a hypothesis is true. It has been shown that the Bayesian approach increases both the accuracy and quality assurance of radiation dose estimates. New software entitled CytoBayesJ has been developed with the aim of bringing Bayesian analysis to cytogenetic biodosimetry laboratory practice. CytoBayesJ takes a number of Bayesian or 'Bayesian like' methods that have been proposed in the literature and presents them to the user in the form of simple user-friendly tools, including testing for the most appropriate model for distribution of chromosome aberrations and calculations of posterior probability distributions. The individual tools are described in detail and relevant examples of the use of the methods and the corresponding CytoBayesJ software tools are given. In this way, the suitability of the Bayesian approach to biological radiation dosimetry is highlighted and its wider application encouraged by providing a user-friendly software interface and manual in English and Russian. Copyright © 2013 Elsevier B.V. All rights reserved.

Predictive distributions for between-study heterogeneity and simple methods for their application in Bayesian meta-analysis

PubMed Central

Turner, Rebecca M; Jackson, Dan; Wei, Yinghui; Thompson, Simon G; Higgins, Julian P T

2015-01-01

Numerous meta-analyses in healthcare research combine results from only a small number of studies, for which the variance representing between-study heterogeneity is estimated imprecisely. A Bayesian approach to estimation allows external evidence on the expected magnitude of heterogeneity to be incorporated. The aim of this paper is to provide tools that improve the accessibility of Bayesian meta-analysis. We present two methods for implementing Bayesian meta-analysis, using numerical integration and importance sampling techniques. Based on 14 886 binary outcome meta-analyses in the Cochrane Database of Systematic Reviews, we derive a novel set of predictive distributions for the degree of heterogeneity expected in 80 settings depending on the outcomes assessed and comparisons made. These can be used as prior distributions for heterogeneity in future meta-analyses. The two methods are implemented in R, for which code is provided. Both methods produce equivalent results to standard but more complex Markov chain Monte Carlo approaches. The priors are derived as log-normal distributions for the between-study variance, applicable to meta-analyses of binary outcomes on the log odds-ratio scale. The methods are applied to two example meta-analyses, incorporating the relevant predictive distributions as prior distributions for between-study heterogeneity. We have provided resources to facilitate Bayesian meta-analysis, in a form accessible to applied researchers, which allow relevant prior information on the degree of heterogeneity to be incorporated. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd. PMID:25475839

Spatial distribution of psychotic disorders in an urban area of France: an ecological study.

PubMed

Pignon, Baptiste; Schürhoff, Franck; Baudin, Grégoire; Ferchiou, Aziz; Richard, Jean-Romain; Saba, Ghassen; Leboyer, Marion; Kirkbride, James B; Szöke, Andrei

2016-05-18

Previous analyses of neighbourhood variations of non-affective psychotic disorders (NAPD) have focused mainly on incidence. However, prevalence studies provide important insights on factors associated with disease evolution as well as for healthcare resource allocation. This study aimed to investigate the distribution of prevalent NAPD cases in an urban area in France. The number of cases in each neighbourhood was modelled as a function of potential confounders and ecological variables, namely: migrant density, economic deprivation and social fragmentation. This was modelled using statistical models of increasing complexity: frequentist models (using Poisson and negative binomial regressions), and several Bayesian models. For each model, assumptions validity were checked and compared as to how this fitted to the data, in order to test for possible spatial variation in prevalence. Data showed significant overdispersion (invalidating the Poisson regression model) and residual autocorrelation (suggesting the need to use Bayesian models). The best Bayesian model was Leroux's model (i.e. a model with both strong correlation between neighbouring areas and weaker correlation between areas further apart), with economic deprivation as an explanatory variable (OR = 1.13, 95% CI [1.02-1.25]). In comparison with frequentist methods, the Bayesian model showed a better fit. The number of cases showed non-random spatial distribution and was linked to economic deprivation.

Structure and stability of genetic variance-covariance matrices: A Bayesian sparse factor analysis of transcriptional variation in the three-spined stickleback.

PubMed

Siren, J; Ovaskainen, O; Merilä, J

2017-10-01

The genetic variance-covariance matrix (G) is a quantity of central importance in evolutionary biology due to its influence on the rate and direction of multivariate evolution. However, the predictive power of empirically estimated G-matrices is limited for two reasons. First, phenotypes are high-dimensional, whereas traditional statistical methods are tuned to estimate and analyse low-dimensional matrices. Second, the stability of G to environmental effects and over time remains poorly understood. Using Bayesian sparse factor analysis (BSFG) designed to estimate high-dimensional G-matrices, we analysed levels variation and covariation in 10,527 expressed genes in a large (n = 563) half-sib breeding design of three-spined sticklebacks subject to two temperature treatments. We found significant differences in the structure of G between the treatments: heritabilities and evolvabilities were higher in the warm than in the low-temperature treatment, suggesting more and faster opportunity to evolve in warm (stressful) conditions. Furthermore, comparison of G and its phenotypic equivalent P revealed the latter is a poor substitute of the former. Most strikingly, the results suggest that the expected impact of G on evolvability-as well as the similarity among G-matrices-may depend strongly on the number of traits included into analyses. In our results, the inclusion of only few traits in the analyses leads to underestimation in the differences between the G-matrices and their predicted impacts on evolution. While the results highlight the challenges involved in estimating G, they also illustrate that by enabling the estimation of large G-matrices, the BSFG method can improve predicted evolutionary responses to selection. © 2017 John Wiley & Sons Ltd.

Glutamatergic model psychoses: prediction error, learning, and inference.

PubMed

Corlett, Philip R; Honey, Garry D; Krystal, John H; Fletcher, Paul C

2011-01-01

Modulating glutamatergic neurotransmission induces alterations in conscious experience that mimic the symptoms of early psychotic illness. We review studies that use intravenous administration of ketamine, focusing on interindividual variability in the profundity of the ketamine experience. We will consider this individual variability within a hypothetical model of brain and cognitive function centered upon learning and inference. Within this model, the brains, neural systems, and even single neurons specify expectations about their inputs and responding to violations of those expectations with new learning that renders future inputs more predictable. We argue that ketamine temporarily deranges this ability by perturbing both the ways in which prior expectations are specified and the ways in which expectancy violations are signaled. We suggest that the former effect is predominantly mediated by NMDA blockade and the latter by augmented and inappropriate feedforward glutamatergic signaling. We suggest that the observed interindividual variability emerges from individual differences in neural circuits that normally underpin the learning and inference processes described. The exact source for that variability is uncertain, although it is likely to arise not only from genetic variation but also from subjects' previous experiences and prior learning. Furthermore, we argue that chronic, unlike acute, NMDA blockade alters the specification of expectancies more profoundly and permanently. Scrutinizing individual differences in the effects of acute and chronic ketamine administration in the context of the Bayesian brain model may generate new insights about the symptoms of psychosis; their underlying cognitive processes and neurocircuitry.

Incorporating approximation error in surrogate based Bayesian inversion

NASA Astrophysics Data System (ADS)

Zhang, J.; Zeng, L.; Li, W.; Wu, L.

2015-12-01

There are increasing interests in applying surrogates for inverse Bayesian modeling to reduce repetitive evaluations of original model. In this way, the computational cost is expected to be saved. However, the approximation error of surrogate model is usually overlooked. This is partly because that it is difficult to evaluate the approximation error for many surrogates. Previous studies have shown that, the direct combination of surrogates and Bayesian methods (e.g., Markov Chain Monte Carlo, MCMC) may lead to biased estimations when the surrogate cannot emulate the highly nonlinear original system. This problem can be alleviated by implementing MCMC in a two-stage manner. However, the computational cost is still high since a relatively large number of original model simulations are required. In this study, we illustrate the importance of incorporating approximation error in inverse Bayesian modeling. Gaussian process (GP) is chosen to construct the surrogate for its convenience in approximation error evaluation. Numerical cases of Bayesian experimental design and parameter estimation for contaminant source identification are used to illustrate this idea. It is shown that, once the surrogate approximation error is well incorporated into Bayesian framework, promising results can be obtained even when the surrogate is directly used, and no further original model simulations are required.

Evaluation of non-animal methods for assessing skin sensitisation hazard: A Bayesian Value-of-Information analysis.

PubMed

Leontaridou, Maria; Gabbert, Silke; Van Ierland, Ekko C; Worth, Andrew P; Landsiedel, Robert

2016-07-01

This paper offers a Bayesian Value-of-Information (VOI) analysis for guiding the development of non-animal testing strategies, balancing information gains from testing with the expected social gains and costs from the adoption of regulatory decisions. Testing is assumed to have value, if, and only if, the information revealed from testing triggers a welfare-improving decision on the use (or non-use) of a substance. As an illustration, our VOI model is applied to a set of five individual non-animal prediction methods used for skin sensitisation hazard assessment, seven battery combinations of these methods, and 236 sequential 2-test and 3-test strategies. Their expected values are quantified and compared to the expected value of the local lymph node assay (LLNA) as the animal method. We find that battery and sequential combinations of non-animal prediction methods reveal a significantly higher expected value than the LLNA. This holds for the entire range of prior beliefs. Furthermore, our results illustrate that the testing strategy with the highest expected value does not necessarily have to follow the order of key events in the sensitisation adverse outcome pathway (AOP). 2016 FRAME.

Bayesian parameter estimation for chiral effective field theory

NASA Astrophysics Data System (ADS)

Wesolowski, Sarah; Furnstahl, Richard; Phillips, Daniel; Klco, Natalie

2016-09-01

The low-energy constants (LECs) of a chiral effective field theory (EFT) interaction in the two-body sector are fit to observable data using a Bayesian parameter estimation framework. By using Bayesian prior probability distributions (pdfs), we quantify relevant physical expectations such as LEC naturalness and include them in the parameter estimation procedure. The final result is a posterior pdf for the LECs, which can be used to propagate uncertainty resulting from the fit to data to the final observable predictions. The posterior pdf also allows an empirical test of operator redundancy and other features of the potential. We compare results of our framework with other fitting procedures, interpreting the underlying assumptions in Bayesian probabilistic language. We also compare results from fitting all partial waves of the interaction simultaneously to cross section data compared to fitting to extracted phase shifts, appropriately accounting for correlations in the data. Supported in part by the NSF and DOE.

Bayesian truncation errors in chiral effective field theory: model checking and accounting for correlations

NASA Astrophysics Data System (ADS)

Melendez, Jordan; Wesolowski, Sarah; Furnstahl, Dick

2017-09-01

Chiral effective field theory (EFT) predictions are necessarily truncated at some order in the EFT expansion, which induces an error that must be quantified for robust statistical comparisons to experiment. A Bayesian model yields posterior probability distribution functions for these errors based on expectations of naturalness encoded in Bayesian priors and the observed order-by-order convergence pattern of the EFT. As a general example of a statistical approach to truncation errors, the model was applied to chiral EFT for neutron-proton scattering using various semi-local potentials of Epelbaum, Krebs, and Meißner (EKM). Here we discuss how our model can learn correlation information from the data and how to perform Bayesian model checking to validate that the EFT is working as advertised. Supported in part by NSF PHY-1614460 and DOE NUCLEI SciDAC DE-SC0008533.

A Bayesian bird's eye view of ‘Replications of important results in social psychology’

PubMed Central

Schönbrodt, Felix D.; Yao, Yuling; Gelman, Andrew; Wagenmakers, Eric-Jan

2017-01-01

We applied three Bayesian methods to reanalyse the preregistered contributions to the Social Psychology special issue ‘Replications of Important Results in Social Psychology’ (Nosek & Lakens. 2014 Registered reports: a method to increase the credibility of published results. Soc. Psychol. 45, 137–141. (doi:10.1027/1864-9335/a000192)). First, individual-experiment Bayesian parameter estimation revealed that for directed effect size measures, only three out of 44 central 95% credible intervals did not overlap with zero and fell in the expected direction. For undirected effect size measures, only four out of 59 credible intervals contained values greater than 0.10 (10% of variance explained) and only 19 intervals contained values larger than 0.05. Second, a Bayesian random-effects meta-analysis for all 38 t-tests showed that only one out of the 38 hierarchically estimated credible intervals did not overlap with zero and fell in the expected direction. Third, a Bayes factor hypothesis test was used to quantify the evidence for the null hypothesis against a default one-sided alternative. Only seven out of 60 Bayes factors indicated non-anecdotal support in favour of the alternative hypothesis (BF10>3), whereas 51 Bayes factors indicated at least some support for the null hypothesis. We hope that future analyses of replication success will embrace a more inclusive statistical approach by adopting a wider range of complementary techniques. PMID:28280547

Bayesian design criteria: computation, comparison, and application to a pharmacokinetic and a pharmacodynamic model.

PubMed

Merlé, Y; Mentré, F

1995-02-01

In this paper 3 criteria to design experiments for Bayesian estimation of the parameters of nonlinear models with respect to their parameters, when a prior distribution is available, are presented: the determinant of the Bayesian information matrix, the determinant of the pre-posterior covariance matrix, and the expected information provided by an experiment. A procedure to simplify the computation of these criteria is proposed in the case of continuous prior distributions and is compared with the criterion obtained from a linearization of the model about the mean of the prior distribution for the parameters. This procedure is applied to two models commonly encountered in the area of pharmacokinetics and pharmacodynamics: the one-compartment open model with bolus intravenous single-dose injection and the Emax model. They both involve two parameters. Additive as well as multiplicative gaussian measurement errors are considered with normal prior distributions. Various combinations of the variances of the prior distribution and of the measurement error are studied. Our attention is restricted to designs with limited numbers of measurements (1 or 2 measurements). This situation often occurs in practice when Bayesian estimation is performed. The optimal Bayesian designs that result vary with the variances of the parameter distribution and with the measurement error. The two-point optimal designs sometimes differ from the D-optimal designs for the mean of the prior distribution and may consist of replicating measurements. For the studied cases, the determinant of the Bayesian information matrix and its linearized form lead to the same optimal designs. In some cases, the pre-posterior covariance matrix can be far from its lower bound, namely, the inverse of the Bayesian information matrix, especially for the Emax model and a multiplicative measurement error. The expected information provided by the experiment and the determinant of the pre-posterior covariance matrix generally lead to the same designs except for the Emax model and the multiplicative measurement error. Results show that these criteria can be easily computed and that they could be incorporated in modules for designing experiments.

Bayesian and “Anti-Bayesian” Biases in Sensory Integration for Action and Perception in the Size–Weight Illusion

PubMed Central

Brayanov, Jordan B.

2010-01-01

Which is heavier: a pound of lead or a pound of feathers? This classic trick question belies a simple but surprising truth: when lifted, the pound of lead feels heavier—a phenomenon known as the size–weight illusion. To estimate the weight of an object, our CNS combines two imperfect sources of information: a prior expectation, based on the object's appearance, and direct sensory information from lifting it. Bayes' theorem (or Bayes' law) defines the statistically optimal way to combine multiple information sources for maximally accurate estimation. Here we asked whether the mechanisms for combining these information sources produce statistically optimal weight estimates for both perceptions and actions. We first studied the ability of subjects to hold one hand steady when the other removed an object from it, under conditions in which sensory information about the object's weight sometimes conflicted with prior expectations based on its size. Since the ability to steady the supporting hand depends on the generation of a motor command that accounts for lift timing and object weight, hand motion can be used to gauge biases in weight estimation by the motor system. We found that these motor system weight estimates reflected the integration of prior expectations with real-time proprioceptive information in a Bayesian, statistically optimal fashion that discounted unexpected sensory information. This produces a motor size–weight illusion that consistently biases weight estimates toward prior expectations. In contrast, when subjects compared the weights of two objects, their perceptions defied Bayes' law, exaggerating the value of unexpected sensory information. This produces a perceptual size–weight illusion that biases weight perceptions away from prior expectations. We term this effect “anti-Bayesian” because the bias is opposite that seen in Bayesian integration. Our findings suggest that two fundamentally different strategies for the integration of prior expectations with sensory information coexist in the nervous system for weight estimation. PMID:20089821

Comparing interval estimates for small sample ordinal CFA models

PubMed Central

Natesan, Prathiba

2015-01-01

Robust maximum likelihood (RML) and asymptotically generalized least squares (AGLS) methods have been recommended for fitting ordinal structural equation models. Studies show that some of these methods underestimate standard errors. However, these studies have not investigated the coverage and bias of interval estimates. An estimate with a reasonable standard error could still be severely biased. This can only be known by systematically investigating the interval estimates. The present study compares Bayesian, RML, and AGLS interval estimates of factor correlations in ordinal confirmatory factor analysis models (CFA) for small sample data. Six sample sizes, 3 factor correlations, and 2 factor score distributions (multivariate normal and multivariate mildly skewed) were studied. Two Bayesian prior specifications, informative and relatively less informative were studied. Undercoverage of confidence intervals and underestimation of standard errors was common in non-Bayesian methods. Underestimated standard errors may lead to inflated Type-I error rates. Non-Bayesian intervals were more positive biased than negatively biased, that is, most intervals that did not contain the true value were greater than the true value. Some non-Bayesian methods had non-converging and inadmissible solutions for small samples and non-normal data. Bayesian empirical standard error estimates for informative and relatively less informative priors were closer to the average standard errors of the estimates. The coverage of Bayesian credibility intervals was closer to what was expected with overcoverage in a few cases. Although some Bayesian credibility intervals were wider, they reflected the nature of statistical uncertainty that comes with the data (e.g., small sample). Bayesian point estimates were also more accurate than non-Bayesian estimates. The results illustrate the importance of analyzing coverage and bias of interval estimates, and how ignoring interval estimates can be misleading. Therefore, editors and policymakers should continue to emphasize the inclusion of interval estimates in research. PMID:26579002

Comparing interval estimates for small sample ordinal CFA models.

PubMed

Natesan, Prathiba

2015-01-01

Robust maximum likelihood (RML) and asymptotically generalized least squares (AGLS) methods have been recommended for fitting ordinal structural equation models. Studies show that some of these methods underestimate standard errors. However, these studies have not investigated the coverage and bias of interval estimates. An estimate with a reasonable standard error could still be severely biased. This can only be known by systematically investigating the interval estimates. The present study compares Bayesian, RML, and AGLS interval estimates of factor correlations in ordinal confirmatory factor analysis models (CFA) for small sample data. Six sample sizes, 3 factor correlations, and 2 factor score distributions (multivariate normal and multivariate mildly skewed) were studied. Two Bayesian prior specifications, informative and relatively less informative were studied. Undercoverage of confidence intervals and underestimation of standard errors was common in non-Bayesian methods. Underestimated standard errors may lead to inflated Type-I error rates. Non-Bayesian intervals were more positive biased than negatively biased, that is, most intervals that did not contain the true value were greater than the true value. Some non-Bayesian methods had non-converging and inadmissible solutions for small samples and non-normal data. Bayesian empirical standard error estimates for informative and relatively less informative priors were closer to the average standard errors of the estimates. The coverage of Bayesian credibility intervals was closer to what was expected with overcoverage in a few cases. Although some Bayesian credibility intervals were wider, they reflected the nature of statistical uncertainty that comes with the data (e.g., small sample). Bayesian point estimates were also more accurate than non-Bayesian estimates. The results illustrate the importance of analyzing coverage and bias of interval estimates, and how ignoring interval estimates can be misleading. Therefore, editors and policymakers should continue to emphasize the inclusion of interval estimates in research.

Measurement of admixture proportions and description of admixture structure in different US populations

PubMed Central

Halder, Indrani; Yang, Bao-Zhu; Kranzler, Henry R.; Stein, Murray B.; Shriver, Mark D.; Gelernter, Joel

2010-01-01

Variation in individual admixture proportions leads to heterogeneity within populations. Though novel methods and marker panels have been developed to quantify individual admixture, empirical data describing individual admixture distributions are limited. We investigated variation in individual admixture in four US populations [European American (EA), African American (AA) and Hispanics from Connecticut (EC) and California (WC)] assuming three-way intermixture among Europeans, Africans and Indigenous Americans. Admixture estimates were inferred using a panel of 36 microsatellites and 1 SNP, which have significant allele frequency differences between ancestral populations, and by using both a maximum likelihood (ML) based method and a Bayesian method implemented in the program STRUCTURE. Simulation studies showed that estimates obtained with this marker panel are within 96% of expected values. EAs had the lowest non-European admixture with both methods, but showed greater homogeneity with STRUCTURE than with ML. All other samples showed a high degree of variation in admixture estimates with both methods, were highly concordant and showed evidence of admixture stratification. With both methods, AA subjects had 16% European and <10% Indigenous American admixture on average. EC Hispanics had higher mean African admixture and the WC Hispanics higher mean Indigenous American admixture, possibly reflecting their different continental origins. PMID:19572378

A Bayesian procedure for evaluating the frequency of calibration factor updates in highway safety manual (HSM) applications.

PubMed

Saha, Dibakar; Alluri, Priyanka; Gan, Albert

2017-01-01

The Highway Safety Manual (HSM) presents statistical models to quantitatively estimate an agency's safety performance. The models were developed using data from only a few U.S. states. To account for the effects of the local attributes and temporal factors on crash occurrence, agencies are required to calibrate the HSM-default models for crash predictions. The manual suggests updating calibration factors every two to three years, or preferably on an annual basis. Given that the calibration process involves substantial time, effort, and resources, a comprehensive analysis of the required calibration factor update frequency is valuable to the agencies. Accordingly, the objective of this study is to evaluate the HSM's recommendation and determine the required frequency of calibration factor updates. A robust Bayesian estimation procedure is used to assess the variation between calibration factors computed annually, biennially, and triennially using data collected from over 2400 miles of segments and over 700 intersections on urban and suburban facilities in Florida. Bayesian model yields a posterior distribution of the model parameters that give credible information to infer whether the difference between calibration factors computed at specified intervals is credibly different from the null value which represents unaltered calibration factors between the comparison years or in other words, zero difference. The concept of the null value is extended to include the range of values that are practically equivalent to zero. Bayesian inference shows that calibration factors based on total crash frequency are required to be updated every two years in cases where the variations between calibration factors are not greater than 0.01. When the variations are between 0.01 and 0.05, calibration factors based on total crash frequency could be updated every three years. Copyright © 2016 Elsevier Ltd. All rights reserved.

Influence of gene flow on divergence dating - implications for the speciation history of Takydromus grass lizards.

PubMed

Tseng, Shu-Ping; Li, Shou-Hsien; Hsieh, Chia-Hung; Wang, Hurng-Yi; Lin, Si-Min

2014-10-01

Dating the time of divergence and understanding speciation processes are central to the study of the evolutionary history of organisms but are notoriously difficult. The difficulty is largely rooted in variations in the ancestral population size or in the genealogy variation across loci. To depict the speciation processes and divergence histories of three monophyletic Takydromus species endemic to Taiwan, we sequenced 20 nuclear loci and combined with one mitochondrial locus published in GenBank. They were analysed by a multispecies coalescent approach within a Bayesian framework. Divergence dating based on the gene tree approach showed high variation among loci, and the divergence was estimated at an earlier date than when derived by the species-tree approach. To test whether variations in the ancestral population size accounted for the majority of this variation, we conducted computer inferences using isolation-with-migration (IM) and approximate Bayesian computation (ABC) frameworks. The results revealed that gene flow during the early stage of speciation was strongly favoured over the isolation model, and the initiation of the speciation process was far earlier than the dates estimated by gene- and species-based divergence dating. Due to their limited dispersal ability, it is suggested that geographical isolation may have played a major role in the divergence of these Takydromus species. Nevertheless, this study reveals a more complex situation and demonstrates that gene flow during the speciation process cannot be overlooked and may have a great impact on divergence dating. By using multilocus data and incorporating Bayesian coalescence approaches, we provide a more biologically realistic framework for delineating the divergence history of Takydromus. © 2014 John Wiley & Sons Ltd.

The influence of taxon sampling on Bayesian divergence time inference under scenarios of rate heterogeneity among lineages.

PubMed

Soares, André E R; Schrago, Carlos G

2015-01-07

Although taxon sampling is commonly considered an important issue in phylogenetic inference, it is rarely considered in the Bayesian estimation of divergence times. In fact, the studies conducted to date have presented ambiguous results, and the relevance of taxon sampling for molecular dating remains unclear. In this study, we developed a series of simulations that, after six hundred Bayesian molecular dating analyses, allowed us to evaluate the impact of taxon sampling on chronological estimates under three scenarios of among-lineage rate heterogeneity. The first scenario allowed us to examine the influence of the number of terminals on the age estimates based on a strict molecular clock. The second scenario imposed an extreme example of lineage specific rate variation, and the third scenario permitted extensive rate variation distributed along the branches. We also analyzed empirical data on selected mitochondrial genomes of mammals. Our results showed that in the strict molecular-clock scenario (Case I), taxon sampling had a minor impact on the accuracy of the time estimates, although the precision of the estimates was greater with an increased number of terminals. The effect was similar in the scenario (Case III) based on rate variation distributed among the branches. Only under intensive rate variation among lineages (Case II) taxon sampling did result in biased estimates. The results of an empirical analysis corroborated the simulation findings. We demonstrate that taxonomic sampling affected divergence time inference but that its impact was significant if the rates deviated from those derived for the strict molecular clock. Increased taxon sampling improved the precision and accuracy of the divergence time estimates, but the impact on precision is more relevant. On average, biased estimates were obtained only if lineage rate variation was pronounced. Copyright © 2014 Elsevier Ltd. All rights reserved.

Range-wide effects of breeding- and nonbreeding-season climate on the abundance of a Neotropical migrant songbird.

PubMed

Wilson, Scott; LaDeau, Shannon L; Tøttrup, Anders P; Marra, Peter P

2011-09-01

Geographic variation in the population dynamics of a species can result from regional variability in climate and how it affects reproduction and survival. Identifying such effects for migratory birds requires the integration of population models with knowledge of migratory connectivity between breeding and nonbreeding areas. We used Bayesian hierarchical models with 26 years of Breeding Bird Survey data (1982-2007) to investigate the impacts of breeding- and nonbreeding-season climate on abundance of American Redstarts (Setophaga ruticilla) across the species range. We focused on 15 populations defined by Bird Conservation Regions, and we included variation across routes and observers as well as temporal trends and climate effects. American Redstart populations that breed in eastern North America showed increased abundance following winters with higher plant productivity in the Caribbean where they are expected to overwinter. In contrast, western breeding populations showed little response to conditions in their expected wintering areas in west Mexico, perhaps reflecting lower migratory connectivity or differential effects of winter rainfall on individuals across the species range. Unlike the case with winter climate, we found few effects of temperature prior to arrival in spring (March-April) or during the nesting period (May-June) on abundance the following year. Eight populations showed significant changes in abundance, with the steepest declines in the Atlantic Northern Forest (-3.4%/yr) and the greatest increases in the Prairie Hardwood Transition (4%/yr). This study emphasizes how the effects of climate on populations of migratory birds are context dependent and can vary depending on geographic location and the period of the annual cycle. Such knowledge is essential for predicting regional variation in how populations of a species might vary in their response to climate change.

Bayesian nonparametric dictionary learning for compressed sensing MRI.

PubMed

Huang, Yue; Paisley, John; Lin, Qin; Ding, Xinghao; Fu, Xueyang; Zhang, Xiao-Ping

2014-12-01

We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRIs) from highly undersampled k -space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta process as a nonparametric dictionary learning prior for representing an image patch as a sparse combination of dictionary elements. The size of the dictionary and patch-specific sparsity pattern are inferred from the data, in addition to other dictionary learning variables. Dictionary learning is performed directly on the compressed image, and so is tailored to the MRI being considered. In addition, we investigate a total variation penalty term in combination with the dictionary learning model, and show how the denoising property of dictionary learning removes dependence on regularization parameters in the noisy setting. We derive a stochastic optimization algorithm based on Markov chain Monte Carlo for the Bayesian model, and use the alternating direction method of multipliers for efficiently performing total variation minimization. We present empirical results on several MRI, which show that the proposed regularization framework can improve reconstruction accuracy over other methods.

Spatiotemporal Bayesian analysis of Lyme disease in New York state, 1990-2000.

PubMed

Chen, Haiyan; Stratton, Howard H; Caraco, Thomas B; White, Dennis J

2006-07-01

Mapping ordinarily increases our understanding of nontrivial spatial and temporal heterogeneities in disease rates. However, the large number of parameters required by the corresponding statistical models often complicates detailed analysis. This study investigates the feasibility of a fully Bayesian hierarchical regression approach to the problem and identifies how it outperforms two more popular methods: crude rate estimates (CRE) and empirical Bayes standardization (EBS). In particular, we apply a fully Bayesian approach to the spatiotemporal analysis of Lyme disease incidence in New York state for the period 1990-2000. These results are compared with those obtained by CRE and EBS in Chen et al. (2005). We show that the fully Bayesian regression model not only gives more reliable estimates of disease rates than the other two approaches but also allows for tractable models that can accommodate more numerous sources of variation and unknown parameters.

A Bayesian approach for incorporating economic factors in sample size design for clinical trials of individual drugs and portfolios of drugs.

PubMed

Patel, Nitin R; Ankolekar, Suresh

2007-11-30

Classical approaches to clinical trial design ignore economic factors that determine economic viability of a new drug. We address the choice of sample size in Phase III trials as a decision theory problem using a hybrid approach that takes a Bayesian view from the perspective of a drug company and a classical Neyman-Pearson view from the perspective of regulatory authorities. We incorporate relevant economic factors in the analysis to determine the optimal sample size to maximize the expected profit for the company. We extend the analysis to account for risk by using a 'satisficing' objective function that maximizes the chance of meeting a management-specified target level of profit. We extend the models for single drugs to a portfolio of clinical trials and optimize the sample sizes to maximize the expected profit subject to budget constraints. Further, we address the portfolio risk and optimize the sample sizes to maximize the probability of achieving a given target of expected profit.

Attention in the predictive mind.

PubMed

Ransom, Madeleine; Fazelpour, Sina; Mole, Christopher

2017-01-01

It has recently become popular to suggest that cognition can be explained as a process of Bayesian prediction error minimization. Some advocates of this view propose that attention should be understood as the optimization of expected precisions in the prediction-error signal (Clark, 2013, 2016; Feldman & Friston, 2010; Hohwy, 2012, 2013). This proposal successfully accounts for several attention-related phenomena. We claim that it cannot account for all of them, since there are certain forms of voluntary attention that it cannot accommodate. We therefore suggest that, although the theory of Bayesian prediction error minimization introduces some powerful tools for the explanation of mental phenomena, its advocates have been wrong to claim that Bayesian prediction error minimization is 'all the brain ever does'. Copyright © 2016 Elsevier Inc. All rights reserved.

Bayesian Hierarchical Model Characterization of Model Error in Ocean Data Assimilation and Forecasts

DTIC Science & Technology

2013-09-30

wind ensemble with the increments in the surface momentum flux control vector in a four-dimensional variational (4dvar) assimilation system. The...stability  effects?   surface  stress   Surface   Momentum  Flux  Ensembles  from  Summaries  of  BHM  Winds  (Mediterranean...surface wind speed given ensemble winds from a Bayesian Hierarchical Model to provide surface momentum flux ensembles. 3 Figure 2: Domain of

Trend of hepatocellular carcinoma incidence after Bayesian correction for misclassified data in Iranian provinces.

PubMed

Hajizadeh, Nastaran; Baghestani, Ahmad Reza; Pourhoseingholi, Mohamad Amin; Ashtari, Sara; Fazeli, Zeinab; Vahedi, Mohsen; Zali, Mohammad Reza

2017-05-28

To study the trend of hepatocellular carcinoma incidence after correcting the misclassification in registering cancer incidence across Iranian provinces in cancer registry data. Incidence data of hepatocellular carcinoma were extracted from Iranian annual of national cancer registration reports 2004 to 2008. A Bayesian method was implemented to estimate the rate of misclassification in registering cancer incidence in neighboring province. A beta prior is considered for misclassification parameter. Each time two neighboring provinces were selected to be entered in the Bayesian model based on their expected coverage of cancer cases which is reported by medical university of the province. It is assumed that some cancer cases from a province that has an expected coverage of cancer cases lower than 100% are registered in their neighboring facilitate province with more than 100% expected coverage. There is an increase in the rate of hepatocellular carcinoma in Iran. Among total of 30 provinces of Iran, 21 provinces were selected to be entered to the Bayesian model for correcting the existed misclassification. Provinces with more medical facilities of Iran are Tehran (capital of the country), Razavi Khorasan in north-east of Iran, East Azerbaijan in north-west of the country, Isfahan in central part and near to Tehran, Khozestan and Fars in south and Mazandaran in north of the Iran, had an expected coverage more than their expectation. Those provinces had significantly higher rates of hepatocellular carcinoma than their neighboring provinces. In years 2004 to 2008, it was estimated to be on average 34% misclassification between North Khorasan province and Razavi Khorasan, 43% between South Khorasan province and Razavi Khorasan, 47% between Sistan and balochestan province and Razavi Khorasan, 23% between West Azerbaijan province and East Azerbaijan province, 25% between Ardebil province and East Azerbaijan province, 41% between Hormozgan province and Fars province, 22% betweenChaharmahal and bakhtyari province and Isfahan province, 22% between Kogiloye and boyerahmad province and Isfahan, 22% between Golestan province and Mazandaran province, 43% between Bushehr province and Khozestan province, 41% between Ilam province and Khuzestan province, 42% between Qazvin province and Tehran province, 44% between Markazi province and Tehran, and 30% between Qom province and Tehran. Accounting and correcting the regional misclassification is necessary for identifying high risk areas and planning for reducing the cancer incidence.

Impact of censoring on learning Bayesian networks in survival modelling.

PubMed

Stajduhar, Ivan; Dalbelo-Basić, Bojana; Bogunović, Nikola

2009-11-01

Bayesian networks are commonly used for presenting uncertainty and covariate interactions in an easily interpretable way. Because of their efficient inference and ability to represent causal relationships, they are an excellent choice for medical decision support systems in diagnosis, treatment, and prognosis. Although good procedures for learning Bayesian networks from data have been defined, their performance in learning from censored survival data has not been widely studied. In this paper, we explore how to use these procedures to learn about possible interactions between prognostic factors and their influence on the variate of interest. We study how censoring affects the probability of learning correct Bayesian network structures. Additionally, we analyse the potential usefulness of the learnt models for predicting the time-independent probability of an event of interest. We analysed the influence of censoring with a simulation on synthetic data sampled from randomly generated Bayesian networks. We used two well-known methods for learning Bayesian networks from data: a constraint-based method and a score-based method. We compared the performance of each method under different levels of censoring to those of the naive Bayes classifier and the proportional hazards model. We did additional experiments on several datasets from real-world medical domains. The machine-learning methods treated censored cases in the data as event-free. We report and compare results for several commonly used model evaluation metrics. On average, the proportional hazards method outperformed other methods in most censoring setups. As part of the simulation study, we also analysed structural similarities of the learnt networks. Heavy censoring, as opposed to no censoring, produces up to a 5% surplus and up to 10% missing total arcs. It also produces up to 50% missing arcs that should originally be connected to the variate of interest. Presented methods for learning Bayesian networks from data can be used to learn from censored survival data in the presence of light censoring (up to 20%) by treating censored cases as event-free. Given intermediate or heavy censoring, the learnt models become tuned to the majority class and would thus require a different approach.

Physics of ultrasonic wave propagation in bone and heart characterized using Bayesian parameter estimation

NASA Astrophysics Data System (ADS)

Anderson, Christian Carl

This Dissertation explores the physics underlying the propagation of ultrasonic waves in bone and in heart tissue through the use of Bayesian probability theory. Quantitative ultrasound is a noninvasive modality used for clinical detection, characterization, and evaluation of bone quality and cardiovascular disease. Approaches that extend the state of knowledge of the physics underpinning the interaction of ultrasound with inherently inhomogeneous and isotropic tissue have the potential to enhance its clinical utility. Simulations of fast and slow compressional wave propagation in cancellous bone were carried out to demonstrate the plausibility of a proposed explanation for the widely reported anomalous negative dispersion in cancellous bone. The results showed that negative dispersion could arise from analysis that proceeded under the assumption that the data consist of only a single ultrasonic wave, when in fact two overlapping and interfering waves are present. The confounding effect of overlapping fast and slow waves was addressed by applying Bayesian parameter estimation to simulated data, to experimental data acquired on bone-mimicking phantoms, and to data acquired in vitro on cancellous bone. The Bayesian approach successfully estimated the properties of the individual fast and slow waves even when they strongly overlapped in the acquired data. The Bayesian parameter estimation technique was further applied to an investigation of the anisotropy of ultrasonic properties in cancellous bone. The degree to which fast and slow waves overlap is partially determined by the angle of insonation of ultrasound relative to the predominant direction of trabecular orientation. In the past, studies of anisotropy have been limited by interference between fast and slow waves over a portion of the range of insonation angles. Bayesian analysis estimated attenuation, velocity, and amplitude parameters over the entire range of insonation angles, allowing a more complete characterization of anisotropy. A novel piecewise linear model for the cyclic variation of ultrasonic backscatter from myocardium was proposed. Models of cyclic variation for 100 type 2 diabetes patients and 43 normal control subjects were constructed using Bayesian parameter estimation. Parameters determined from the model, specifically rise time and slew rate, were found to be more reliable in differentiating between subject groups than the previously employed magnitude parameter.

A flexible Bayesian assessment for the expected impact of data on prediction confidence for optimal sampling designs

NASA Astrophysics Data System (ADS)

Leube, Philipp; Geiges, Andreas; Nowak, Wolfgang

2010-05-01

Incorporating hydrogeological data, such as head and tracer data, into stochastic models of subsurface flow and transport helps to reduce prediction uncertainty. Considering limited financial resources available for the data acquisition campaign, information needs towards the prediction goal should be satisfied in a efficient and task-specific manner. For finding the best one among a set of design candidates, an objective function is commonly evaluated, which measures the expected impact of data on prediction confidence, prior to their collection. An appropriate approach to this task should be stochastically rigorous, master non-linear dependencies between data, parameters and model predictions, and allow for a wide variety of different data types. Existing methods fail to fulfill all these requirements simultaneously. For this reason, we introduce a new method, denoted as CLUE (Cross-bred Likelihood Uncertainty Estimator), that derives the essential distributions and measures of data utility within a generalized, flexible and accurate framework. The method makes use of Bayesian GLUE (Generalized Likelihood Uncertainty Estimator) and extends it to an optimal design method by marginalizing over the yet unknown data values. Operating in a purely Bayesian Monte-Carlo framework, CLUE is a strictly formal information processing scheme free of linearizations. It provides full flexibility associated with the type of measurements (linear, non-linear, direct, indirect) and accounts for almost arbitrary sources of uncertainty (e.g. heterogeneity, geostatistical assumptions, boundary conditions, model concepts) via stochastic simulation and Bayesian model averaging. This helps to minimize the strength and impact of possible subjective prior assumptions, that would be hard to defend prior to data collection. Our study focuses on evaluating two different uncertainty measures: (i) expected conditional variance and (ii) expected relative entropy of a given prediction goal. The applicability and advantages are shown in a synthetic example. Therefor, we consider a contaminant source, posing a threat on a drinking water well in an aquifer. Furthermore, we assume uncertainty in geostatistical parameters, boundary conditions and hydraulic gradient. The two mentioned measures evaluate the sensitivity of (1) general prediction confidence and (2) exceedance probability of a legal regulatory threshold value on sampling locations.

A Bayesian Model of the Memory Colour Effect.

PubMed

Witzel, Christoph; Olkkonen, Maria; Gegenfurtner, Karl R

2018-01-01

According to the memory colour effect, the colour of a colour-diagnostic object is not perceived independently of the object itself. Instead, it has been shown through an achromatic adjustment method that colour-diagnostic objects still appear slightly in their typical colour, even when they are colourimetrically grey. Bayesian models provide a promising approach to capture the effect of prior knowledge on colour perception and to link these effects to more general effects of cue integration. Here, we model memory colour effects using prior knowledge about typical colours as priors for the grey adjustments in a Bayesian model. This simple model does not involve any fitting of free parameters. The Bayesian model roughly captured the magnitude of the measured memory colour effect for photographs of objects. To some extent, the model predicted observed differences in memory colour effects across objects. The model could not account for the differences in memory colour effects across different levels of realism in the object images. The Bayesian model provides a particularly simple account of memory colour effects, capturing some of the multiple sources of variation of these effects.

A Bayesian Model of the Memory Colour Effect

PubMed Central

Olkkonen, Maria; Gegenfurtner, Karl R.

2018-01-01

According to the memory colour effect, the colour of a colour-diagnostic object is not perceived independently of the object itself. Instead, it has been shown through an achromatic adjustment method that colour-diagnostic objects still appear slightly in their typical colour, even when they are colourimetrically grey. Bayesian models provide a promising approach to capture the effect of prior knowledge on colour perception and to link these effects to more general effects of cue integration. Here, we model memory colour effects using prior knowledge about typical colours as priors for the grey adjustments in a Bayesian model. This simple model does not involve any fitting of free parameters. The Bayesian model roughly captured the magnitude of the measured memory colour effect for photographs of objects. To some extent, the model predicted observed differences in memory colour effects across objects. The model could not account for the differences in memory colour effects across different levels of realism in the object images. The Bayesian model provides a particularly simple account of memory colour effects, capturing some of the multiple sources of variation of these effects. PMID:29760874

Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain

NASA Astrophysics Data System (ADS)

Beck, Joakim; Dia, Ben Mansour; Espath, Luis F. R.; Long, Quan; Tempone, Raúl

2018-06-01

In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. These drawbacks can be avoided by using an importance sampling approach. We present a computationally efficient method for optimal Bayesian experimental design that introduces importance sampling based on the Laplace method to the inner loop. We derive the optimal values for the method parameters in which the average computational cost is minimized according to the desired error tolerance. We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a more recent single-loop Monte Carlo method that uses the Laplace method as an approximation of the return value of the inner loop. The first example is a scalar problem that is linear in the uncertain parameter. The second example is a nonlinear scalar problem. The third example deals with the optimal sensor placement for an electrical impedance tomography experiment to recover the fiber orientation in laminate composites.

Bayesian analysis of U.S. hurricane climate

USGS Publications Warehouse

Elsner, James B.; Bossak, Brian H.

2001-01-01

Predictive climate distributions of U.S. landfalling hurricanes are estimated from observational records over the period 1851–2000. The approach is Bayesian, combining the reliable records of hurricane activity during the twentieth century with the less precise accounts of activity during the nineteenth century to produce a best estimate of the posterior distribution on the annual rates. The methodology provides a predictive distribution of future activity that serves as a climatological benchmark. Results are presented for the entire coast as well as for the Gulf Coast, Florida, and the East Coast. Statistics on the observed annual counts of U.S. hurricanes, both for the entire coast and by region, are similar within each of the three consecutive 50-yr periods beginning in 1851. However, evidence indicates that the records during the nineteenth century are less precise. Bayesian theory provides a rational approach for defining hurricane climate that uses all available information and that makes no assumption about whether the 150-yr record of hurricanes has been adequately or uniformly monitored. The analysis shows that the number of major hurricanes expected to reach the U.S. coast over the next 30 yr is 18 and the number of hurricanes expected to hit Florida is 20.

Bayesian nonparametric adaptive control using Gaussian processes.

PubMed

Chowdhary, Girish; Kingravi, Hassan A; How, Jonathan P; Vela, Patricio A

2015-03-01

Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element is radial basis function networks (RBFNs), with RBF centers preallocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become noneffective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semiglobal in nature. This paper investigates a Gaussian process-based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. The GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed-loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.

Analyzing degradation data with a random effects spline regression model

DOE PAGES

Fugate, Michael Lynn; Hamada, Michael Scott; Weaver, Brian Phillip

2017-03-17

This study proposes using a random effects spline regression model to analyze degradation data. Spline regression avoids having to specify a parametric function for the true degradation of an item. A distribution for the spline regression coefficients captures the variation of the true degradation curves from item to item. We illustrate the proposed methodology with a real example using a Bayesian approach. The Bayesian approach allows prediction of degradation of a population over time and estimation of reliability is easy to perform.

Analyzing degradation data with a random effects spline regression model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fugate, Michael Lynn; Hamada, Michael Scott; Weaver, Brian Phillip

This study proposes using a random effects spline regression model to analyze degradation data. Spline regression avoids having to specify a parametric function for the true degradation of an item. A distribution for the spline regression coefficients captures the variation of the true degradation curves from item to item. We illustrate the proposed methodology with a real example using a Bayesian approach. The Bayesian approach allows prediction of degradation of a population over time and estimation of reliability is easy to perform.

Efficient Mean Field Variational Algorithm for Data Assimilation (Invited)

NASA Astrophysics Data System (ADS)

Vrettas, M. D.; Cornford, D.; Opper, M.

2013-12-01

Data assimilation algorithms combine available observations of physical systems with the assumed model dynamics in a systematic manner, to produce better estimates of initial conditions for prediction. Broadly they can be categorized in three main approaches: (a) sequential algorithms, (b) sampling methods and (c) variational algorithms which transform the density estimation problem to an optimization problem. However, given finite computational resources, only a handful of ensemble Kalman filters and 4DVar algorithms have been applied operationally to very high dimensional geophysical applications, such as weather forecasting. In this paper we present a recent extension to our variational Bayesian algorithm which seeks the ';optimal' posterior distribution over the continuous time states, within a family of non-stationary Gaussian processes. Our initial work on variational Bayesian approaches to data assimilation, unlike the well-known 4DVar method which seeks only the most probable solution, computes the best time varying Gaussian process approximation to the posterior smoothing distribution for dynamical systems that can be represented by stochastic differential equations. This approach was based on minimising the Kullback-Leibler divergence, over paths, between the true posterior and our Gaussian process approximation. Whilst the observations were informative enough to keep the posterior smoothing density close to Gaussian the algorithm proved very effective on low dimensional systems (e.g. O(10)D). However for higher dimensional systems, the high computational demands make the algorithm prohibitively expensive. To overcome the difficulties presented in the original framework and make our approach more efficient in higher dimensional systems we have been developing a new mean field version of the algorithm which treats the state variables at any given time as being independent in the posterior approximation, while still accounting for their relationships in the mean solution arising from the original system dynamics. Here we present this new mean field approach, illustrating its performance on a range of benchmark data assimilation problems whose dimensionality varies from O(10) to O(10^3)D. We emphasise that the variational Bayesian approach we adopt, unlike other variational approaches, provides a natural bound on the marginal likelihood of the observations given the model parameters which also allows for inference of (hyper-) parameters such as observational errors, parameters in the dynamical model and model error representation. We also stress that since our approach is intrinsically parallel it can be implemented very efficiently to address very long data assimilation time windows. Moreover, like most traditional variational approaches our Bayesian variational method has the benefit of being posed as an optimisation problem therefore its complexity can be tuned to the available computational resources. We finish with a sketch of possible future directions.

Hierarchical structure of the Sicilian goats revealed by Bayesian analyses of microsatellite information.

PubMed

Siwek, M; Finocchiaro, R; Curik, I; Portolano, B

2011-02-01

Genetic structure and relationship amongst the main goat populations in Sicily (Girgentana, Derivata di Siria, Maltese and Messinese) were analysed using information from 19 microsatellite markers genotyped on 173 individuals. A posterior Bayesian approach implemented in the program STRUCTURE revealed a hierarchical structure with two clusters at the first level (Girgentana vs. Messinese, Derivata di Siria and Maltese), explaining 4.8% of variation (amovaФ(ST) estimate). Seven clusters nested within these first two clusters (further differentiations of Girgentana, Derivata di Siria and Maltese), explaining 8.5% of variation (amovaФ(SC) estimate). The analyses and methods applied in this study indicate their power to detect subtle population structure. © 2010 The Authors, Animal Genetics © 2010 Stichting International Foundation for Animal Genetics.

Speeded Reaching Movements around Invisible Obstacles

PubMed Central

Hudson, Todd E.; Wolfe, Uta; Maloney, Laurence T.

2012-01-01

We analyze the problem of obstacle avoidance from a Bayesian decision-theoretic perspective using an experimental task in which reaches around a virtual obstacle were made toward targets on an upright monitor. Subjects received monetary rewards for touching the target and incurred losses for accidentally touching the intervening obstacle. The locations of target-obstacle pairs within the workspace were varied from trial to trial. We compared human performance to that of a Bayesian ideal movement planner (who chooses motor strategies maximizing expected gain) using the Dominance Test employed in Hudson et al. (2007). The ideal movement planner suffers from the same sources of noise as the human, but selects movement plans that maximize expected gain in the presence of that noise. We find good agreement between the predictions of the model and actual performance in most but not all experimental conditions. PMID:23028276

An Anticipatory Model of Cavitation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Allgood, G.O.; Dress, W.B., Jr.; Hylton, J.O.

1999-04-05

The Anticipatory System (AS) formalism developed by Robert Rosen provides some insight into the problem of embedding intelligent behavior in machines. AS emulates the anticipatory behavior of biological systems. AS bases its behavior on its expectations about the near future and those expectations are modified as the system gains experience. The expectation is based on an internal model that is drawn from an appeal to physical reality. To be adaptive, the model must be able to update itself. To be practical, the model must run faster than real-time. The need for a physical model and the requirement that the modelmore » execute at extreme speeds, has held back the application of AS to practical problems. Two recent advances make it possible to consider the use of AS for practical intelligent sensors. First, advances in transducer technology make it possible to obtain previously unavailable data from which a model can be derived. For example, acoustic emissions (AE) can be fed into a Bayesian system identifier that enables the separation of a weak characterizing signal, such as the signature of pump cavitation precursors, from a strong masking signal, such as a pump vibration feature. The second advance is the development of extremely fast, but inexpensive, digital signal processing hardware on which it is possible to run an adaptive Bayesian-derived model faster than real-time. This paper reports the investigation of an AS using a model of cavitation based on hydrodynamic principles and Bayesian analysis of data from high-performance AE sensors.« less

Bayesian accounts of covert selective attention: A tutorial review.

PubMed

Vincent, Benjamin T

2015-05-01

Decision making and optimal observer models offer an important theoretical approach to the study of covert selective attention. While their probabilistic formulation allows quantitative comparison to human performance, the models can be complex and their insights are not always immediately apparent. Part 1 establishes the theoretical appeal of the Bayesian approach, and introduces the way in which probabilistic approaches can be applied to covert search paradigms. Part 2 presents novel formulations of Bayesian models of 4 important covert attention paradigms, illustrating optimal observer predictions over a range of experimental manipulations. Graphical model notation is used to present models in an accessible way and Supplementary Code is provided to help bridge the gap between model theory and practical implementation. Part 3 reviews a large body of empirical and modelling evidence showing that many experimental phenomena in the domain of covert selective attention are a set of by-products. These effects emerge as the result of observers conducting Bayesian inference with noisy sensory observations, prior expectations, and knowledge of the generative structure of the stimulus environment.

Confidence of compliance: a Bayesian approach for percentile standards.

PubMed

McBride, G B; Ellis, J C

2001-04-01

Rules for assessing compliance with percentile standards commonly limit the number of exceedances permitted in a batch of samples taken over a defined assessment period. Such rules are commonly developed using classical statistical methods. Results from alternative Bayesian methods are presented (using beta-distributed prior information and a binomial likelihood), resulting in "confidence of compliance" graphs. These allow simple reading of the consumer's risk and the supplier's risks for any proposed rule. The influence of the prior assumptions required by the Bayesian technique on the confidence results is demonstrated, using two reference priors (uniform and Jeffreys') and also using optimistic and pessimistic user-defined priors. All four give less pessimistic results than does the classical technique, because interpreting classical results as "confidence of compliance" actually invokes a Bayesian approach with an extreme prior distribution. Jeffreys' prior is shown to be the most generally appropriate choice of prior distribution. Cost savings can be expected using rules based on this approach.

Assessment of Manual Operation Time for the Manufacturing of Thin Film Transistor Liquid Crystal Display: A Bayesian Approach

NASA Astrophysics Data System (ADS)

Shen, Chien-wen

2009-01-01

During the processes of TFT-LCD manufacturing, steps like visual inspection of panel surface defects still heavily rely on manual operations. As the manual inspection time of TFT-LCD manufacturing could range from 4 hours to 1 day, the reliability of time forecasting is thus important for production planning, scheduling and customer response. This study would like to propose a practical and easy-to-implement prediction model through the approach of Bayesian networks for time estimation of manual operated procedures in TFT-LCD manufacturing. Given the lack of prior knowledge about manual operation time, algorithms of necessary path condition and expectation-maximization are used for structural learning and estimation of conditional probability distributions respectively. This study also applied Bayesian inference to evaluate the relationships between explanatory variables and manual operation time. With the empirical applications of this proposed forecasting model, approach of Bayesian networks demonstrates its practicability and prediction accountability.

Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach.

PubMed

Duarte, Belmiro P M; Wong, Weng Kee

2015-08-01

This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted.

Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach

PubMed Central

Duarte, Belmiro P. M.; Wong, Weng Kee

2014-01-01

Summary This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted. PMID:26512159

Application of Bayesian Approach to Cost-Effectiveness Analysis of Antiviral Treatments in Chronic Hepatitis B.

PubMed

Zhang, Hua; Huo, Mingdong; Chao, Jianqian; Liu, Pei

2016-01-01

Hepatitis B virus (HBV) infection is a major problem for public health; timely antiviral treatment can significantly prevent the progression of liver damage from HBV by slowing down or stopping the virus from reproducing. In the study we applied Bayesian approach to cost-effectiveness analysis, using Markov Chain Monte Carlo (MCMC) simulation methods for the relevant evidence input into the model to evaluate cost-effectiveness of entecavir (ETV) and lamivudine (LVD) therapy for chronic hepatitis B (CHB) in Jiangsu, China, thus providing information to the public health system in the CHB therapy. Eight-stage Markov model was developed, a hypothetical cohort of 35-year-old HBeAg-positive patients with CHB was entered into the model. Treatment regimens were LVD100mg daily and ETV 0.5 mg daily. The transition parameters were derived either from systematic reviews of the literature or from previous economic studies. The outcome measures were life-years, quality-adjusted lifeyears (QALYs), and expected costs associated with the treatments and disease progression. For the Bayesian models all the analysis was implemented by using WinBUGS version 1.4. Expected cost, life expectancy, QALYs decreased with age. Cost-effectiveness increased with age. Expected cost of ETV was less than LVD, while life expectancy and QALYs were higher than that of LVD, ETV strategy was more cost-effective. Costs and benefits of the Monte Carlo simulation were very close to the results of exact form among the group, but standard deviation of each group indicated there was a big difference between individual patients. Compared with lamivudine, entecavir is the more cost-effective option. CHB patients should accept antiviral treatment as soon as possible as the lower age the more cost-effective. Monte Carlo simulation obtained costs and effectiveness distribution, indicate our Markov model is of good robustness.

Bayesian adaptive trials offer advantages in comparative effectiveness trials: an example in status epilepticus.

PubMed

Connor, Jason T; Elm, Jordan J; Broglio, Kristine R

2013-08-01

We present a novel Bayesian adaptive comparative effectiveness trial comparing three treatments for status epilepticus that uses adaptive randomization with potential early stopping. The trial will enroll 720 unique patients in emergency departments and uses a Bayesian adaptive design. The trial design is compared to a trial without adaptive randomization and produces an efficient trial in which a higher proportion of patients are likely to be randomized to the most effective treatment arm while generally using fewer total patients and offers higher power than an analogous trial with fixed randomization when identifying a superior treatment. When one treatment is superior to the other two, the trial design provides better patient care, higher power, and a lower expected sample size. Copyright © 2013 Elsevier Inc. All rights reserved.

Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modeling.

PubMed

Strelioff, Christopher C; Crutchfield, James P; Hübler, Alfred W

2007-07-01

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer kth order Markov chains, for arbitrary k , from finite data by applying Bayesian methods to both parameter estimation and model-order selection. Extending existing results for multinomial models of discrete data, we connect inference to statistical mechanics through information-theoretic (type theory) techniques. We establish a direct relationship between Bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Finally, we introduce a method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes.

Bayesian Retrieval of Complete Posterior PDFs of Oceanic Rain Rate From Microwave Observations

NASA Technical Reports Server (NTRS)

Chiu, J. Christine; Petty, Grant W.

2005-01-01

This paper presents a new Bayesian algorithm for retrieving surface rain rate from Tropical Rainfall Measurements Mission (TRMM) Microwave Imager (TMI) over the ocean, along with validations against estimates from the TRMM Precipitation Radar (PR). The Bayesian approach offers a rigorous basis for optimally combining multichannel observations with prior knowledge. While other rain rate algorithms have been published that are based at least partly on Bayesian reasoning, this is believed to be the first self-contained algorithm that fully exploits Bayes Theorem to yield not just a single rain rate, but rather a continuous posterior probability distribution of rain rate. To advance our understanding of theoretical benefits of the Bayesian approach, we have conducted sensitivity analyses based on two synthetic datasets for which the true conditional and prior distribution are known. Results demonstrate that even when the prior and conditional likelihoods are specified perfectly, biased retrievals may occur at high rain rates. This bias is not the result of a defect of the Bayesian formalism but rather represents the expected outcome when the physical constraint imposed by the radiometric observations is weak, due to saturation effects. It is also suggested that the choice of the estimators and the prior information are both crucial to the retrieval. In addition, the performance of our Bayesian algorithm is found to be comparable to that of other benchmark algorithms in real-world applications, while having the additional advantage of providing a complete continuous posterior probability distribution of surface rain rate.

Fast genomic predictions via Bayesian G-BLUP and multilocus models of threshold traits including censored Gaussian data.

PubMed

Kärkkäinen, Hanni P; Sillanpää, Mikko J

2013-09-04

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed.

Fast Genomic Predictions via Bayesian G-BLUP and Multilocus Models of Threshold Traits Including Censored Gaussian Data

PubMed Central

Kärkkäinen, Hanni P.; Sillanpää, Mikko J.

2013-01-01

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed. PMID:23821618

Strelka: accurate somatic small-variant calling from sequenced tumor-normal sample pairs.

PubMed

Saunders, Christopher T; Wong, Wendy S W; Swamy, Sajani; Becq, Jennifer; Murray, Lisa J; Cheetham, R Keira

2012-07-15

Whole genome and exome sequencing of matched tumor-normal sample pairs is becoming routine in cancer research. The consequent increased demand for somatic variant analysis of paired samples requires methods specialized to model this problem so as to sensitively call variants at any practical level of tumor impurity. We describe Strelka, a method for somatic SNV and small indel detection from sequencing data of matched tumor-normal samples. The method uses a novel Bayesian approach which represents continuous allele frequencies for both tumor and normal samples, while leveraging the expected genotype structure of the normal. This is achieved by representing the normal sample as a mixture of germline variation with noise, and representing the tumor sample as a mixture of the normal sample with somatic variation. A natural consequence of the model structure is that sensitivity can be maintained at high tumor impurity without requiring purity estimates. We demonstrate that the method has superior accuracy and sensitivity on impure samples compared with approaches based on either diploid genotype likelihoods or general allele-frequency tests. The Strelka workflow source code is available at ftp://strelka@ftp.illumina.com/. csaunders@illumina.com

A Bayesian approach to parameter and reliability estimation in the Poisson distribution.

NASA Technical Reports Server (NTRS)

Canavos, G. C.

1972-01-01

For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.

Using Bayesian analysis in repeated preclinical in vivo studies for a more effective use of animals.

PubMed

Walley, Rosalind; Sherington, John; Rastrick, Joe; Detrait, Eric; Hanon, Etienne; Watt, Gillian

2016-05-01

Whilst innovative Bayesian approaches are increasingly used in clinical studies, in the preclinical area Bayesian methods appear to be rarely used in the reporting of pharmacology data. This is particularly surprising in the context of regularly repeated in vivo studies where there is a considerable amount of data from historical control groups, which has potential value. This paper describes our experience with introducing Bayesian analysis for such studies using a Bayesian meta-analytic predictive approach. This leads naturally either to an informative prior for a control group as part of a full Bayesian analysis of the next study or using a predictive distribution to replace a control group entirely. We use quality control charts to illustrate study-to-study variation to the scientists and describe informative priors in terms of their approximate effective numbers of animals. We describe two case studies of animal models: the lipopolysaccharide-induced cytokine release model used in inflammation and the novel object recognition model used to screen cognitive enhancers, both of which show the advantage of a Bayesian approach over the standard frequentist analysis. We conclude that using Bayesian methods in stable repeated in vivo studies can result in a more effective use of animals, either by reducing the total number of animals used or by increasing the precision of key treatment differences. This will lead to clearer results and supports the "3Rs initiative" to Refine, Reduce and Replace animals in research. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Quantitative trait nucleotide analysis using Bayesian model selection.

PubMed

Blangero, John; Goring, Harald H H; Kent, Jack W; Williams, Jeff T; Peterson, Charles P; Almasy, Laura; Dyer, Thomas D

2005-10-01

Although much attention has been given to statistical genetic methods for the initial localization and fine mapping of quantitative trait loci (QTLs), little methodological work has been done to date on the problem of statistically identifying the most likely functional polymorphisms using sequence data. In this paper we provide a general statistical genetic framework, called Bayesian quantitative trait nucleotide (BQTN) analysis, for assessing the likely functional status of genetic variants. The approach requires the initial enumeration of all genetic variants in a set of resequenced individuals. These polymorphisms are then typed in a large number of individuals (potentially in families), and marker variation is related to quantitative phenotypic variation using Bayesian model selection and averaging. For each sequence variant a posterior probability of effect is obtained and can be used to prioritize additional molecular functional experiments. An example of this quantitative nucleotide analysis is provided using the GAW12 simulated data. The results show that the BQTN method may be useful for choosing the most likely functional variants within a gene (or set of genes). We also include instructions on how to use our computer program, SOLAR, for association analysis and BQTN analysis.

Patterns of genetic variation across inversions: geographic variation in the In(2L)t inversion in populations of Drosophila melanogaster from eastern Australia.

PubMed

Kennington, W Jason; Hoffmann, Ary A

2013-05-20

Chromosomal inversions are increasingly being recognized as important in adaptive shifts and are expected to influence patterns of genetic variation, but few studies have examined genetic patterns in inversion polymorphisms across and within populations. Here, we examine genetic variation at 20 microsatellite loci and the alcohol dehydrogenase gene (Adh) located within and near the In(2L)t inversion of Drosophila melanogaster at three different sites along a latitudinal cline on the east coast of Australia. We found significant genetic differentiation between the standard and inverted chromosomal arrangements at each site as well as significant, but smaller differences among sites in the same arrangement. Genetic differentiation between pairs of sites was higher for inverted chromosomes than standard chromosomes, while inverted chromosomes had lower levels of genetic variation even well away from inversion breakpoints. Bayesian clustering analysis provided evidence of genetic exchange between chromosomal arrangements at each site. The strong differentiation between arrangements and reduced variation in the inverted chromosomes are likely to reflect ongoing selection at multiple loci within the inverted region. They may also reflect lower effective population sizes of In(2L)t chromosomes and colonization of Australia, although there was no consistent evidence of a recent bottleneck and simulations suggest that differences between arrangements would not persist unless rates of gene exchange between them were low. Genetic patterns therefore support the notion of selection and linkage disequilibrium contributing to inversion polymorphisms, although more work is needed to determine whether there are spatially varying targets of selection within this inversion. They also support the idea that the allelic content within an inversion can vary between geographic locations.

A Bayesian Hybrid Adaptive Randomisation Design for Clinical Trials with Survival Outcomes.

PubMed

Moatti, M; Chevret, S; Zohar, S; Rosenberger, W F

2016-01-01

Response-adaptive randomisation designs have been proposed to improve the efficiency of phase III randomised clinical trials and improve the outcomes of the clinical trial population. In the setting of failure time outcomes, Zhang and Rosenberger (2007) developed a response-adaptive randomisation approach that targets an optimal allocation, based on a fixed sample size. The aim of this research is to propose a response-adaptive randomisation procedure for survival trials with an interim monitoring plan, based on the following optimal criterion: for fixed variance of the estimated log hazard ratio, what allocation minimizes the expected hazard of failure? We demonstrate the utility of the design by redesigning a clinical trial on multiple myeloma. To handle continuous monitoring of data, we propose a Bayesian response-adaptive randomisation procedure, where the log hazard ratio is the effect measure of interest. Combining the prior with the normal likelihood, the mean posterior estimate of the log hazard ratio allows derivation of the optimal target allocation. We perform a simulation study to assess and compare the performance of this proposed Bayesian hybrid adaptive design to those of fixed, sequential or adaptive - either frequentist or fully Bayesian - designs. Non informative normal priors of the log hazard ratio were used, as well as mixture of enthusiastic and skeptical priors. Stopping rules based on the posterior distribution of the log hazard ratio were computed. The method is then illustrated by redesigning a phase III randomised clinical trial of chemotherapy in patients with multiple myeloma, with mixture of normal priors elicited from experts. As expected, there was a reduction in the proportion of observed deaths in the adaptive vs. non-adaptive designs; this reduction was maximized using a Bayes mixture prior, with no clear-cut improvement by using a fully Bayesian procedure. The use of stopping rules allows a slight decrease in the observed proportion of deaths under the alternate hypothesis compared with the adaptive designs with no stopping rules. Such Bayesian hybrid adaptive survival trials may be promising alternatives to traditional designs, reducing the duration of survival trials, as well as optimizing the ethical concerns for patients enrolled in the trial.

Technical note: Bayesian calibration of dynamic ruminant nutrition models.

PubMed

Reed, K F; Arhonditsis, G B; France, J; Kebreab, E

2016-08-01

Mechanistic models of ruminant digestion and metabolism have advanced our understanding of the processes underlying ruminant animal physiology. Deterministic modeling practices ignore the inherent variation within and among individual animals and thus have no way to assess how sources of error influence model outputs. We introduce Bayesian calibration of mathematical models to address the need for robust mechanistic modeling tools that can accommodate error analysis by remaining within the bounds of data-based parameter estimation. For the purpose of prediction, the Bayesian approach generates a posterior predictive distribution that represents the current estimate of the value of the response variable, taking into account both the uncertainty about the parameters and model residual variability. Predictions are expressed as probability distributions, thereby conveying significantly more information than point estimates in regard to uncertainty. Our study illustrates some of the technical advantages of Bayesian calibration and discusses the future perspectives in the context of animal nutrition modeling. Copyright © 2016 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

2D Bayesian automated tilted-ring fitting of disc galaxies in large H I galaxy surveys: 2DBAT

NASA Astrophysics Data System (ADS)

Oh, Se-Heon; Staveley-Smith, Lister; Spekkens, Kristine; Kamphuis, Peter; Koribalski, Bärbel S.

2018-01-01

We present a novel algorithm based on a Bayesian method for 2D tilted-ring analysis of disc galaxy velocity fields. Compared to the conventional algorithms based on a chi-squared minimization procedure, this new Bayesian-based algorithm suffers less from local minima of the model parameters even with highly multimodal posterior distributions. Moreover, the Bayesian analysis, implemented via Markov Chain Monte Carlo sampling, only requires broad ranges of posterior distributions of the parameters, which makes the fitting procedure fully automated. This feature will be essential when performing kinematic analysis on the large number of resolved galaxies expected to be detected in neutral hydrogen (H I) surveys with the Square Kilometre Array and its pathfinders. The so-called 2D Bayesian Automated Tilted-ring fitter (2DBAT) implements Bayesian fits of 2D tilted-ring models in order to derive rotation curves of galaxies. We explore 2DBAT performance on (a) artificial H I data cubes built based on representative rotation curves of intermediate-mass and massive spiral galaxies, and (b) Australia Telescope Compact Array H I data from the Local Volume H I Survey. We find that 2DBAT works best for well-resolved galaxies with intermediate inclinations (20° < i < 70°), complementing 3D techniques better suited to modelling inclined galaxies.

A Bayesian elicitation of veterinary beliefs regarding systemic dry cow therapy: variation and importance for clinical trial design.

PubMed

Higgins, H M; Dryden, I L; Green, M J

2012-09-15

The two key aims of this research were: (i) to conduct a probabilistic elicitation to quantify the variation in veterinarians' beliefs regarding the efficacy of systemic antibiotics when used as an adjunct to intra-mammary dry cow therapy and (ii) to investigate (in a Bayesian statistical framework) the strength of future research evidence required (in theory) to change the beliefs of practising veterinary surgeons regarding the efficacy of systemic antibiotics, given their current clinical beliefs. The beliefs of 24 veterinarians in 5 practices in England were quantified as probability density functions. Classic multidimensional scaling revealed major variations in beliefs both within and between veterinary practices which included: confident optimism, confident pessimism and considerable uncertainty. Of the 9 veterinarians interviewed holding further cattle qualifications, 6 shared a confidently pessimistic belief in the efficacy of systemic therapy and whilst 2 were more optimistic, they were also more uncertain. A Bayesian model based on a synthetic dataset from a randomised clinical trial (showing no benefit with systemic therapy) predicted how each of the 24 veterinarians' prior beliefs would alter as the size of the clinical trial increased, assuming that practitioners would update their beliefs rationally in accordance with Bayes' theorem. The study demonstrated the usefulness of probabilistic elicitation for evaluating the diversity and strength of practitioners' beliefs. The major variation in beliefs observed raises interest in the veterinary profession's approach to prescribing essential medicines. Results illustrate the importance of eliciting prior beliefs when designing clinical trials in order to increase the chance that trial data are of sufficient strength to alter the clinical beliefs of practitioners and do not merely serve to satisfy researchers. Copyright © 2012 Elsevier B.V. All rights reserved.

Bridging Inter- and Intraspecific Trait Evolution with a Hierarchical Bayesian Approach.

PubMed

Kostikova, Anna; Silvestro, Daniele; Pearman, Peter B; Salamin, Nicolas

2016-05-01

The evolution of organisms is crucially dependent on the evolution of intraspecific variation. Its interactions with selective agents in the biotic and abiotic environments underlie many processes, such as intraspecific competition, resource partitioning and, eventually, species formation. Nevertheless, comparative models of trait evolution neither allow explicit testing of hypotheses related to the evolution of intraspecific variation nor do they simultaneously estimate rates of trait evolution by accounting for both trait mean and variance. Here, we present a model of phenotypic trait evolution using a hierarchical Bayesian approach that simultaneously incorporates interspecific and intraspecific variation. We assume that species-specific trait means evolve under a simple Brownian motion process, whereas species-specific trait variances are modeled with Brownian or Ornstein-Uhlenbeck processes. After evaluating the power of the method through simulations, we examine whether life-history traits impact evolution of intraspecific variation in the Eriogonoideae (buckwheat family, Polygonaceae). Our model is readily extendible to more complex scenarios of the evolution of inter- and intraspecific variation and presents a step toward more comprehensive comparative models for macroevolutionary studies. © The Author(s) 2016. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Learning oncogenetic networks by reducing to mixed integer linear programming.

PubMed

Shahrabi Farahani, Hossein; Lagergren, Jens

2013-01-01

Cancer can be a result of accumulation of different types of genetic mutations such as copy number aberrations. The data from tumors are cross-sectional and do not contain the temporal order of the genetic events. Finding the order in which the genetic events have occurred and progression pathways are of vital importance in understanding the disease. In order to model cancer progression, we propose Progression Networks, a special case of Bayesian networks, that are tailored to model disease progression. Progression networks have similarities with Conjunctive Bayesian Networks (CBNs) [1],a variation of Bayesian networks also proposed for modeling disease progression. We also describe a learning algorithm for learning Bayesian networks in general and progression networks in particular. We reduce the hard problem of learning the Bayesian and progression networks to Mixed Integer Linear Programming (MILP). MILP is a Non-deterministic Polynomial-time complete (NP-complete) problem for which very good heuristics exists. We tested our algorithm on synthetic and real cytogenetic data from renal cell carcinoma. We also compared our learned progression networks with the networks proposed in earlier publications. The software is available on the website https://bitbucket.org/farahani/diprog.

A Bayesian CUSUM plot: Diagnosing quality of treatment.

PubMed

Rosthøj, Steen; Jacobsen, Rikke-Line

2017-12-01

To present a CUSUM plot based on Bayesian diagnostic reasoning displaying evidence in favour of "healthy" rather than "sick" quality of treatment (QOT), and to demonstrate a technique using Kaplan-Meier survival curves permitting application to case series with ongoing follow-up. For a case series with known final outcomes: Consider each case a diagnostic test of good versus poor QOT (expected vs. increased failure rates), determine the likelihood ratio (LR) of the observed outcome, convert LR to weight taking log to base 2, and add up weights sequentially in a plot showing how many times odds in favour of good QOT have been doubled. For a series with observed survival times and an expected survival curve: Divide the curve into time intervals, determine "healthy" and specify "sick" risks of failure in each interval, construct a "sick" survival curve, determine the LR of survival or failure at the given observation times, convert to weights, and add up. The Bayesian plot was applied retrospectively to 39 children with acute lymphoblastic leukaemia with completed follow-up, using Nordic collaborative results as reference, showing equal odds between good and poor QOT. In the ongoing treatment trial, with 22 of 37 children still at risk for event, QOT has been monitored with average survival curves as reference, odds so far favoring good QOT 2:1. QOT in small patient series can be assessed with a Bayesian CUSUM plot, retrospectively when all treatment outcomes are known, but also in ongoing series with unfinished follow-up. © 2017 John Wiley & Sons, Ltd.

A Bayesian approach to meta-analysis of plant pathology studies.

PubMed

Mila, A L; Ngugi, H K

2011-01-01

Bayesian statistical methods are used for meta-analysis in many disciplines, including medicine, molecular biology, and engineering, but have not yet been applied for quantitative synthesis of plant pathology studies. In this paper, we illustrate the key concepts of Bayesian statistics and outline the differences between Bayesian and classical (frequentist) methods in the way parameters describing population attributes are considered. We then describe a Bayesian approach to meta-analysis and present a plant pathological example based on studies evaluating the efficacy of plant protection products that induce systemic acquired resistance for the management of fire blight of apple. In a simple random-effects model assuming a normal distribution of effect sizes and no prior information (i.e., a noninformative prior), the results of the Bayesian meta-analysis are similar to those obtained with classical methods. Implementing the same model with a Student's t distribution and a noninformative prior for the effect sizes, instead of a normal distribution, yields similar results for all but acibenzolar-S-methyl (Actigard) which was evaluated only in seven studies in this example. Whereas both the classical (P = 0.28) and the Bayesian analysis with a noninformative prior (95% credibility interval [CRI] for the log response ratio: -0.63 to 0.08) indicate a nonsignificant effect for Actigard, specifying a t distribution resulted in a significant, albeit variable, effect for this product (CRI: -0.73 to -0.10). These results confirm the sensitivity of the analytical outcome (i.e., the posterior distribution) to the choice of prior in Bayesian meta-analyses involving a limited number of studies. We review some pertinent literature on more advanced topics, including modeling of among-study heterogeneity, publication bias, analyses involving a limited number of studies, and methods for dealing with missing data, and show how these issues can be approached in a Bayesian framework. Bayesian meta-analysis can readily include information not easily incorporated in classical methods, and allow for a full evaluation of competing models. Given the power and flexibility of Bayesian methods, we expect them to become widely adopted for meta-analysis of plant pathology studies.

Estimating abundance without recaptures of marked pallid sturgeon in the Mississippi River.

PubMed

Friedenberg, Nicholas A; Hoover, Jan Jeffrey; Boysen, Krista; Killgore, K Jack

2018-04-01

Abundance estimates are essential for assessing the viability of populations and the risks posed by alternative management actions. An effort to estimate abundance via a repeated mark-recapture experiment may fail to recapture marked individuals. We devised a method for obtaining lower bounds on abundance in the absence of recaptures for both panmictic and spatially structured populations. The method assumes few enough recaptures were expected to be missed by random chance. The upper Bayesian credible limit on expected recaptures allows probabilistic statements about the minimum number of individuals present in the population. We applied this method to data from a 12-year survey of pallid sturgeon (Scaphirhynchus albus) in the lower and middle Mississippi River (U.S.A.). None of the 241 individuals marked was recaptured in the survey. After accounting for survival and movement, our model-averaged estimate of the total abundance of pallid sturgeon ≥3 years old in the study area had a 1%, 5%, or 25% chance of being <4,600, 7,000, or 15,000, respectively. When we assumed fish were distributed in proportion to survey catch per unit effort, the farthest downstream reach in the survey hosted at least 4.5-15 fish per river kilometer (rkm), whereas the remainder of the reaches in the lower and middle Mississippi River hosted at least 2.6-8.5 fish/rkm for all model variations examined. The lower Mississippi River had an average density of pallid sturgeon ≥3 years old of at least 3.0-9.8 fish/rkm. The choice of Bayesian prior was the largest source of uncertainty we considered but did not alter the order of magnitude of lower bounds. Nil-recapture estimates of abundance are highly uncertain and require careful communication but can deliver insights from experiments that might otherwise be considered a failure. © 2017 Society for Conservation Biology.

Development of a standardized transfusion ratio as a metric for evaluating dialysis facility anemia management practices.

PubMed

Liu, Jiannong; Li, Suying; Gilbertson, David T; Monda, Keri L; Bradbury, Brian D; Collins, Allan J

2014-10-01

Because transfusion avoidance has been the cornerstone of anemia treatment for patients with kidney disease, direct measurement of red blood cell transfusion use to assess dialysis facility anemia management performance is reasonable. We aimed to explore methods for estimating facility-level standardized transfusion ratios (STfRs) to assess provider anemia treatment practices. Retrospective cohort study. Point prevalent US hemodialysis patients on January 1, 2009, with Medicare as primary payer and dialysis duration of 90 days or longer were included (n = 223,901). All dialysis facilities with eligible patients were included (n = 5,345). Dialysis facility assignment. Receiving a red blood cell transfusion in the inpatient or outpatient setting. We evaluated 3 approaches for estimating STfR: ratio of observed to expected numbers of transfusions (STfR(obs)), a Bayesian approach (STfR(Bayes)), and a modified version of the Bayesian approach (STfR(modBayes)). The overall national transfusion rate in 2009 was 23.2 per 100 patient-years. Our model for predicting the expected number of transfusions performed well. For large facilities, all 3 STfRs worked well. However, for small facilities, while the STfR(modBayes) worked well, STfR(obs) values demonstrated instability and the STfR(Bayes) may produce more bias. Administration of transfusions to dialysis patients reflects medical practice both within and outside the dialysis unit. Some transfusions may be deemed unavoidable and transfusion practices are subject to considerable regional variation. Development of an STfR metric is feasible and reasonable for assessing anemia treatment at dialysis facilities. The STfR(obs) is simple to calculate and works well for larger dialysis facilities. The STfR(modBayes) is more analytically complex, but facilitates comparisons across all dialysis facilities, including small facilities. Copyright © 2014 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.

Robust Bayesian Experimental Design for Conceptual Model Discrimination

NASA Astrophysics Data System (ADS)

Pham, H. V.; Tsai, F. T. C.

2015-12-01

A robust Bayesian optimal experimental design under uncertainty is presented to provide firm information for model discrimination, given the least number of pumping wells and observation wells. Firm information is the maximum information of a system can be guaranteed from an experimental design. The design is based on the Box-Hill expected entropy decrease (EED) before and after the experiment design and the Bayesian model averaging (BMA) framework. A max-min programming is introduced to choose the robust design that maximizes the minimal Box-Hill EED subject to that the highest expected posterior model probability satisfies a desired probability threshold. The EED is calculated by the Gauss-Hermite quadrature. The BMA method is used to predict future observations and to quantify future observation uncertainty arising from conceptual and parametric uncertainties in calculating EED. Monte Carlo approach is adopted to quantify the uncertainty in the posterior model probabilities. The optimal experimental design is tested by a synthetic 5-layer anisotropic confined aquifer. Nine conceptual groundwater models are constructed due to uncertain geological architecture and boundary condition. High-performance computing is used to enumerate all possible design solutions in order to identify the most plausible groundwater model. Results highlight the impacts of scedasticity in future observation data as well as uncertainty sources on potential pumping and observation locations.

The interaction of Bayesian priors and sensory data and its neural circuit implementation in visually-guided movement

PubMed Central

Yang, Jin; Lee, Joonyeol; Lisberger, Stephen G.

2012-01-01

Sensory-motor behavior results from a complex interaction of noisy sensory data with priors based on recent experience. By varying the stimulus form and contrast for the initiation of smooth pursuit eye movements in monkeys, we show that visual motion inputs compete with two independent priors: one prior biases eye speed toward zero; the other prior attracts eye direction according to the past several days’ history of target directions. The priors bias the speed and direction of the initiation of pursuit for the weak sensory data provided by the motion of a low-contrast sine wave grating. However, the priors have relatively little effect on pursuit speed and direction when the visual stimulus arises from the coherent motion of a high-contrast patch of dots. For any given stimulus form, the mean and variance of eye speed co-vary in the initiation of pursuit, as expected for signal-dependent noise. This relationship suggests that pursuit implements a trade-off between movement accuracy and variation, reducing both when the sensory signals are noisy. The tradeoff is implemented as a competition of sensory data and priors that follows the rules of Bayesian estimation. Computer simulations show that the priors can be understood as direction specific control of the strength of visual-motor transmission, and can be implemented in a neural-network model that makes testable predictions about the population response in the smooth eye movement region of the frontal eye fields. PMID:23223286

Bayesian Population Genomic Inference of Crossing Over and Gene Conversion

PubMed Central

Padhukasahasram, Badri; Rannala, Bruce

2011-01-01

Meiotic recombination is a fundamental cellular mechanism in sexually reproducing organisms and its different forms, crossing over and gene conversion both play an important role in shaping genetic variation in populations. Here, we describe a coalescent-based full-likelihood Markov chain Monte Carlo (MCMC) method for jointly estimating the crossing-over, gene-conversion, and mean tract length parameters from population genomic data under a Bayesian framework. Although computationally more expensive than methods that use approximate likelihoods, the relative efficiency of our method is expected to be optimal in theory. Furthermore, it is also possible to obtain a posterior sample of genealogies for the data using this method. We first check the performance of the new method on simulated data and verify its correctness. We also extend the method for inference under models with variable gene-conversion and crossing-over rates and demonstrate its ability to identify recombination hotspots. Then, we apply the method to two empirical data sets that were sequenced in the telomeric regions of the X chromosome of Drosophila melanogaster. Our results indicate that gene conversion occurs more frequently than crossing over in the su-w and su-s gene sequences while the local rates of crossing over as inferred by our program are not low. The mean tract lengths for gene-conversion events are estimated to be ∼70 bp and 430 bp, respectively, for these data sets. Finally, we discuss ideas and optimizations for reducing the execution time of our algorithm. PMID:21840857

Bertrand and Cournot oligopolies when rivals' costs are unknown

NASA Astrophysics Data System (ADS)

Ferreira, Fernanda A.; Ferreira, Flávio

2010-10-01

We study Bertrand and Cournot oligopoly models with incomplete information about rivals' costs, where the uncertainty is given by a uniform distribution. We compute the Bayesian-Nash equilibrium of both games, the ex-ante expected profits and the ex-post profits of each firm. We see that, in the price competition, even though only one firm produces in equilibrium, all firms have a positive ex-ante expected profit.

Mixture class recovery in GMM under varying degrees of class separation: frequentist versus Bayesian estimation.

PubMed

Depaoli, Sarah

2013-06-01

Growth mixture modeling (GMM) represents a technique that is designed to capture change over time for unobserved subgroups (or latent classes) that exhibit qualitatively different patterns of growth. The aim of the current article was to explore the impact of latent class separation (i.e., how similar growth trajectories are across latent classes) on GMM performance. Several estimation conditions were compared: maximum likelihood via the expectation maximization (EM) algorithm and the Bayesian framework implementing diffuse priors, "accurate" informative priors, weakly informative priors, data-driven informative priors, priors reflecting partial-knowledge of parameters, and "inaccurate" (but informative) priors. The main goal was to provide insight about the optimal estimation condition under different degrees of latent class separation for GMM. Results indicated that optimal parameter recovery was obtained though the Bayesian approach using "accurate" informative priors, and partial-knowledge priors showed promise for the recovery of the growth trajectory parameters. Maximum likelihood and the remaining Bayesian estimation conditions yielded poor parameter recovery for the latent class proportions and the growth trajectories. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

Enhanced optical alignment of a digital micro mirror device through Bayesian adaptive exploration

NASA Astrophysics Data System (ADS)

Wynne, Kevin B.; Knuth, Kevin H.; Petruccelli, Jonathan

2017-12-01

As the use of Digital Micro Mirror Devices (DMDs) becomes more prevalent in optics research, the ability to precisely locate the Fourier "footprint" of an image beam at the Fourier plane becomes a pressing need. In this approach, Bayesian adaptive exploration techniques were employed to characterize the size and position of the beam on a DMD located at the Fourier plane. It couples a Bayesian inference engine with an inquiry engine to implement the search. The inquiry engine explores the DMD by engaging mirrors and recording light intensity values based on the maximization of the expected information gain. Using the data collected from this exploration, the Bayesian inference engine updates the posterior probability describing the beam's characteristics. The process is iterated until the beam is located to within the desired precision. This methodology not only locates the center and radius of the beam with remarkable precision but accomplishes the task in far less time than a brute force search. The employed approach has applications to system alignment for both Fourier processing and coded aperture design.

Entropy-Bayesian Inversion of Time-Lapse Tomographic GPR data for Monitoring Dielectric Permittivity and Soil Moisture Variations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hou, Z; Terry, N; Hubbard, S S

2013-02-12

In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniquenessmore » and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability distribution functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSim) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes advantage of the spatial-temporal correlation of the state variables. We first apply the inversion framework to a static synthetic example and then to a time-lapse GPR tomographic dataset collected during a dynamic experiment conducted at the Hanford Site in Richland, WA. We demonstrate that the MRE-Bayesian inversion enables us to merge various data types, quantify uncertainty, evaluate nonlinear models, and produce more detailed and better resolved estimates than straight-ray based inversion; therefore, it has the potential to improve estimates of inter-wellbore dielectric permittivity and soil moisture content and to monitor their temporal dynamics more accurately.« less

Entropy-Bayesian Inversion of Time-Lapse Tomographic GPR data for Monitoring Dielectric Permittivity and Soil Moisture Variations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hou, Zhangshuan; Terry, Neil C.; Hubbard, Susan S.

2013-02-22

In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniquenessmore » and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability density functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSIM) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes advantage of the spatial-temporal correlation of the state variables. We first apply the inversion framework to a static synthetic example and then to a time-lapse GPR tomographic dataset collected during a dynamic experiment conducted at the Hanford Site in Richland, WA. We demonstrate that the MRE-Bayesian inversion enables us to merge various data types, quantify uncertainty, evaluate nonlinear models, and produce more detailed and better resolved estimates than straight-ray based inversion; therefore, it has the potential to improve estimates of inter-wellbore dielectric permittivity and soil moisture content and to monitor their temporal dynamics more accurately.« less

Advances in Applications of Hierarchical Bayesian Methods with Hydrological Models

NASA Astrophysics Data System (ADS)

Alexander, R. B.; Schwarz, G. E.; Boyer, E. W.

2017-12-01

Mechanistic and empirical watershed models are increasingly used to inform water resource decisions. Growing access to historical stream measurements and data from in-situ sensor technologies has increased the need for improved techniques for coupling models with hydrological measurements. Techniques that account for the intrinsic uncertainties of both models and measurements are especially needed. Hierarchical Bayesian methods provide an efficient modeling tool for quantifying model and prediction uncertainties, including those associated with measurements. Hierarchical methods can also be used to explore spatial and temporal variations in model parameters and uncertainties that are informed by hydrological measurements. We used hierarchical Bayesian methods to develop a hybrid (statistical-mechanistic) SPARROW (SPAtially Referenced Regression On Watershed attributes) model of long-term mean annual streamflow across diverse environmental and climatic drainages in 18 U.S. hydrological regions. Our application illustrates the use of a new generation of Bayesian methods that offer more advanced computational efficiencies than the prior generation. Evaluations of the effects of hierarchical (regional) variations in model coefficients and uncertainties on model accuracy indicates improved prediction accuracies (median of 10-50%) but primarily in humid eastern regions, where model uncertainties are one-third of those in arid western regions. Generally moderate regional variability is observed for most hierarchical coefficients. Accounting for measurement and structural uncertainties, using hierarchical state-space techniques, revealed the effects of spatially-heterogeneous, latent hydrological processes in the "localized" drainages between calibration sites; this improved model precision, with only minor changes in regional coefficients. Our study can inform advances in the use of hierarchical methods with hydrological models to improve their integration with stream measurements.

Modeling Soot Oxidation and Gasification with Bayesian Statistics

DOE PAGES

Josephson, Alexander J.; Gaffin, Neal D.; Smith, Sean T.; ...

2017-08-22

This paper presents a statistical method for model calibration using data collected from literature. The method is used to calibrate parameters for global models of soot consumption in combustion systems. This consumption is broken into two different submodels: first for oxidation where soot particles are attacked by certain oxidizing agents; second for gasification where soot particles are attacked by H 2O or CO 2 molecules. Rate data were collected from 19 studies in the literature and evaluated using Bayesian statistics to calibrate the model parameters. Bayesian statistics are valued in their ability to quantify uncertainty in modeling. The calibrated consumptionmore » model with quantified uncertainty is presented here along with a discussion of associated implications. The oxidation results are found to be consistent with previous studies. Significant variation is found in the CO 2 gasification rates.« less

Modeling Soot Oxidation and Gasification with Bayesian Statistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Josephson, Alexander J.; Gaffin, Neal D.; Smith, Sean T.

This paper presents a statistical method for model calibration using data collected from literature. The method is used to calibrate parameters for global models of soot consumption in combustion systems. This consumption is broken into two different submodels: first for oxidation where soot particles are attacked by certain oxidizing agents; second for gasification where soot particles are attacked by H 2O or CO 2 molecules. Rate data were collected from 19 studies in the literature and evaluated using Bayesian statistics to calibrate the model parameters. Bayesian statistics are valued in their ability to quantify uncertainty in modeling. The calibrated consumptionmore » model with quantified uncertainty is presented here along with a discussion of associated implications. The oxidation results are found to be consistent with previous studies. Significant variation is found in the CO 2 gasification rates.« less

Evaluating scaling models in biology using hierarchical Bayesian approaches

PubMed Central

Price, Charles A; Ogle, Kiona; White, Ethan P; Weitz, Joshua S

2009-01-01

Theoretical models for allometric relationships between organismal form and function are typically tested by comparing a single predicted relationship with empirical data. Several prominent models, however, predict more than one allometric relationship, and comparisons among alternative models have not taken this into account. Here we evaluate several different scaling models of plant morphology within a hierarchical Bayesian framework that simultaneously fits multiple scaling relationships to three large allometric datasets. The scaling models include: inflexible universal models derived from biophysical assumptions (e.g. elastic similarity or fractal networks), a flexible variation of a fractal network model, and a highly flexible model constrained only by basic algebraic relationships. We demonstrate that variation in intraspecific allometric scaling exponents is inconsistent with the universal models, and that more flexible approaches that allow for biological variability at the species level outperform universal models, even when accounting for relative increases in model complexity. PMID:19453621

Prior elicitation and Bayesian analysis of the Steroids for Corneal Ulcers Trial.

PubMed

See, Craig W; Srinivasan, Muthiah; Saravanan, Somu; Oldenburg, Catherine E; Esterberg, Elizabeth J; Ray, Kathryn J; Glaser, Tanya S; Tu, Elmer Y; Zegans, Michael E; McLeod, Stephen D; Acharya, Nisha R; Lietman, Thomas M

2012-12-01

To elicit expert opinion on the use of adjunctive corticosteroid therapy in bacterial corneal ulcers. To perform a Bayesian analysis of the Steroids for Corneal Ulcers Trial (SCUT), using expert opinion as a prior probability. The SCUT was a placebo-controlled trial assessing visual outcomes in patients receiving topical corticosteroids or placebo as adjunctive therapy for bacterial keratitis. Questionnaires were conducted at scientific meetings in India and North America to gauge expert consensus on the perceived benefit of corticosteroids as adjunct treatment. Bayesian analysis, using the questionnaire data as a prior probability and the primary outcome of SCUT as a likelihood, was performed. For comparison, an additional Bayesian analysis was performed using the results of the SCUT pilot study as a prior distribution. Indian respondents believed there to be a 1.21 Snellen line improvement, and North American respondents believed there to be a 1.24 line improvement with corticosteroid therapy. The SCUT primary outcome found a non-significant 0.09 Snellen line benefit with corticosteroid treatment. The results of the Bayesian analysis estimated a slightly greater benefit than did the SCUT primary analysis (0.19 lines verses 0.09 lines). Indian and North American experts had similar expectations on the effectiveness of corticosteroids in bacterial corneal ulcers; that corticosteroids would markedly improve visual outcomes. Bayesian analysis produced results very similar to those produced by the SCUT primary analysis. The similarity in result is likely due to the large sample size of SCUT and helps validate the results of SCUT.

Bayesian network modeling applied to coastal geomorphology: lessons learned from a decade of experimentation and application

NASA Astrophysics Data System (ADS)

Plant, N. G.; Thieler, E. R.; Gutierrez, B.; Lentz, E. E.; Zeigler, S. L.; Van Dongeren, A.; Fienen, M. N.

2016-12-01

We evaluate the strengths and weaknesses of Bayesian networks that have been used to address scientific and decision-support questions related to coastal geomorphology. We will provide an overview of coastal geomorphology research that has used Bayesian networks and describe what this approach can do and when it works (or fails to work). Over the past decade, Bayesian networks have been formulated to analyze the multi-variate structure and evolution of coastal morphology and associated human and ecological impacts. The approach relates observable system variables to each other by estimating discrete correlations. The resulting Bayesian-networks make predictions that propagate errors, conduct inference via Bayes rule, or both. In scientific applications, the model results are useful for hypothesis testing, using confidence estimates to gage the strength of tests while applications to coastal resource management are aimed at decision-support, where the probabilities of desired ecosystems outcomes are evaluated. The range of Bayesian-network applications to coastal morphology includes emulation of high-resolution wave transformation models to make oceanographic predictions, morphologic response to storms and/or sea-level rise, groundwater response to sea-level rise and morphologic variability, habitat suitability for endangered species, and assessment of monetary or human-life risk associated with storms. All of these examples are based on vast observational data sets, numerical model output, or both. We will discuss the progression of our experiments, which has included testing whether the Bayesian-network approach can be implemented and is appropriate for addressing basic and applied scientific problems and evaluating the hindcast and forecast skill of these implementations. We will present and discuss calibration/validation tests that are used to assess the robustness of Bayesian-network models and we will compare these results to tests of other models. This will demonstrate how Bayesian networks are used to extract new insights about coastal morphologic behavior, assess impacts to societal and ecological systems, and communicate probabilistic predictions to decision makers.

Landscape genetics of Schistocephalus solidus parasites in threespine stickleback (Gasterosteus aculeatus) from Alaska.

PubMed

Sprehn, C Grace; Blum, Michael J; Quinn, Thomas P; Heins, David C

2015-01-01

The nature of gene flow in parasites with complex life cycles is poorly understood, particularly when intermediate and definitive hosts have contrasting movement potential. We examined whether the fine-scale population genetic structure of the diphyllobothriidean cestode Schistocephalus solidus reflects the habits of intermediate threespine stickleback hosts or those of its definitive hosts, semi-aquatic piscivorous birds, to better understand complex host-parasite interactions. Seventeen lakes in the Cook Inlet region of south-central Alaska were sampled, including ten in the Matanuska-Susitna Valley, five on the Kenai Peninsula, and two in the Bristol Bay drainage. We analyzed sequence variation across a 759 bp region of the mitochondrial DNA (mtDNA) cytochrome oxidase I region for 1,026 S. solidus individuals sampled from 2009-2012. We also analyzed allelic variation at 8 microsatellite loci for 1,243 individuals. Analysis of mtDNA haplotype and microsatellite genotype variation recovered evidence of significant population genetic structure within S. solidus. Host, location, and year were factors in structuring observed genetic variation. Pairwise measures revealed significant differentiation among lakes, including a pattern of isolation-by-distance. Bayesian analysis identified three distinct genotypic clusters in the study region, little admixture within hosts and lakes, and a shift in genotype frequencies over time. Evidence of fine-scale population structure in S. solidus indicates that movement of its vagile, definitive avian hosts has less influence on gene flow than expected based solely on movement potential. Observed patterns of genetic variation may reflect genetic drift, behaviors of definitive hosts that constrain dispersal, life history of intermediate hosts, and adaptive specificity of S. solidus to intermediate host genotype.

Sparse Bayesian learning for DOA estimation with mutual coupling.

PubMed

Dai, Jisheng; Hu, Nan; Xu, Weichao; Chang, Chunqi

2015-10-16

Sparse Bayesian learning (SBL) has given renewed interest to the problem of direction-of-arrival (DOA) estimation. It is generally assumed that the measurement matrix in SBL is precisely known. Unfortunately, this assumption may be invalid in practice due to the imperfect manifold caused by unknown or misspecified mutual coupling. This paper describes a modified SBL method for joint estimation of DOAs and mutual coupling coefficients with uniform linear arrays (ULAs). Unlike the existing method that only uses stationary priors, our new approach utilizes a hierarchical form of the Student t prior to enforce the sparsity of the unknown signal more heavily. We also provide a distinct Bayesian inference for the expectation-maximization (EM) algorithm, which can update the mutual coupling coefficients more efficiently. Another difference is that our method uses an additional singular value decomposition (SVD) to reduce the computational complexity of the signal reconstruction process and the sensitivity to the measurement noise.

Bayesian analysis of energy and count rate data for detection of low count rate radioactive sources

DOE Office of Scientific and Technical Information (OSTI.GOV)

Klumpp, John

We propose a radiation detection system which generates its own discrete sampling distribution based on past measurements of background. The advantage to this approach is that it can take into account variations in background with respect to time, location, energy spectra, detector-specific characteristics (i.e. different efficiencies at different count rates and energies), etc. This would therefore be a 'machine learning' approach, in which the algorithm updates and improves its characterization of background over time. The system would have a 'learning mode,' in which it measures and analyzes background count rates, and a 'detection mode,' in which it compares measurements frommore » an unknown source against its unique background distribution. By characterizing and accounting for variations in the background, general purpose radiation detectors can be improved with little or no increase in cost. The statistical and computational techniques to perform this kind of analysis have already been developed. The necessary signal analysis can be accomplished using existing Bayesian algorithms which account for multiple channels, multiple detectors, and multiple time intervals. Furthermore, Bayesian machine-learning techniques have already been developed which, with trivial modifications, can generate appropriate decision thresholds based on the comparison of new measurements against a nonparametric sampling distribution. (authors)« less

Quantum Bayesian networks with application to games displaying Parrondo's paradox

NASA Astrophysics Data System (ADS)

Pejic, Michael

Bayesian networks and their accompanying graphical models are widely used for prediction and analysis across many disciplines. We will reformulate these in terms of linear maps. This reformulation will suggest a natural extension, which we will show is equivalent to standard textbook quantum mechanics. Therefore, this extension will be termed quantum. However, the term quantum should not be taken to imply this extension is necessarily only of utility in situations traditionally thought of as in the domain of quantum mechanics. In principle, it may be employed in any modelling situation, say forecasting the weather or the stock market---it is up to experiment to determine if this extension is useful in practice. Even restricting to the domain of quantum mechanics, with this new formulation the advantages of Bayesian networks can be maintained for models incorporating quantum and mixed classical-quantum behavior. The use of these will be illustrated by various basic examples. Parrondo's paradox refers to the situation where two, multi-round games with a fixed winning criteria, both with probability greater than one-half for one player to win, are combined. Using a possibly biased coin to determine the rule to employ for each round, paradoxically, the previously losing player now wins the combined game with probabilitygreater than one-half. Using the extended Bayesian networks, we will formulate and analyze classical observed, classical hidden, and quantum versions of a game that displays this paradox, finding bounds for the discrepancy from naive expectations for the occurrence of the paradox. A quantum paradox inspired by Parrondo's paradox will also be analyzed. We will prove a bound for the discrepancy from naive expectations for this paradox as well. Games involving quantum walks that achieve this bound will be presented.

Bayesian neural adjustment of inhibitory control predicts emergence of problem stimulant use.

PubMed

Harlé, Katia M; Stewart, Jennifer L; Zhang, Shunan; Tapert, Susan F; Yu, Angela J; Paulus, Martin P

2015-11-01

Bayesian ideal observer models quantify individuals' context- and experience-dependent beliefs and expectations about their environment, which provides a powerful approach (i) to link basic behavioural mechanisms to neural processing; and (ii) to generate clinical predictors for patient populations. Here, we focus on (ii) and determine whether individual differences in the neural representation of the need to stop in an inhibitory task can predict the development of problem use (i.e. abuse or dependence) in individuals experimenting with stimulants. One hundred and fifty-seven non-dependent occasional stimulant users, aged 18-24, completed a stop-signal task while undergoing functional magnetic resonance imaging. These individuals were prospectively followed for 3 years and evaluated for stimulant use and abuse/dependence symptoms. At follow-up, 38 occasional stimulant users met criteria for a stimulant use disorder (problem stimulant users), while 50 had discontinued use (desisted stimulant users). We found that those individuals who showed greater neural responses associated with Bayesian prediction errors, i.e. the difference between actual and expected need to stop on a given trial, in right medial prefrontal cortex/anterior cingulate cortex, caudate, anterior insula, and thalamus were more likely to exhibit problem use 3 years later. Importantly, these computationally based neural predictors outperformed clinical measures and non-model based neural variables in predicting clinical status. In conclusion, young adults who show exaggerated brain processing underlying whether to 'stop' or to 'go' are more likely to develop stimulant abuse. Thus, Bayesian cognitive models provide both a computational explanation and potential predictive biomarkers of belief processing deficits in individuals at risk for stimulant addiction. © The Author (2015). Published by Oxford University Press on behalf of the Guarantors of Brain. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

True versus Apparent Malaria Infection Prevalence: The Contribution of a Bayesian Approach

PubMed Central

Claes, Filip; Van Hong, Nguyen; Torres, Kathy; Mao, Sokny; Van den Eede, Peter; Thi Thinh, Ta; Gamboa, Dioni; Sochantha, Tho; Thang, Ngo Duc; Coosemans, Marc; Büscher, Philippe; D'Alessandro, Umberto; Berkvens, Dirk; Erhart, Annette

2011-01-01

Aims To present a new approach for estimating the “true prevalence” of malaria and apply it to datasets from Peru, Vietnam, and Cambodia. Methods Bayesian models were developed for estimating both the malaria prevalence using different diagnostic tests (microscopy, PCR & ELISA), without the need of a gold standard, and the tests' characteristics. Several sources of information, i.e. data, expert opinions and other sources of knowledge can be integrated into the model. This approach resulting in an optimal and harmonized estimate of malaria infection prevalence, with no conflict between the different sources of information, was tested on data from Peru, Vietnam and Cambodia. Results Malaria sero-prevalence was relatively low in all sites, with ELISA showing the highest estimates. The sensitivity of microscopy and ELISA were statistically lower in Vietnam than in the other sites. Similarly, the specificities of microscopy, ELISA and PCR were significantly lower in Vietnam than in the other sites. In Vietnam and Peru, microscopy was closer to the “true” estimate than the other 2 tests while as expected ELISA, with its lower specificity, usually overestimated the prevalence. Conclusions Bayesian methods are useful for analyzing prevalence results when no gold standard diagnostic test is available. Though some results are expected, e.g. PCR more sensitive than microscopy, a standardized and context-independent quantification of the diagnostic tests' characteristics (sensitivity and specificity) and the underlying malaria prevalence may be useful for comparing different sites. Indeed, the use of a single diagnostic technique could strongly bias the prevalence estimation. This limitation can be circumvented by using a Bayesian framework taking into account the imperfect characteristics of the currently available diagnostic tests. As discussed in the paper, this approach may further support global malaria burden estimation initiatives. PMID:21364745

Joint inversion for transponder localization and sound-speed profile temporal variation in high-precision acoustic surveys.

PubMed

Li, Zhao; Dosso, Stan E; Sun, Dajun

2016-07-01

This letter develops a Bayesian inversion for localizing underwater acoustic transponders using a surface ship which compensates for sound-speed profile (SSP) temporal variation during the survey. The method is based on dividing observed acoustic travel-time data into time segments and including depth-independent SSP variations for each segment as additional unknown parameters to approximate the SSP temporal variation. SSP variations are estimated jointly with transponder locations, rather than calculated separately as in existing two-step inversions. Simulation and sea-trial results show this localization/SSP joint inversion performs better than two-step inversion in terms of localization accuracy, agreement with measured SSP variations, and computational efficiency.

Probability, statistics, and computational science.

PubMed

Beerenwinkel, Niko; Siebourg, Juliane

2012-01-01

In this chapter, we review basic concepts from probability theory and computational statistics that are fundamental to evolutionary genomics. We provide a very basic introduction to statistical modeling and discuss general principles, including maximum likelihood and Bayesian inference. Markov chains, hidden Markov models, and Bayesian network models are introduced in more detail as they occur frequently and in many variations in genomics applications. In particular, we discuss efficient inference algorithms and methods for learning these models from partially observed data. Several simple examples are given throughout the text, some of which point to models that are discussed in more detail in subsequent chapters.

The effect of regional politics on regional life expectancy in Italy (1980-2010).

PubMed

Jonker, Marcel F; D'Ippolito, Edoardo; Eikemo, Terje A; Congdon, Peter D; Nante, Nicola; Mackenbach, Johan P; Kamphuis, Carlijn B M

2017-03-01

The evidence on the association between politics and health is scarce considering the importance of this topic for population health. Studies that investigated the effect of different political regimes on health outcomes show inconsistent results. Bayesian time-series cross-section analyses are used to examine the overall impact of regional politics on variations in Italian regional life expectancy (LE) at birth during the period 1980-2010. Our analyses control for trends in and unobserved determinants of regional LE, correct for temporal as well as spatial autocorrelation, and employ a flexible specification for the timing of the political effects. In the period from 1980 to 1995, we find no evidence that the communist, left-oriented coalitions and Christian Democratic, centre-oriented coalitions have had an effect on regional LE. In the period from 1995 onwards, after a major reconfiguration of Italy's political regimes and a major healthcare reform, we again find no evidence that the Centre-Left and Centre-Right coalitions have had a significant impact on regional LE. The presented results provide no support for the notion that different regional political regimes in Italy have had a differential effect on regional LE, even though Italian regions have had considerable and increasing autonomy over healthcare and health-related policies and expenditures.

Quantity Competition in a Differentiated Duopoly

NASA Astrophysics Data System (ADS)

Ferreira, Fernanda A.; Ferreira, Flávio; Ferreira, Miguel; Pinto, Alberto A.

In this paper, we consider a Stackelberg duopoly competition with differentiated goods, linear and symmetric demand and with unknown costs. In our model, the two firms play a non-cooperative game with two stages: in a first stage, firm F 1 chooses the quantity, q 1, that is going to produce; in the second stage, firm F 2 observes the quantity q 1 produced by firm F 1 and chooses its own quantity q 2. Firms choose their output levels in order to maximise their profits. We suppose that each firm has two different technologies, and uses one of them following a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We show that there is exactly one perfect Bayesian equilibrium for this game. We analyse the variations of the expected profits with the parameters of the model, namely with the parameters of the probability distributions, and with the parameters of the demand and differentiation.

The PoGO+ view on Crab off-pulse hard X-ray polarization

NASA Astrophysics Data System (ADS)

Chauvin, M.; Florén, H.-G.; Friis, M.; Jackson, M.; Kamae, T.; Kataoka, J.; Kawano, T.; Kiss, M.; Mikhalev, V.; Mizuno, T.; Tajima, H.; Takahashi, H.; Uchida, N.; Pearce, M.

2018-06-01

The linear polarization fraction (PF) and angle of the hard X-ray emission from the Crab provide unique insight into high-energy radiation mechanisms, complementing the usual imaging, timing, and spectroscopic approaches. Results have recently been presented by two missions operating in partially overlapping energy bands, PoGO+ (18-160 keV) and AstroSat CZTI (100-380 keV). We previously reported PoGO+ results on the polarization parameters integrated across the light curve and for the entire nebula-dominated off-pulse region. We now introduce finer phase binning, in light of the AstroSat CZTI claim that the PF varies across the off-pulse region. Since both missions are operating in a regime where errors on the reconstructed polarization parameters are non-Gaussian, we adopt a Bayesian approach to compare results from each mission. We find no statistically significant variation in off-pulse polarization parameters, neither when considering the mission data separately nor when they are combined. This supports expectations from standard high-energy emission models.

Bayesian Probabilistic Projections of Life Expectancy for All Countries

PubMed Central

Raftery, Adrian E.; Chunn, Jennifer L.; Gerland, Patrick; Ševčíková, Hana

2014-01-01

We propose a Bayesian hierarchical model for producing probabilistic forecasts of male period life expectancy at birth for all the countries of the world from the present to 2100. Such forecasts would be an input to the production of probabilistic population projections for all countries, which is currently being considered by the United Nations. To evaluate the method, we did an out-of-sample cross-validation experiment, fitting the model to the data from 1950–1995, and using the estimated model to forecast for the subsequent ten years. The ten-year predictions had a mean absolute error of about 1 year, about 40% less than the current UN methodology. The probabilistic forecasts were calibrated, in the sense that (for example) the 80% prediction intervals contained the truth about 80% of the time. We illustrate our method with results from Madagascar (a typical country with steadily improving life expectancy), Latvia (a country that has had a mortality crisis), and Japan (a leading country). We also show aggregated results for South Asia, a region with eight countries. Free publicly available R software packages called bayesLife and bayesDem are available to implement the method. PMID:23494599

An accessible method for implementing hierarchical models with spatio-temporal abundance data

USGS Publications Warehouse

Ross, Beth E.; Hooten, Melvin B.; Koons, David N.

2012-01-01

A common goal in ecology and wildlife management is to determine the causes of variation in population dynamics over long periods of time and across large spatial scales. Many assumptions must nevertheless be overcome to make appropriate inference about spatio-temporal variation in population dynamics, such as autocorrelation among data points, excess zeros, and observation error in count data. To address these issues, many scientists and statisticians have recommended the use of Bayesian hierarchical models. Unfortunately, hierarchical statistical models remain somewhat difficult to use because of the necessary quantitative background needed to implement them, or because of the computational demands of using Markov Chain Monte Carlo algorithms to estimate parameters. Fortunately, new tools have recently been developed that make it more feasible for wildlife biologists to fit sophisticated hierarchical Bayesian models (i.e., Integrated Nested Laplace Approximation, ‘INLA’). We present a case study using two important game species in North America, the lesser and greater scaup, to demonstrate how INLA can be used to estimate the parameters in a hierarchical model that decouples observation error from process variation, and accounts for unknown sources of excess zeros as well as spatial and temporal dependence in the data. Ultimately, our goal was to make unbiased inference about spatial variation in population trends over time.

Genetic diversity and structure of Lolium perenne ssp. multiflorum in California vineyards and orchards indicate potential for spread of herbicide resistance via gene flow.

PubMed

Karn, Elizabeth; Jasieniuk, Marie

2017-07-01

Management of agroecosystems with herbicides imposes strong selection pressures on weedy plants leading to the evolution of resistance against those herbicides. Resistance to glyphosate in populations of Lolium perenne L. ssp. multiflorum is increasingly common in California, USA, causing economic losses and the loss of effective management tools. To gain insights into the recent evolution of glyphosate resistance in L. perenne in perennial cropping systems of northwest California and to inform management, we investigated the frequency of glyphosate resistance and the genetic diversity and structure of 14 populations. The sampled populations contained frequencies of resistant plants ranging from 10% to 89%. Analyses of neutral genetic variation using microsatellite markers indicated very high genetic diversity within all populations regardless of resistance frequency. Genetic variation was distributed predominantly among individuals within populations rather than among populations or sampled counties, as would be expected for a wide-ranging outcrossing weed species. Bayesian clustering analysis provided evidence of population structuring with extensive admixture between two genetic clusters or gene pools. High genetic diversity and admixture, and low differentiation between populations, strongly suggest the potential for spread of resistance through gene flow and the need for management that limits seed and pollen dispersal in L. perenne .

Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Peng, E-mail: peng@ices.utexas.edu; Schwab, Christoph, E-mail: christoph.schwab@sam.math.ethz.ch

2016-07-01

We extend the reduced basis (RB) accelerated Bayesian inversion methods for affine-parametric, linear operator equations which are considered in [16,17] to non-affine, nonlinear parametric operator equations. We generalize the analysis of sparsity of parametric forward solution maps in [20] and of Bayesian inversion in [48,49] to the fully discrete setting, including Petrov–Galerkin high-fidelity (“HiFi”) discretization of the forward maps. We develop adaptive, stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold. The nonaffinity and nonlinearity with respect to (w.r.t.) the distributed, uncertain parameters and the unknown solution is collocated; specifically, by themore » so-called Empirical Interpolation Method (EIM). For the corresponding Bayesian inversion problems, computational efficiency is enhanced in two ways: first, expectations w.r.t. the posterior are computed by adaptive quadratures with dimension-independent convergence rates proposed in [49]; the present work generalizes [49] to account for the impact of the PG discretization in the forward maps on the convergence rates of the Quantities of Interest (QoI for short). Second, we propose to perform the Bayesian estimation only w.r.t. a parsimonious, RB approximation of the posterior density. Based on the approximation results in [49], the infinite-dimensional parametric, deterministic forward map and operator admit N-term RB and EIM approximations which converge at rates which depend only on the sparsity of the parametric forward map. In several numerical experiments, the proposed algorithms exhibit dimension-independent convergence rates which equal, at least, the currently known rate estimates for N-term approximation. We propose to accelerate Bayesian estimation by first offline construction of reduced basis surrogates of the Bayesian posterior density. The parsimonious surrogates can then be employed for online data assimilation and for Bayesian estimation. They also open a perspective for optimal experimental design.« less

The decisive future of inflation

NASA Astrophysics Data System (ADS)

Hardwick, Robert J.; Vennin, Vincent; Wands, David

2018-05-01

How much more will we learn about single-field inflationary models in the future? We address this question in the context of Bayesian design and information theory. We develop a novel method to compute the expected utility of deciding between models and apply it to a set of futuristic measurements. This necessarily requires one to evaluate the Bayesian evidence many thousands of times over, which is numerically challenging. We show how this can be done using a number of simplifying assumptions and discuss their validity. We also modify the form of the expected utility, as previously introduced in the literature in different contexts, in order to partition each possible future into either the rejection of models at the level of the maximum likelihood or the decision between models using Bayesian model comparison. We then quantify the ability of future experiments to constrain the reheating temperature and the scalar running. Our approach allows us to discuss possible strategies for maximising information from future cosmological surveys. In particular, our conclusions suggest that, in the context of inflationary model selection, a decrease in the measurement uncertainty of the scalar spectral index would be more decisive than a decrease in the uncertainty in the tensor-to-scalar ratio. We have incorporated our approach into a publicly available python class, foxi,1 that can be readily applied to any survey optimisation problem.

Application of Bayesian Networks to hindcast barrier island morphodynamics

USGS Publications Warehouse

Wilson, Kathleen E.; Adams, Peter N.; Hapke, Cheryl J.; Lentz, Erika E.; Brenner, Owen T.

2015-01-01

We refine a preliminary Bayesian Network by 1) increasing model experience through additional observations, 2) including anthropogenic modification history, and 3) replacing parameterized wave impact values with maximum run-up elevation. Further, we develop and train a pair of generalized models with an additional dataset encompassing a different storm event, which expands the observations beyond our hindcast objective. We compare the skill of the generalized models against the Nor'Ida specific model formulation, balancing the reduced skill with an expectation of increased transferability. Results of Nor'Ida hindcasts ranged in skill from 0.37 to 0.51 and accuracy of 65.0 to 81.9%.

Nonparametric Bayesian Segmentation of a Multivariate Inhomogeneous Space-Time Poisson Process.

PubMed

Ding, Mingtao; He, Lihan; Dunson, David; Carin, Lawrence

2012-12-01

A nonparametric Bayesian model is proposed for segmenting time-evolving multivariate spatial point process data. An inhomogeneous Poisson process is assumed, with a logistic stick-breaking process (LSBP) used to encourage piecewise-constant spatial Poisson intensities. The LSBP explicitly favors spatially contiguous segments, and infers the number of segments based on the observed data. The temporal dynamics of the segmentation and of the Poisson intensities are modeled with exponential correlation in time, implemented in the form of a first-order autoregressive model for uniformly sampled discrete data, and via a Gaussian process with an exponential kernel for general temporal sampling. We consider and compare two different inference techniques: a Markov chain Monte Carlo sampler, which has relatively high computational complexity; and an approximate and efficient variational Bayesian analysis. The model is demonstrated with a simulated example and a real example of space-time crime events in Cincinnati, Ohio, USA.

Bayesian spatio-temporal modeling of particulate matter concentrations in Peninsular Malaysia

NASA Astrophysics Data System (ADS)

Manga, Edna; Awang, Norhashidah

2016-06-01

This article presents an application of a Bayesian spatio-temporal Gaussian process (GP) model on particulate matter concentrations from Peninsular Malaysia. We analyze daily PM10 concentration levels from 35 monitoring sites in June and July 2011. The spatiotemporal model set in a Bayesian hierarchical framework allows for inclusion of informative covariates, meteorological variables and spatiotemporal interactions. Posterior density estimates of the model parameters are obtained by Markov chain Monte Carlo methods. Preliminary data analysis indicate information on PM10 levels at sites classified as industrial locations could explain part of the space time variations. We include the site-type indicator in our modeling efforts. Results of the parameter estimates for the fitted GP model show significant spatio-temporal structure and positive effect of the location-type explanatory variable. We also compute some validation criteria for the out of sample sites that show the adequacy of the model for predicting PM10 at unmonitored sites.

Bayesian Computation for Log-Gaussian Cox Processes: A Comparative Analysis of Methods

PubMed Central

Teng, Ming; Nathoo, Farouk S.; Johnson, Timothy D.

2017-01-01

The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point pattern data. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Various methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulation studies as well as through two applications, the first examining ecological data and the second involving neuroimaging data. PMID:29200537

To P or Not to P: Backing Bayesian Statistics.

PubMed

Buchinsky, Farrel J; Chadha, Neil K

2017-12-01

In biomedical research, it is imperative to differentiate chance variation from truth before we generalize what we see in a sample of subjects to the wider population. For decades, we have relied on null hypothesis significance testing, where we calculate P values for our data to decide whether to reject a null hypothesis. This methodology is subject to substantial misinterpretation and errant conclusions. Instead of working backward by calculating the probability of our data if the null hypothesis were true, Bayesian statistics allow us instead to work forward, calculating the probability of our hypothesis given the available data. This methodology gives us a mathematical means of incorporating our "prior probabilities" from previous study data (if any) to produce new "posterior probabilities." Bayesian statistics tell us how confidently we should believe what we believe. It is time to embrace and encourage their use in our otolaryngology research.

Modeling the Association of Space, Time, and Host Species with Variation of the HA, NA, and NS Genes of H5N1 Highly Pathogenic Avian Influenza Viruses Isolated from Birds in Romania in 2005–2007

PubMed Central

Alkhamis, Mohammad; Perez, Andres; Batey, Nicole; Howard, Wendy; Baillie, Greg; Watson, Simon; Franz, Stephanie; Focosi-Snyman, Raffaella; Onita, Iuliana; Cioranu, Raluca; Turcitu, Mihai; Kellam, Paul; Brown, Ian H.; Breed, Andrew C.

2014-01-01

SUMMARY Molecular characterization studies of a diverse collection of avian influenza viruses (AIVs) have demonstrated that AIVs’ greatest genetic variability lies in the HA, NA, and NS genes. The objective here was to quantify the association between geographical locations, periods of time, and host species and pairwise nucleotide variation in the HA, NA, and NS genes of 70 isolates of H5N1 highly pathogenic avian influenza virus (HPAIV) collected from October 2005 to December 2007 from birds in Romania. A mixed-binomial Bayesian regression model was used to quantify the probability of nucleotide variation between isolates and its association with space, time, and host species. As expected for the three target genes, a higher probability of nucleotide differences (odds ratios [ORs] > 1) was found between viruses sampled from places at greater geographical distances from each other, viruses sampled over greater periods of time, and viruses derived from different species. The modeling approach in the present study maybe useful in further understanding the molecular epidemiology of H5N1 HPAI virus in bird populations. The methodology presented here will be useful in predicting the most likely genetic distance for any of the three gene segments of viruses that have not yet been isolated or sequenced based on space, time, and host species during the course of an epidemic. PMID:24283126

Modeling the association of space, time, and host species with variation of the HA, NA, and NS genes of H5N1 highly pathogenic avian influenza viruses isolated from birds in Romania in 2005-2007.

PubMed

Alkhamis, Mohammad; Perez, Andres; Batey, Nicole; Howard, Wendy; Baillie, Greg; Watson, Simon; Franz, Stephanie; Focosi-Snyman, Raffaella; Onita, Iuliana; Cioranu, Raluca; Turcitu, Mihai; Kellam, Paul; Brown, Ian H; Breed, Andrew C

2013-09-01

Molecular characterization studies of a diverse collection of avian influenza viruses (AIVs) have demonstrated that AIVs' greatest genetic variability lies in the HA, NA, and NS genes. The objective here was to quantify the association between geographical locations, periods of time, and host species and pairwise nucleotide variation in the HA, NA, and NS genes of 70 isolates of H5N1 highly pathogenic avian influenza virus (HPAIV) collected from October 2005 to December 2007 from birds in Romania. A mixed-binomial Bayesian regression model was used to quantify the probability of nucleotide variation between isolates and its association with space, time, and host species. As expected for the three target genes, a higher probability of nucleotide differences (odds ratios [ORs] > 1) was found between viruses sampled from places at greater geographical distances from each other, viruses sampled over greater periods of time, and viruses derived from different species. The modeling approach in the present study maybe useful in further understanding the molecular epidemiology of H5N1 HPAI virus in bird populations. The methodology presented here will be useful in predicting the most likely genetic distance for any of the three gene segments of viruses that have not yet been isolated or sequenced based on space, time, and host species during the course of an epidemic.

From Wald to Savage: homo economicus becomes a Bayesian statistician.

PubMed

Giocoli, Nicola

2013-01-01

Bayesian rationality is the paradigm of rational behavior in neoclassical economics. An economic agent is deemed rational when she maximizes her subjective expected utility and consistently revises her beliefs according to Bayes's rule. The paper raises the question of how, when and why this characterization of rationality came to be endorsed by mainstream economists. Though no definitive answer is provided, it is argued that the question is of great historiographic importance. The story begins with Abraham Wald's behaviorist approach to statistics and culminates with Leonard J. Savage's elaboration of subjective expected utility theory in his 1954 classic The Foundations of Statistics. The latter's acknowledged fiasco to achieve a reinterpretation of traditional inference techniques along subjectivist and behaviorist lines raises the puzzle of how a failed project in statistics could turn into such a big success in economics. Possible answers call into play the emphasis on consistency requirements in neoclassical theory and the impact of the postwar transformation of U.S. business schools. © 2012 Wiley Periodicals, Inc.

When Absence of Evidence Is Evidence of Absence: Rational Inferences From Absent Data.

PubMed

Hsu, Anne S; Horng, Andy; Griffiths, Thomas L; Chater, Nick

2017-05-01

Identifying patterns in the world requires noticing not only unusual occurrences, but also unusual absences. We examined how people learn from absences, manipulating the extent to which an absence is expected. People can make two types of inferences from the absence of an event: either the event is possible but has not yet occurred, or the event never occurs. A rational analysis using Bayesian inference predicts that inferences from absent data should depend on how much the absence is expected to occur, with less probable absences being more salient. We tested this prediction in two experiments in which we elicited people's judgments about patterns in the data as a function of absence salience. We found that people were able to decide that absences either were mere coincidences or were indicative of a significant pattern in the data in a manner that was consistent with predictions of a simple Bayesian model. Copyright © 2016 Cognitive Science Society, Inc.

Spatial Distribution of the Coefficient of Variation and Bayesian Forecast for the Paleo-Earthquakes in Japan

NASA Astrophysics Data System (ADS)

Nomura, Shunichi; Ogata, Yosihiko

2016-04-01

We propose a Bayesian method of probability forecasting for recurrent earthquakes of inland active faults in Japan. Renewal processes with the Brownian Passage Time (BPT) distribution are applied for over a half of active faults in Japan by the Headquarters for Earthquake Research Promotion (HERP) of Japan. Long-term forecast with the BPT distribution needs two parameters; the mean and coefficient of variation (COV) for recurrence intervals. The HERP applies a common COV parameter for all of these faults because most of them have very few specified paleoseismic events, which is not enough to estimate reliable COV values for respective faults. However, different COV estimates are proposed for the same paleoseismic catalog by some related works. It can make critical difference in forecast to apply different COV estimates and so COV should be carefully selected for individual faults. Recurrence intervals on a fault are, on the average, determined by the long-term slip rate caused by the tectonic motion but fluctuated by nearby seismicities which influence surrounding stress field. The COVs of recurrence intervals depend on such stress perturbation and so have spatial trends due to the heterogeneity of tectonic motion and seismicity. Thus we introduce a spatial structure on its COV parameter by Bayesian modeling with a Gaussian process prior. The COVs on active faults are correlated and take similar values for closely located faults. It is found that the spatial trends in the estimated COV values coincide with the density of active faults in Japan. We also show Bayesian forecasts by the proposed model using Markov chain Monte Carlo method. Our forecasts are different from HERP's forecast especially on the active faults where HERP's forecasts are very high or low.

Variational Bayesian Learning for Wavelet Independent Component Analysis

NASA Astrophysics Data System (ADS)

Roussos, E.; Roberts, S.; Daubechies, I.

2005-11-01

In an exploratory approach to data analysis, it is often useful to consider the observations as generated from a set of latent generators or "sources" via a generally unknown mapping. For the noisy overcomplete case, where we have more sources than observations, the problem becomes extremely ill-posed. Solutions to such inverse problems can, in many cases, be achieved by incorporating prior knowledge about the problem, captured in the form of constraints. This setting is a natural candidate for the application of the Bayesian methodology, allowing us to incorporate "soft" constraints in a natural manner. The work described in this paper is mainly driven by problems in functional magnetic resonance imaging of the brain, for the neuro-scientific goal of extracting relevant "maps" from the data. This can be stated as a `blind' source separation problem. Recent experiments in the field of neuroscience show that these maps are sparse, in some appropriate sense. The separation problem can be solved by independent component analysis (ICA), viewed as a technique for seeking sparse components, assuming appropriate distributions for the sources. We derive a hybrid wavelet-ICA model, transforming the signals into a domain where the modeling assumption of sparsity of the coefficients with respect to a dictionary is natural. We follow a graphical modeling formalism, viewing ICA as a probabilistic generative model. We use hierarchical source and mixing models and apply Bayesian inference to the problem. This allows us to perform model selection in order to infer the complexity of the representation, as well as automatic denoising. Since exact inference and learning in such a model is intractable, we follow a variational Bayesian mean-field approach in the conjugate-exponential family of distributions, for efficient unsupervised learning in multi-dimensional settings. The performance of the proposed algorithm is demonstrated on some representative experiments.

Analyzing small data sets using Bayesian estimation: the case of posttraumatic stress symptoms following mechanical ventilation in burn survivors

PubMed Central

van de Schoot, Rens; Broere, Joris J.; Perryck, Koen H.; Zondervan-Zwijnenburg, Mariëlle; van Loey, Nancy E.

2015-01-01

Background The analysis of small data sets in longitudinal studies can lead to power issues and often suffers from biased parameter values. These issues can be solved by using Bayesian estimation in conjunction with informative prior distributions. By means of a simulation study and an empirical example concerning posttraumatic stress symptoms (PTSS) following mechanical ventilation in burn survivors, we demonstrate the advantages and potential pitfalls of using Bayesian estimation. Methods First, we show how to specify prior distributions and by means of a sensitivity analysis we demonstrate how to check the exact influence of the prior (mis-) specification. Thereafter, we show by means of a simulation the situations in which the Bayesian approach outperforms the default, maximum likelihood and approach. Finally, we re-analyze empirical data on burn survivors which provided preliminary evidence of an aversive influence of a period of mechanical ventilation on the course of PTSS following burns. Results Not suprisingly, maximum likelihood estimation showed insufficient coverage as well as power with very small samples. Only when Bayesian analysis, in conjunction with informative priors, was used power increased to acceptable levels. As expected, we showed that the smaller the sample size the more the results rely on the prior specification. Conclusion We show that two issues often encountered during analysis of small samples, power and biased parameters, can be solved by including prior information into Bayesian analysis. We argue that the use of informative priors should always be reported together with a sensitivity analysis. PMID:25765534

Analyzing small data sets using Bayesian estimation: the case of posttraumatic stress symptoms following mechanical ventilation in burn survivors.

PubMed

van de Schoot, Rens; Broere, Joris J; Perryck, Koen H; Zondervan-Zwijnenburg, Mariëlle; van Loey, Nancy E

2015-01-01

Background : The analysis of small data sets in longitudinal studies can lead to power issues and often suffers from biased parameter values. These issues can be solved by using Bayesian estimation in conjunction with informative prior distributions. By means of a simulation study and an empirical example concerning posttraumatic stress symptoms (PTSS) following mechanical ventilation in burn survivors, we demonstrate the advantages and potential pitfalls of using Bayesian estimation. Methods : First, we show how to specify prior distributions and by means of a sensitivity analysis we demonstrate how to check the exact influence of the prior (mis-) specification. Thereafter, we show by means of a simulation the situations in which the Bayesian approach outperforms the default, maximum likelihood and approach. Finally, we re-analyze empirical data on burn survivors which provided preliminary evidence of an aversive influence of a period of mechanical ventilation on the course of PTSS following burns. Results : Not suprisingly, maximum likelihood estimation showed insufficient coverage as well as power with very small samples. Only when Bayesian analysis, in conjunction with informative priors, was used power increased to acceptable levels. As expected, we showed that the smaller the sample size the more the results rely on the prior specification. Conclusion : We show that two issues often encountered during analysis of small samples, power and biased parameters, can be solved by including prior information into Bayesian analysis. We argue that the use of informative priors should always be reported together with a sensitivity analysis.

Prior Elicitation and Bayesian Analysis of the Steroids for Corneal Ulcers Trial

PubMed Central

See, Craig W.; Srinivasan, Muthiah; Saravanan, Somu; Oldenburg, Catherine E.; Esterberg, Elizabeth J.; Ray, Kathryn J.; Glaser, Tanya S.; Tu, Elmer Y.; Zegans, Michael E.; McLeod, Stephen D.; Acharya, Nisha R.; Lietman, Thomas M.

2013-01-01

Purpose To elicit expert opinion on the use of adjunctive corticosteroid therapy in bacterial corneal ulcers. To perform a Bayesian analysis of the Steroids for Corneal Ulcers Trial (SCUT), using expert opinion as a prior probability. Methods The SCUT was a placebo-controlled trial assessing visual outcomes in patients receiving topical corticosteroids or placebo as adjunctive therapy for bacterial keratitis. Questionnaires were conducted at scientific meetings in India and North America to gauge expert consensus on the perceived benefit of corticosteroids as adjunct treatment. Bayesian analysis, using the questionnaire data as a prior probability and the primary outcome of SCUT as a likelihood, was performed. For comparison, an additional Bayesian analysis was performed using the results of the SCUT pilot study as a prior distribution. Results Indian respondents believed there to be a 1.21 Snellen line improvement, and North American respondents believed there to be a 1.24 line improvement with corticosteroid therapy. The SCUT primary outcome found a non-significant 0.09 Snellen line benefit with corticosteroid treatment. The results of the Bayesian analysis estimated a slightly greater benefit than did the SCUT primary analysis (0.19 lines verses 0.09 lines). Conclusion Indian and North American experts had similar expectations on the effectiveness of corticosteroids in bacterial corneal ulcers; that corticosteroids would markedly improve visual outcomes. Bayesian analysis produced results very similar to those produced by the SCUT primary analysis. The similarity in result is likely due to the large sample size of SCUT and helps validate the results of SCUT. PMID:23171211

Application of bayesian networks to real-time flood risk estimation

NASA Astrophysics Data System (ADS)

Garrote, L.; Molina, M.; Blasco, G.

2003-04-01

This paper presents the application of a computational paradigm taken from the field of artificial intelligence - the bayesian network - to model the behaviour of hydrologic basins during floods. The final goal of this research is to develop representation techniques for hydrologic simulation models in order to define, develop and validate a mechanism, supported by a software environment, oriented to build decision models for the prediction and management of river floods in real time. The emphasis is placed on providing decision makers with tools to incorporate their knowledge of basin behaviour, usually formulated in terms of rainfall-runoff models, in the process of real-time decision making during floods. A rainfall-runoff model is only a step in the process of decision making. If a reliable rainfall forecast is available and the rainfall-runoff model is well calibrated, decisions can be based mainly on model results. However, in most practical situations, uncertainties in rainfall forecasts or model performance have to be incorporated in the decision process. The computation paradigm adopted for the simulation of hydrologic processes is the bayesian network. A bayesian network is a directed acyclic graph that represents causal influences between linked variables. Under this representation, uncertain qualitative variables are related through causal relations quantified with conditional probabilities. The solution algorithm allows the computation of the expected probability distribution of unknown variables conditioned to the observations. An approach to represent hydrologic processes by bayesian networks with temporal and spatial extensions is presented in this paper, together with a methodology for the development of bayesian models using results produced by deterministic hydrologic simulation models

Bayesian aggregation versus majority vote in the characterization of non-specific arm pain based on quantitative needle electromyography

PubMed Central

2010-01-01

Background Methods for the calculation and application of quantitative electromyographic (EMG) statistics for the characterization of EMG data detected from forearm muscles of individuals with and without pain associated with repetitive strain injury are presented. Methods A classification procedure using a multi-stage application of Bayesian inference is presented that characterizes a set of motor unit potentials acquired using needle electromyography. The utility of this technique in characterizing EMG data obtained from both normal individuals and those presenting with symptoms of "non-specific arm pain" is explored and validated. The efficacy of the Bayesian technique is compared with simple voting methods. Results The aggregate Bayesian classifier presented is found to perform with accuracy equivalent to that of majority voting on the test data, with an overall accuracy greater than 0.85. Theoretical foundations of the technique are discussed, and are related to the observations found. Conclusions Aggregation of motor unit potential conditional probability distributions estimated using quantitative electromyographic analysis, may be successfully used to perform electrodiagnostic characterization of "non-specific arm pain." It is expected that these techniques will also be able to be applied to other types of electrodiagnostic data. PMID:20156353

Bayesian Computation Emerges in Generic Cortical Microcircuits through Spike-Timing-Dependent Plasticity

PubMed Central

Nessler, Bernhard; Pfeiffer, Michael; Buesing, Lars; Maass, Wolfgang

2013-01-01

The principles by which networks of neurons compute, and how spike-timing dependent plasticity (STDP) of synaptic weights generates and maintains their computational function, are unknown. Preceding work has shown that soft winner-take-all (WTA) circuits, where pyramidal neurons inhibit each other via interneurons, are a common motif of cortical microcircuits. We show through theoretical analysis and computer simulations that Bayesian computation is induced in these network motifs through STDP in combination with activity-dependent changes in the excitability of neurons. The fundamental components of this emergent Bayesian computation are priors that result from adaptation of neuronal excitability and implicit generative models for hidden causes that are created in the synaptic weights through STDP. In fact, a surprising result is that STDP is able to approximate a powerful principle for fitting such implicit generative models to high-dimensional spike inputs: Expectation Maximization. Our results suggest that the experimentally observed spontaneous activity and trial-to-trial variability of cortical neurons are essential features of their information processing capability, since their functional role is to represent probability distributions rather than static neural codes. Furthermore it suggests networks of Bayesian computation modules as a new model for distributed information processing in the cortex. PMID:23633941

Quantum Inference on Bayesian Networks

NASA Astrophysics Data System (ADS)

Yoder, Theodore; Low, Guang Hao; Chuang, Isaac

2014-03-01

Because quantum physics is naturally probabilistic, it seems reasonable to expect physical systems to describe probabilities and their evolution in a natural fashion. Here, we use quantum computation to speedup sampling from a graphical probability model, the Bayesian network. A specialization of this sampling problem is approximate Bayesian inference, where the distribution on query variables is sampled given the values e of evidence variables. Inference is a key part of modern machine learning and artificial intelligence tasks, but is known to be NP-hard. Classically, a single unbiased sample is obtained from a Bayesian network on n variables with at most m parents per node in time (nmP(e) - 1 / 2) , depending critically on P(e) , the probability the evidence might occur in the first place. However, by implementing a quantum version of rejection sampling, we obtain a square-root speedup, taking (n2m P(e) -1/2) time per sample. The speedup is the result of amplitude amplification, which is proving to be broadly applicable in sampling and machine learning tasks. In particular, we provide an explicit and efficient circuit construction that implements the algorithm without the need for oracle access.

Valence-Dependent Belief Updating: Computational Validation

PubMed Central

Kuzmanovic, Bojana; Rigoux, Lionel

2017-01-01

People tend to update beliefs about their future outcomes in a valence-dependent way: they are likely to incorporate good news and to neglect bad news. However, belief formation is a complex process which depends not only on motivational factors such as the desire for favorable conclusions, but also on multiple cognitive variables such as prior beliefs, knowledge about personal vulnerabilities and resources, and the size of the probabilities and estimation errors. Thus, we applied computational modeling in order to test for valence-induced biases in updating while formally controlling for relevant cognitive factors. We compared biased and unbiased Bayesian models of belief updating, and specified alternative models based on reinforcement learning. The experiment consisted of 80 trials with 80 different adverse future life events. In each trial, participants estimated the base rate of one of these events and estimated their own risk of experiencing the event before and after being confronted with the actual base rate. Belief updates corresponded to the difference between the two self-risk estimates. Valence-dependent updating was assessed by comparing trials with good news (better-than-expected base rates) with trials with bad news (worse-than-expected base rates). After receiving bad relative to good news, participants' updates were smaller and deviated more strongly from rational Bayesian predictions, indicating a valence-induced bias. Model comparison revealed that the biased (i.e., optimistic) Bayesian model of belief updating better accounted for data than the unbiased (i.e., rational) Bayesian model, confirming that the valence of the new information influenced the amount of updating. Moreover, alternative computational modeling based on reinforcement learning demonstrated higher learning rates for good than for bad news, as well as a moderating role of personal knowledge. Finally, in this specific experimental context, the approach based on reinforcement learning was superior to the Bayesian approach. The computational validation of valence-dependent belief updating represents a novel support for a genuine optimism bias in human belief formation. Moreover, the precise control of relevant cognitive variables justifies the conclusion that the motivation to adopt the most favorable self-referential conclusions biases human judgments. PMID:28706499

Valence-Dependent Belief Updating: Computational Validation.

PubMed

Kuzmanovic, Bojana; Rigoux, Lionel

2017-01-01

People tend to update beliefs about their future outcomes in a valence-dependent way: they are likely to incorporate good news and to neglect bad news. However, belief formation is a complex process which depends not only on motivational factors such as the desire for favorable conclusions, but also on multiple cognitive variables such as prior beliefs, knowledge about personal vulnerabilities and resources, and the size of the probabilities and estimation errors. Thus, we applied computational modeling in order to test for valence-induced biases in updating while formally controlling for relevant cognitive factors. We compared biased and unbiased Bayesian models of belief updating, and specified alternative models based on reinforcement learning. The experiment consisted of 80 trials with 80 different adverse future life events. In each trial, participants estimated the base rate of one of these events and estimated their own risk of experiencing the event before and after being confronted with the actual base rate. Belief updates corresponded to the difference between the two self-risk estimates. Valence-dependent updating was assessed by comparing trials with good news (better-than-expected base rates) with trials with bad news (worse-than-expected base rates). After receiving bad relative to good news, participants' updates were smaller and deviated more strongly from rational Bayesian predictions, indicating a valence-induced bias. Model comparison revealed that the biased (i.e., optimistic) Bayesian model of belief updating better accounted for data than the unbiased (i.e., rational) Bayesian model, confirming that the valence of the new information influenced the amount of updating. Moreover, alternative computational modeling based on reinforcement learning demonstrated higher learning rates for good than for bad news, as well as a moderating role of personal knowledge. Finally, in this specific experimental context, the approach based on reinforcement learning was superior to the Bayesian approach. The computational validation of valence-dependent belief updating represents a novel support for a genuine optimism bias in human belief formation. Moreover, the precise control of relevant cognitive variables justifies the conclusion that the motivation to adopt the most favorable self-referential conclusions biases human judgments.

Decision scenario analysis for addressing sediment accumulation in Lago Lucchetti, Puerto Rico

EPA Science Inventory

A Bayesian belief network (BBN) was used to characterize the effects of sediment accumulation on water storage capacity of a reservoir (Lago Lucchetti) in southwest Puerto Rico and the potential of different management options to increase reservoir life expectancy. Water and sedi...

Social deprivation, inequality, and the neighborhood-level incidence of psychotic syndromes in East London.

PubMed

Kirkbride, James B; Jones, Peter B; Ullrich, Simone; Coid, Jeremy W

2014-01-01

Although urban birth, upbringing, and living are associated with increased risk of nonaffective psychotic disorders, few studies have used appropriate multilevel techniques accounting for spatial dependency in risk to investigate social, economic, or physical determinants of psychosis incidence. We adopted Bayesian hierarchical modeling to investigate the sociospatial distribution of psychosis risk in East London for DSM-IV nonaffective and affective psychotic disorders, ascertained over a 2-year period in the East London first-episode psychosis study. We included individual and environmental data on 427 subjects experiencing first-episode psychosis to estimate the incidence of disorder across 56 neighborhoods, having standardized for age, sex, ethnicity, and socioeconomic status. A Bayesian model that included spatially structured neighborhood-level random effects identified substantial unexplained variation in nonaffective psychosis risk after controlling for individual-level factors. This variation was independently associated with greater levels of neighborhood income inequality (SD increase in inequality: Bayesian relative risks [RR]: 1.25; 95% CI: 1.04-1.49), absolute deprivation (RR: 1.28; 95% CI: 1.08-1.51) and population density (RR: 1.18; 95% CI: 1.00-1.41). Neighborhood ethnic composition effects were associated with incidence of nonaffective psychosis for people of black Caribbean and black African origin. No variation in the spatial distribution of the affective psychoses was identified, consistent with the possibility of differing etiological origins of affective and nonaffective psychoses. Our data suggest that both absolute and relative measures of neighborhood social composition are associated with the incidence of nonaffective psychosis. We suggest these associations are consistent with a role for social stressors in psychosis risk, particularly when people live in more unequal communities.

Selected aspects of prior and likelihood information for a Bayesian classifier in a road safety analysis.

PubMed

Nowakowska, Marzena

2017-04-01

The development of the Bayesian logistic regression model classifying the road accident severity is discussed. The already exploited informative priors (method of moments, maximum likelihood estimation, and two-stage Bayesian updating), along with the original idea of a Boot prior proposal, are investigated when no expert opinion has been available. In addition, two possible approaches to updating the priors, in the form of unbalanced and balanced training data sets, are presented. The obtained logistic Bayesian models are assessed on the basis of a deviance information criterion (DIC), highest probability density (HPD) intervals, and coefficients of variation estimated for the model parameters. The verification of the model accuracy has been based on sensitivity, specificity and the harmonic mean of sensitivity and specificity, all calculated from a test data set. The models obtained from the balanced training data set have a better classification quality than the ones obtained from the unbalanced training data set. The two-stage Bayesian updating prior model and the Boot prior model, both identified with the use of the balanced training data set, outperform the non-informative, method of moments, and maximum likelihood estimation prior models. It is important to note that one should be careful when interpreting the parameters since different priors can lead to different models. Copyright © 2017 Elsevier Ltd. All rights reserved.

A new prior for bayesian anomaly detection: application to biosurveillance.

PubMed

Shen, Y; Cooper, G F

2010-01-01

Bayesian anomaly detection computes posterior probabilities of anomalous events by combining prior beliefs and evidence from data. However, the specification of prior probabilities can be challenging. This paper describes a Bayesian prior in the context of disease outbreak detection. The goal is to provide a meaningful, easy-to-use prior that yields a posterior probability of an outbreak that performs at least as well as a standard frequentist approach. If this goal is achieved, the resulting posterior could be usefully incorporated into a decision analysis about how to act in light of a possible disease outbreak. This paper describes a Bayesian method for anomaly detection that combines learning from data with a semi-informative prior probability over patterns of anomalous events. A univariate version of the algorithm is presented here for ease of illustration of the essential ideas. The paper describes the algorithm in the context of disease-outbreak detection, but it is general and can be used in other anomaly detection applications. For this application, the semi-informative prior specifies that an increased count over baseline is expected for the variable being monitored, such as the number of respiratory chief complaints per day at a given emergency department. The semi-informative prior is derived based on the baseline prior, which is estimated from using historical data. The evaluation reported here used semi-synthetic data to evaluate the detection performance of the proposed Bayesian method and a control chart method, which is a standard frequentist algorithm that is closest to the Bayesian method in terms of the type of data it uses. The disease-outbreak detection performance of the Bayesian method was statistically significantly better than that of the control chart method when proper baseline periods were used to estimate the baseline behavior to avoid seasonal effects. When using longer baseline periods, the Bayesian method performed as well as the control chart method. The time complexity of the Bayesian algorithm is linear in the number of the observed events being monitored, due to a novel, closed-form derivation that is introduced in the paper. This paper introduces a novel prior probability for Bayesian outbreak detection that is expressive, easy-to-apply, computationally efficient, and performs as well or better than a standard frequentist method.

Bayesian estimation of self-similarity exponent

NASA Astrophysics Data System (ADS)

Makarava, Natallia; Benmehdi, Sabah; Holschneider, Matthias

2011-08-01

In this study we propose a Bayesian approach to the estimation of the Hurst exponent in terms of linear mixed models. Even for unevenly sampled signals and signals with gaps, our method is applicable. We test our method by using artificial fractional Brownian motion of different length and compare it with the detrended fluctuation analysis technique. The estimation of the Hurst exponent of a Rosenblatt process is shown as an example of an H-self-similar process with non-Gaussian dimensional distribution. Additionally, we perform an analysis with real data, the Dow-Jones Industrial Average closing values, and analyze its temporal variation of the Hurst exponent.

Bayesian molecular dating: opening up the black box.

PubMed

Bromham, Lindell; Duchêne, Sebastián; Hua, Xia; Ritchie, Andrew M; Duchêne, David A; Ho, Simon Y W

2018-05-01

Molecular dating analyses allow evolutionary timescales to be estimated from genetic data, offering an unprecedented capacity for investigating the evolutionary past of all species. These methods require us to make assumptions about the relationship between genetic change and evolutionary time, often referred to as a 'molecular clock'. Although initially regarded with scepticism, molecular dating has now been adopted in many areas of biology. This broad uptake has been due partly to the development of Bayesian methods that allow complex aspects of molecular evolution, such as variation in rates of change across lineages, to be taken into account. But in order to do this, Bayesian dating methods rely on a range of assumptions about the evolutionary process, which vary in their degree of biological realism and empirical support. These assumptions can have substantial impacts on the estimates produced by molecular dating analyses. The aim of this review is to open the 'black box' of Bayesian molecular dating and have a look at the machinery inside. We explain the components of these dating methods, the important decisions that researchers must make in their analyses, and the factors that need to be considered when interpreting results. We illustrate the effects that the choices of different models and priors can have on the outcome of the analysis, and suggest ways to explore these impacts. We describe some major research directions that may improve the reliability of Bayesian dating. The goal of our review is to help researchers to make informed choices when using Bayesian phylogenetic methods to estimate evolutionary rates and timescales. © 2017 Cambridge Philosophical Society.

Functional Bregman Divergence and Bayesian Estimation of Distributions (Preprint)

DTIC Science & Technology

2008-01-01

shows that if the set of possible minimizers A includes EPF [F ], then g∗ = EPF [F ] minimizes the expectation of any Bregman divergence. Note the theorem...probability distribution PF defined over the set M. Let A be a set of functions that includes EPF [F ] if it exists. Suppose the function g∗ minimizes...the expected Bregman divergence between the random function F and any function g ∈ A such that g∗ = arg inf g∈A EPF [dφ(F, g)]. Then, if g∗ exists

A Bayesian estimate of the concordance correlation coefficient with skewed data.

PubMed

Feng, Dai; Baumgartner, Richard; Svetnik, Vladimir

2015-01-01

Concordance correlation coefficient (CCC) is one of the most popular scaled indices used to evaluate agreement. Most commonly, it is used under the assumption that data is normally distributed. This assumption, however, does not apply to skewed data sets. While methods for the estimation of the CCC of skewed data sets have been introduced and studied, the Bayesian approach and its comparison with the previous methods has been lacking. In this study, we propose a Bayesian method for the estimation of the CCC of skewed data sets and compare it with the best method previously investigated. The proposed method has certain advantages. It tends to outperform the best method studied before when the variation of the data is mainly from the random subject effect instead of error. Furthermore, it allows for greater flexibility in application by enabling incorporation of missing data, confounding covariates, and replications, which was not considered previously. The superiority of this new approach is demonstrated using simulation as well as real-life biomarker data sets used in an electroencephalography clinical study. The implementation of the Bayesian method is accessible through the Comprehensive R Archive Network. Copyright © 2015 John Wiley & Sons, Ltd.

PEER Transportation Research Program | PEER Transportation Research Program

Science.gov Websites

methodologies, integrating fundamental knowledge, enabling technologies, and systems. We further expect that the Bayesian Framework for Performance Assessment and Risk Management of Transportation Systems subject to Earthquakes Directivity Modeling for NGA West2 Ground Motion Studies for Transportation Systems Performance

A Bayesian Method for Managing Uncertainties Relating to Distributed Multistatic Sensor Search

DTIC Science & Technology

2006-07-01

before - detect process. There will also be an increased probability of high signal-to-noise ratio (SNR) detections associated with specular and near...and high target strength and high Doppler opportunities give rise to the expectation of an increased number of detections that could feed a track

Bayesian Spatiotemporal Analysis of Socio-Ecologic Drivers of Ross River Virus Transmission in Queensland, Australia

PubMed Central

Hu, Wenbiao; Clements, Archie; Williams, Gail; Tong, Shilu; Mengersen, Kerrie

2010-01-01

This study aims to examine the impact of socio-ecologic factors on the transmission of Ross River virus (RRV) infection and to identify areas prone to social and ecologic-driven epidemics in Queensland, Australia. We used a Bayesian spatiotemporal conditional autoregressive model to quantify the relationship between monthly variation of RRV incidence and socio-ecologic factors and to determine spatiotemporal patterns. Our results show that the average increase in monthly RRV incidence was 2.4% (95% credible interval (CrI): 0.1–4.5%) and 2.0% (95% CrI: 1.6–2.3%) for a 1°C increase in monthly average maximum temperature and a 10 mm increase in monthly average rainfall, respectively. A significant spatiotemporal variation and interactive effect between temperature and rainfall on RRV incidence were found. No association between Socio-economic Index for Areas (SEIFA) and RRV was observed. The transmission of RRV in Queensland, Australia appeared to be primarily driven by ecologic variables rather than social factors. PMID:20810846

Reproductive success of a keystone herbivore is more variable and responsive to climate in habitats with lower resource diversity.

PubMed

Iles, David T; Rockwell, Robert F; Koons, David N

2018-07-01

The effects of climate on wild populations are often channelled through species interactions. Population responses to climate variation can therefore differ across habitats, owing to variation in the biotic community. Theory predicts that consumer demography should be less variable and less responsive to climate in habitats with greater resource diversity. We tested these predictions using a long-term study of breeding lesser snow geese along the western coast of Hudson Bay, Manitoba, Canada. Reproductive success was measured in 22 years from 114 locations, in either coastal or inland habitat types. We used Bayesian analysis to estimate the response of reproductive success to climate in each habitat type, along with residual variation not explained by climate. We then quantified gosling diet composition in each habitat type to test the prediction that reproductive success would be less variable and more responsive to climate in habitats with lower resource diversity. Reproductive success responded positively to seasonal warmness, but this response was much stronger in inland habitats than in coastal habitats. Site- and year-level random effects were also three to five times more variable in inland habitats. Simultaneously, land cover diversity and gosling diet diversity were lower in inland habitats. Our study illustrates that spatial variation in resource diversity (and thus, species interactions) can have important effects on consumer responses to climate. In this system, climate change is expected to disproportionately increase the reproductive success of snow geese in vast inland habitats, potentially counteracting management efforts to reduce the abundance of this keystone herbivore. © 2018 The Authors. Journal of Animal Ecology © 2018 British Ecological Society.

Tests of species-specific models reveal the importance of drought in postglacial range shifts of a Mediterranean-climate tree: insights from integrative distributional, demographic and coalescent modelling and ABC model selection.

PubMed

Bemmels, Jordan B; Title, Pascal O; Ortego, Joaquín; Knowles, L Lacey

2016-10-01

Past climate change has caused shifts in species distributions and undoubtedly impacted patterns of genetic variation, but the biological processes mediating responses to climate change, and their genetic signatures, are often poorly understood. We test six species-specific biologically informed hypotheses about such processes in canyon live oak (Quercus chrysolepis) from the California Floristic Province. These hypotheses encompass the potential roles of climatic niche, niche multidimensionality, physiological trade-offs in functional traits, and local-scale factors (microsites and local adaptation within ecoregions) in structuring genetic variation. Specifically, we use ecological niche models (ENMs) to construct temporally dynamic landscapes where the processes invoked by each hypothesis are reflected by differences in local habitat suitabilities. These landscapes are used to simulate expected patterns of genetic variation under each model and evaluate the fit of empirical data from 13 microsatellite loci genotyped in 226 individuals from across the species range. Using approximate Bayesian computation (ABC), we obtain very strong support for two statistically indistinguishable models: a trade-off model in which growth rate and drought tolerance drive habitat suitability and genetic structure, and a model based on the climatic niche estimated from a generic ENM, in which the variables found to make the most important contribution to the ENM have strong conceptual links to drought stress. The two most probable models for explaining the patterns of genetic variation thus share a common component, highlighting the potential importance of seasonal drought in driving historical range shifts in a temperate tree from a Mediterranean climate where summer drought is common. © 2016 John Wiley & Sons Ltd.

Joint association discovery and diagnosis of Alzheimer's disease by supervised heterogeneous multiview learning.

PubMed

Zhe, Shandian; Xu, Zenglin; Qi, Yuan; Yu, Peng

2014-01-01

A key step for Alzheimer's disease (AD) study is to identify associations between genetic variations and intermediate phenotypes (e.g., brain structures). At the same time, it is crucial to develop a noninvasive means for AD diagnosis. Although these two tasks-association discovery and disease diagnosis-have been treated separately by a variety of approaches, they are tightly coupled due to their common biological basis. We hypothesize that the two tasks can potentially benefit each other by a joint analysis, because (i) the association study discovers correlated biomarkers from different data sources, which may help improve diagnosis accuracy, and (ii) the disease status may help identify disease-sensitive associations between genetic variations and MRI features. Based on this hypothesis, we present a new sparse Bayesian approach for joint association study and disease diagnosis. In this approach, common latent features are extracted from different data sources based on sparse projection matrices and used to predict multiple disease severity levels based on Gaussian process ordinal regression; in return, the disease status is used to guide the discovery of relationships between the data sources. The sparse projection matrices not only reveal the associations but also select groups of biomarkers related to AD. To learn the model from data, we develop an efficient variational expectation maximization algorithm. Simulation results demonstrate that our approach achieves higher accuracy in both predicting ordinal labels and discovering associations between data sources than alternative methods. We apply our approach to an imaging genetics dataset of AD. Our joint analysis approach not only identifies meaningful and interesting associations between genetic variations, brain structures, and AD status, but also achieves significantly higher accuracy for predicting ordinal AD stages than the competing methods.

Gaussian process tomography for soft x-ray spectroscopy at WEST without equilibrium information

NASA Astrophysics Data System (ADS)

Wang, T.; Mazon, D.; Svensson, J.; Li, D.; Jardin, A.; Verdoolaege, G.

2018-06-01

Gaussian process tomography (GPT) is a recently developed tomography method based on the Bayesian probability theory [J. Svensson, JET Internal Report EFDA-JET-PR(11)24, 2011 and Li et al., Rev. Sci. Instrum. 84, 083506 (2013)]. By modeling the soft X-ray (SXR) emissivity field in a poloidal cross section as a Gaussian process, the Bayesian SXR tomography can be carried out in a robust and extremely fast way. Owing to the short execution time of the algorithm, GPT is an important candidate for providing real-time reconstructions with a view to impurity transport and fast magnetohydrodynamic control. In addition, the Bayesian formalism allows quantifying uncertainty on the inferred parameters. In this paper, the GPT technique is validated using a synthetic data set expected from the WEST tokamak, and the results are shown of its application to the reconstruction of SXR emissivity profiles measured on Tore Supra. The method is compared with the standard algorithm based on minimization of the Fisher information.

A Bayesian Approach for Measurements of Stray Neutrons at Proton Therapy Facilities: Quantifying Neutron Dose Uncertainty.

PubMed

Dommert, M; Reginatto, M; Zboril, M; Fiedler, F; Helmbrecht, S; Enghardt, W; Lutz, B

2017-11-28

Bonner sphere measurements are typically analyzed using unfolding codes. It is well known that it is difficult to get reliable estimates of uncertainties for standard unfolding procedures. An alternative approach is to analyze the data using Bayesian parameter estimation. This method provides reliable estimates of the uncertainties of neutron spectra leading to rigorous estimates of uncertainties of the dose. We extend previous Bayesian approaches and apply the method to stray neutrons in proton therapy environments by introducing a new parameterized model which describes the main features of the expected neutron spectra. The parameterization is based on information that is available from measurements and detailed Monte Carlo simulations. The validity of this approach has been validated with results of an experiment using Bonner spheres carried out at the experimental hall of the OncoRay proton therapy facility in Dresden. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Cancer incidence and mortality projections up to 2020 in Catalonia by means of Bayesian models.

PubMed

Ribes, J; Esteban, L; Clèries, R; Galceran, J; Marcos-Gragera, R; Gispert, R; Ameijide, A; Vilardell, M L; Borras, J; Puigdefabregas, A; Buxó, M; Freitas, A; Izquierdo, A; Borras, J M

2014-08-01

To predict the burden of cancer in Catalonia by 2020 assessing changes in demography and cancer risk during 2010-2020. Data were obtained from Tarragona and Girona cancer registries and Catalan mortality registry. Population age distribution was obtained from the Catalan Institute of Statistics. Predicted cases in Catalonia were estimated through autoregressive Bayesian age-period-cohort models. There will be diagnosed 26,455 incident cases among men and 18,345 among women during 2020, which means an increase of 22.5 and 24.5 % comparing with the cancer incidence figures of 2010. In men, the increase of cases (22.5 %) can be partitioned in three components: 12 % due to ageing, 8 % due to increase in population size and 2 % due to cancer risk. In women, the role of each component was 9, 8 and 8 %, respectively. The increased risk is mainly expected to be observed in tobacco-related tumours among women and in colorectal and liver cancers among men. During 2010-2020 a mortality decline is expected in both sexes. The expected increase of cancer incidence, mainly due to tobacco-related tumours in women and colorectal in men, reinforces the need to strengthen smoking prevention and the expansion of early detection of colorectal cancer in Catalonia.

Implementing informative priors for heterogeneity in meta-analysis using meta-regression and pseudo data.

PubMed

Rhodes, Kirsty M; Turner, Rebecca M; White, Ian R; Jackson, Dan; Spiegelhalter, David J; Higgins, Julian P T

2016-12-20

Many meta-analyses combine results from only a small number of studies, a situation in which the between-study variance is imprecisely estimated when standard methods are applied. Bayesian meta-analysis allows incorporation of external evidence on heterogeneity, providing the potential for more robust inference on the effect size of interest. We present a method for performing Bayesian meta-analysis using data augmentation, in which we represent an informative conjugate prior for between-study variance by pseudo data and use meta-regression for estimation. To assist in this, we derive predictive inverse-gamma distributions for the between-study variance expected in future meta-analyses. These may serve as priors for heterogeneity in new meta-analyses. In a simulation study, we compare approximate Bayesian methods using meta-regression and pseudo data against fully Bayesian approaches based on importance sampling techniques and Markov chain Monte Carlo (MCMC). We compare the frequentist properties of these Bayesian methods with those of the commonly used frequentist DerSimonian and Laird procedure. The method is implemented in standard statistical software and provides a less complex alternative to standard MCMC approaches. An importance sampling approach produces almost identical results to standard MCMC approaches, and results obtained through meta-regression and pseudo data are very similar. On average, data augmentation provides closer results to MCMC, if implemented using restricted maximum likelihood estimation rather than DerSimonian and Laird or maximum likelihood estimation. The methods are applied to real datasets, and an extension to network meta-analysis is described. The proposed method facilitates Bayesian meta-analysis in a way that is accessible to applied researchers. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

ChemStable: a web server for rule-embedded naïve Bayesian learning approach to predict compound stability.

PubMed

Liu, Zhihong; Zheng, Minghao; Yan, Xin; Gu, Qiong; Gasteiger, Johann; Tijhuis, Johan; Maas, Peter; Li, Jiabo; Xu, Jun

2014-09-01

Predicting compound chemical stability is important because unstable compounds can lead to either false positive or to false negative conclusions in bioassays. Experimental data (COMDECOM) measured from DMSO/H2O solutions stored at 50 °C for 105 days were used to predicted stability by applying rule-embedded naïve Bayesian learning, based upon atom center fragment (ACF) features. To build the naïve Bayesian classifier, we derived ACF features from 9,746 compounds in the COMDECOM dataset. By recursively applying naïve Bayesian learning from the data set, each ACF is assigned with an expected stable probability (p(s)) and an unstable probability (p(uns)). 13,340 ACFs, together with their p(s) and p(uns) data, were stored in a knowledge base for use by the Bayesian classifier. For a given compound, its ACFs were derived from its structure connection table with the same protocol used to drive ACFs from the training data. Then, the Bayesian classifier assigned p(s) and p(uns) values to the compound ACFs by a structural pattern recognition algorithm, which was implemented in-house. Compound instability is calculated, with Bayes' theorem, based upon the p(s) and p(uns) values of the compound ACFs. We were able to achieve performance with an AUC value of 84% and a tenfold cross validation accuracy of 76.5%. To reduce false negatives, a rule-based approach has been embedded in the classifier. The rule-based module allows the program to improve its predictivity by expanding its compound instability knowledge base, thus further reducing the possibility of false negatives. To our knowledge, this is the first in silico prediction service for the prediction of the stabilities of organic compounds.

An efficient Bayesian data-worth analysis using a multilevel Monte Carlo method

NASA Astrophysics Data System (ADS)

Lu, Dan; Ricciuto, Daniel; Evans, Katherine

2018-03-01

Improving the understanding of subsurface systems and thus reducing prediction uncertainty requires collection of data. As the collection of subsurface data is costly, it is important that the data collection scheme is cost-effective. Design of a cost-effective data collection scheme, i.e., data-worth analysis, requires quantifying model parameter, prediction, and both current and potential data uncertainties. Assessment of these uncertainties in large-scale stochastic subsurface hydrological model simulations using standard Monte Carlo (MC) sampling or surrogate modeling is extremely computationally intensive, sometimes even infeasible. In this work, we propose an efficient Bayesian data-worth analysis using a multilevel Monte Carlo (MLMC) method. Compared to the standard MC that requires a significantly large number of high-fidelity model executions to achieve a prescribed accuracy in estimating expectations, the MLMC can substantially reduce computational costs using multifidelity approximations. Since the Bayesian data-worth analysis involves a great deal of expectation estimation, the cost saving of the MLMC in the assessment can be outstanding. While the proposed MLMC-based data-worth analysis is broadly applicable, we use it for a highly heterogeneous two-phase subsurface flow simulation to select an optimal candidate data set that gives the largest uncertainty reduction in predicting mass flow rates at four production wells. The choices made by the MLMC estimation are validated by the actual measurements of the potential data, and consistent with the standard MC estimation. But compared to the standard MC, the MLMC greatly reduces the computational costs.

Presentation of the results of a Bayesian automatic event detection and localization program to human analysts

NASA Astrophysics Data System (ADS)

Kushida, N.; Kebede, F.; Feitio, P.; Le Bras, R.

2016-12-01

The Preparatory Commission for the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) has been developing and testing NET-VISA (Arora et al., 2013), a Bayesian automatic event detection and localization program, and evaluating its performance in a realistic operational mode. In our preliminary testing at the CTBTO, NET-VISA shows better performance than its currently operating automatic localization program. However, given CTBTO's role and its international context, a new technology should be introduced cautiously when it replaces a key piece of the automatic processing. We integrated the results of NET-VISA into the Analyst Review Station, extensively used by the analysts so that they can check the accuracy and robustness of the Bayesian approach. We expect the workload of the analysts to be reduced because of the better performance of NET-VISA in finding missed events and getting a more complete set of stations than the current system which has been operating for nearly twenty years. The results of a series of tests indicate that the expectations born from the automatic tests, which show an overall overlap improvement of 11%, meaning that the missed events rate is cut by 42%, hold for the integrated interactive module as well. New events are found by analysts, which qualify for the CTBTO Reviewed Event Bulletin, beyond the ones analyzed through the standard procedures. Arora, N., Russell, S., and Sudderth, E., NET-VISA: Network Processing Vertically Integrated Seismic Analysis, 2013, Bull. Seismol. Soc. Am., 103, 709-729.

Assessing spatial variation of corn response to irrigation using a bayesian semiparametric model

USDA-ARS?s Scientific Manuscript database

Spatial irrigation of agricultural crops using site-specific variable-rate irrigation (VRI) systems is beginning to have wide-spread acceptance. However, optimizing the management of these VRI systems to conserve natural resources and increase profitability requires an understanding of the spatial ...

Spatial and temporal patterns of chronic wasting disease: Fine-scale mapping of a wildlife epidemic in Wisconsin

USGS Publications Warehouse

Osnas, E.E.; Heisey, D.M.; Rolley, R.E.; Samuel, M.D.

2009-01-01

Emerging infectious diseases threaten wildlife populations and human health. Understanding the spatial distributions of these new diseases is important for disease management and policy makers; however, the data are complicated by heterogeneities across host classes, sampling variance, sampling biases, and the space-time epidemic process. Ignoring these issues can lead to false conclusions or obscure important patterns in the data, such as spatial variation in disease prevalence. Here, we applied hierarchical Bayesian disease mapping methods to account for risk factors and to estimate spatial and temporal patterns of infection by chronic wasting disease (CWD) in white-tailed deer (Odocoileus virginianus) of Wisconsin, USA. We found significant heterogeneities for infection due to age, sex, and spatial location. Infection probability increased with age for all young deer, increased with age faster for young males, and then declined for some older animals, as expected from disease-associated mortality and age-related changes in infection risk. We found that disease prevalence was clustered in a central location, as expected under a simple spatial epidemic process where disease prevalence should increase with time and expand spatially. However, we could not detect any consistent temporal or spatiotemporal trends in CWD prevalence. Estimates of the temporal trend indicated that prevalence may have decreased or increased with nearly equal posterior probability, and the model without temporal or spatiotemporal effects was nearly equivalent to models with these effects based on deviance information criteria. For maximum interpretability of the role of location as a disease risk factor, we used the technique of direct standardization for prevalence mapping, which we develop and describe. These mapping results allow disease management actions to be employed with reference to the estimated spatial distribution of the disease and to those host classes most at risk. Future wildlife epidemiology studies should employ hierarchical Bayesian methods to smooth estimated quantities across space and time, account for heterogeneities, and then report disease rates based on an appropriate standardization. ?? 2009 by the Ecological Society of America.

Prediction of road accidents: A Bayesian hierarchical approach.

PubMed

Deublein, Markus; Schubert, Matthias; Adey, Bryan T; Köhler, Jochen; Faber, Michael H

2013-03-01

In this paper a novel methodology for the prediction of the occurrence of road accidents is presented. The methodology utilizes a combination of three statistical methods: (1) gamma-updating of the occurrence rates of injury accidents and injured road users, (2) hierarchical multivariate Poisson-lognormal regression analysis taking into account correlations amongst multiple dependent model response variables and effects of discrete accident count data e.g. over-dispersion, and (3) Bayesian inference algorithms, which are applied by means of data mining techniques supported by Bayesian Probabilistic Networks in order to represent non-linearity between risk indicating and model response variables, as well as different types of uncertainties which might be present in the development of the specific models. Prior Bayesian Probabilistic Networks are first established by means of multivariate regression analysis of the observed frequencies of the model response variables, e.g. the occurrence of an accident, and observed values of the risk indicating variables, e.g. degree of road curvature. Subsequently, parameter learning is done using updating algorithms, to determine the posterior predictive probability distributions of the model response variables, conditional on the values of the risk indicating variables. The methodology is illustrated through a case study using data of the Austrian rural motorway network. In the case study, on randomly selected road segments the methodology is used to produce a model to predict the expected number of accidents in which an injury has occurred and the expected number of light, severe and fatally injured road users. Additionally, the methodology is used for geo-referenced identification of road sections with increased occurrence probabilities of injury accident events on a road link between two Austrian cities. It is shown that the proposed methodology can be used to develop models to estimate the occurrence of road accidents for any road network provided that the required data are available. Copyright © 2012 Elsevier Ltd. All rights reserved.

Expectation-maximization of the potential of mean force and diffusion coefficient in Langevin dynamics from single molecule FRET data photon by photon.

PubMed

Haas, Kevin R; Yang, Haw; Chu, Jhih-Wei

2013-12-12

The dynamics of a protein along a well-defined coordinate can be formally projected onto the form of an overdamped Lagevin equation. Here, we present a comprehensive statistical-learning framework for simultaneously quantifying the deterministic force (the potential of mean force, PMF) and the stochastic force (characterized by the diffusion coefficient, D) from single-molecule Förster-type resonance energy transfer (smFRET) experiments. The likelihood functional of the Langevin parameters, PMF and D, is expressed by a path integral of the latent smFRET distance that follows Langevin dynamics and realized by the donor and the acceptor photon emissions. The solution is made possible by an eigen decomposition of the time-symmetrized form of the corresponding Fokker-Planck equation coupled with photon statistics. To extract the Langevin parameters from photon arrival time data, we advance the expectation-maximization algorithm in statistical learning, originally developed for and mostly used in discrete-state systems, to a general form in the continuous space that allows for a variational calculus on the continuous PMF function. We also introduce the regularization of the solution space in this Bayesian inference based on a maximum trajectory-entropy principle. We use a highly nontrivial example with realistically simulated smFRET data to illustrate the application of this new method.

Bayesian-based localization of wireless capsule endoscope using received signal strength.

PubMed

Nadimi, Esmaeil S; Blanes-Vidal, Victoria; Tarokh, Vahid; Johansen, Per Michael

2014-01-01

In wireless body area sensor networking (WBASN) applications such as gastrointestinal (GI) tract monitoring using wireless video capsule endoscopy (WCE), the performance of out-of-body wireless link propagating through different body media (i.e. blood, fat, muscle and bone) is still under investigation. Most of the localization algorithms are vulnerable to the variations of path-loss coefficient resulting in unreliable location estimation. In this paper, we propose a novel robust probabilistic Bayesian-based approach using received-signal-strength (RSS) measurements that accounts for Rayleigh fading, variable path-loss exponent and uncertainty in location information received from the neighboring nodes and anchors. The results of this study showed that the localization root mean square error of our Bayesian-based method was 1.6 mm which was very close to the optimum Cramer-Rao lower bound (CRLB) and significantly smaller than that of other existing localization approaches (i.e. classical MDS (64.2mm), dwMDS (32.2mm), MLE (36.3mm) and POCS (2.3mm)).

pyblocxs: Bayesian Low-Counts X-ray Spectral Analysis in Sherpa

NASA Astrophysics Data System (ADS)

Siemiginowska, A.; Kashyap, V.; Refsdal, B.; van Dyk, D.; Connors, A.; Park, T.

2011-07-01

Typical X-ray spectra have low counts and should be modeled using the Poisson distribution. However, χ2 statistic is often applied as an alternative and the data are assumed to follow the Gaussian distribution. A variety of weights to the statistic or a binning of the data is performed to overcome the low counts issues. However, such modifications introduce biases or/and a loss of information. Standard modeling packages such as XSPEC and Sherpa provide the Poisson likelihood and allow computation of rudimentary MCMC chains, but so far do not allow for setting a full Bayesian model. We have implemented a sophisticated Bayesian MCMC-based algorithm to carry out spectral fitting of low counts sources in the Sherpa environment. The code is a Python extension to Sherpa and allows to fit a predefined Sherpa model to high-energy X-ray spectral data and other generic data. We present the algorithm and discuss several issues related to the implementation, including flexible definition of priors and allowing for variations in the calibration information.

Environmentally adaptive processing for shallow ocean applications: A sequential Bayesian approach.

PubMed

Candy, J V

2015-09-01

The shallow ocean is a changing environment primarily due to temperature variations in its upper layers directly affecting sound propagation throughout. The need to develop processors capable of tracking these changes implies a stochastic as well as an environmentally adaptive design. Bayesian techniques have evolved to enable a class of processors capable of performing in such an uncertain, nonstationary (varying statistics), non-Gaussian, variable shallow ocean environment. A solution to this problem is addressed by developing a sequential Bayesian processor capable of providing a joint solution to the modal function tracking and environmental adaptivity problem. Here, the focus is on the development of both a particle filter and an unscented Kalman filter capable of providing reasonable performance for this problem. These processors are applied to hydrophone measurements obtained from a vertical array. The adaptivity problem is attacked by allowing the modal coefficients and/or wavenumbers to be jointly estimated from the noisy measurement data along with tracking of the modal functions while simultaneously enhancing the noisy pressure-field measurements.

Robust nonlinear system identification: Bayesian mixture of experts using the t-distribution

NASA Astrophysics Data System (ADS)

Baldacchino, Tara; Worden, Keith; Rowson, Jennifer

2017-02-01

A novel variational Bayesian mixture of experts model for robust regression of bifurcating and piece-wise continuous processes is introduced. The mixture of experts model is a powerful model which probabilistically splits the input space allowing different models to operate in the separate regions. However, current methods have no fail-safe against outliers. In this paper, a robust mixture of experts model is proposed which consists of Student-t mixture models at the gates and Student-t distributed experts, trained via Bayesian inference. The Student-t distribution has heavier tails than the Gaussian distribution, and so it is more robust to outliers, noise and non-normality in the data. Using both simulated data and real data obtained from the Z24 bridge this robust mixture of experts performs better than its Gaussian counterpart when outliers are present. In particular, it provides robustness to outliers in two forms: unbiased parameter regression models, and robustness to overfitting/complex models.

Convergence among cave catfishes: long-branch attraction and a Bayesian relative rates test.

PubMed

Wilcox, T P; García de León, F J; Hendrickson, D A; Hillis, D M

2004-06-01

Convergence has long been of interest to evolutionary biologists. Cave organisms appear to be ideal candidates for studying convergence in morphological, physiological, and developmental traits. Here we report apparent convergence in two cave-catfishes that were described on morphological grounds as congeners: Prietella phreatophila and Prietella lundbergi. We collected mitochondrial DNA sequence data from 10 species of catfishes, representing five of the seven genera in Ictaluridae, as well as seven species from a broad range of siluriform outgroups. Analysis of the sequence data under parsimony supports a monophyletic Prietella. However, both maximum-likelihood and Bayesian analyses support polyphyly of the genus, with P. lundbergi sister to Ictalurus and P. phreatophila sister to Ameiurus. The topological difference between parsimony and the other methods appears to result from long-branch attraction between the Prietella species. Similarly, the sequence data do not support several other relationships within Ictaluridae supported by morphology. We develop a new Bayesian method for examining variation in molecular rates of evolution across a phylogeny.

Applying Bayesian Item Selection Approaches to Adaptive Tests Using Polytomous Items

ERIC Educational Resources Information Center

Penfield, Randall D.

2006-01-01

This study applied the maximum expected information (MEI) and the maximum posterior-weighted information (MPI) approaches of computer adaptive testing item selection to the case of a test using polytomous items following the partial credit model. The MEI and MPI approaches are described. A simulation study compared the efficiency of ability…

Methods for Measuring the Influence of Concept Mapping on Student Information Literacy.

ERIC Educational Resources Information Center

Gordon, Carol A.

2002-01-01

Discusses research traditions in education and in information retrieval and explores the theory of expected information which uses formulas derived from the Fano measure and Bayesian statistics. Demonstrates its application in a study on the effects of concept mapping on the search behavior of tenth-grade biology students. (Author/LRW)

The Student-Customer Orientation Questionnaire (SCOQ): Application of Customer Metaphor to Higher Education

ERIC Educational Resources Information Center

Koris, Riina; Nokelainen, Petri

2015-01-01

Purpose: The purpose of this paper is to study Bayesian dependency modelling (BDM) to validate the model of educational experiences and the student-customer orientation questionnaire (SCOQ), and to identify the categories of educatonal experience in which students expect a higher educational institutions (HEI) to be student-customer oriented.…

MixSIAR: A Bayesian stable isotope mixing model for characterizing intrapopulation niche variation

EPA Science Inventory

Background/Question/Methods The science of stable isotope mixing models has tended towards the development of modeling products (e.g. IsoSource, MixSIR, SIAR), where methodological advances or syntheses of the current state of the art are published in parity with software packa...

Investigating Psychometric Isomorphism for Traditional and Performance-Based Assessment

ERIC Educational Resources Information Center

Fay, Derek M.; Levy, Roy; Mehta, Vandhana

2018-01-01

A common practice in educational assessment is to construct multiple forms of an assessment that consists of tasks with similar psychometric properties. This study utilizes a Bayesian multilevel item response model and descriptive graphical representations to evaluate the psychometric similarity of variations of the same task. These approaches for…

Bayesian Community Detection in the Space of Group-Level Functional Differences

PubMed Central

Venkataraman, Archana; Yang, Daniel Y.-J.; Pelphrey, Kevin A.; Duncan, James S.

2017-01-01

We propose a unified Bayesian framework to detect both hyper- and hypo-active communities within whole-brain fMRI data. Specifically, our model identifies dense subgraphs that exhibit population-level differences in functional synchrony between a control and clinical group. We derive a variational EM algorithm to solve for the latent posterior distributions and parameter estimates, which subsequently inform us about the afflicted network topology. We demonstrate that our method provides valuable insights into the neural mechanisms underlying social dysfunction in autism, as verified by the Neurosynth meta-analytic database. In contrast, both univariate testing and community detection via recursive edge elimination fail to identify stable functional communities associated with the disorder. PMID:26955022

Bayesian Community Detection in the Space of Group-Level Functional Differences.

PubMed

Venkataraman, Archana; Yang, Daniel Y-J; Pelphrey, Kevin A; Duncan, James S

2016-08-01

We propose a unified Bayesian framework to detect both hyper- and hypo-active communities within whole-brain fMRI data. Specifically, our model identifies dense subgraphs that exhibit population-level differences in functional synchrony between a control and clinical group. We derive a variational EM algorithm to solve for the latent posterior distributions and parameter estimates, which subsequently inform us about the afflicted network topology. We demonstrate that our method provides valuable insights into the neural mechanisms underlying social dysfunction in autism, as verified by the Neurosynth meta-analytic database. In contrast, both univariate testing and community detection via recursive edge elimination fail to identify stable functional communities associated with the disorder.

cosmoabc: Likelihood-free inference for cosmology

NASA Astrophysics Data System (ADS)

Ishida, Emille E. O.; Vitenti, Sandro D. P.; Penna-Lima, Mariana; Trindade, Arlindo M.; Cisewski, Jessi; M.; de Souza, Rafael; Cameron, Ewan; Busti, Vinicius C.

2015-05-01

Approximate Bayesian Computation (ABC) enables parameter inference for complex physical systems in cases where the true likelihood function is unknown, unavailable, or computationally too expensive. It relies on the forward simulation of mock data and comparison between observed and synthetic catalogs. cosmoabc is a Python Approximate Bayesian Computation (ABC) sampler featuring a Population Monte Carlo variation of the original ABC algorithm, which uses an adaptive importance sampling scheme. The code can be coupled to an external simulator to allow incorporation of arbitrary distance and prior functions. When coupled with the numcosmo library, it has been used to estimate posterior probability distributions over cosmological parameters based on measurements of galaxy clusters number counts without computing the likelihood function.

Divergent trait and environment relationships among parallel radiations in Pelargonium (Geraniaceae): a role for evolutionary legacy?

PubMed

Moore, Timothy E; Schlichting, Carl D; Aiello-Lammens, Matthew E; Mocko, Kerri; Jones, Cynthia S

2018-05-11

Functional traits in closely related lineages are expected to vary similarly along common environmental gradients as a result of shared evolutionary and biogeographic history, or legacy effects, and as a result of biophysical tradeoffs in construction. We test these predictions in Pelargonium, a relatively recent evolutionary radiation. Bayesian phylogenetic mixed effects models assessed, at the subclade level, associations between plant height, leaf area, leaf nitrogen content and leaf mass per area (LMA), and five environmental variables capturing temperature and rainfall gradients across the Greater Cape Floristic Region of South Africa. Trait-trait integration was assessed via pairwise correlations within subclades. Of 20 trait-environment associations, 17 differed among subclades. Signs of regression coefficients diverged for height, leaf area and leaf nitrogen content, but not for LMA. Subclades also differed in trait-trait relationships and these differences were modulated by rainfall seasonality. Leave-one-out cross-validation revealed that whether trait variation was better predicted by environmental predictors or trait-trait integration depended on the clade and trait in question. Legacy signals in trait-environment and trait-trait relationships were apparently lost during the earliest diversification of Pelargonium, but then retained during subsequent subclade evolution. Overall, we demonstrate that global-scale patterns are poor predictors of patterns of trait variation at finer geographic and taxonomic scales. © 2018 The Authors. New Phytologist © 2018 New Phytologist Trust.

Individual differences in social information gathering revealed through Bayesian hierarchical models

PubMed Central

Pearson, John M.; Watson, Karli K.; Klein, Jeffrey T.; Ebitz, R. Becket; Platt, Michael L.

2013-01-01

As studies of the neural circuits underlying choice expand to include more complicated behaviors, analysis of behaviors elicited in laboratory paradigms has grown increasingly difficult. Social behaviors present a particular challenge, since inter- and intra-individual variation are expected to play key roles. However, due to limitations on data collection, studies must often choose between pooling data across all subjects or using individual subjects' data in isolation. Hierarchical models mediate between these two extremes by modeling individual subjects as drawn from a population distribution, allowing the population at large to serve as prior information about individuals' behavior. Here, we apply this method to data collected across multiple experimental sessions from a set of rhesus macaques performing a social information valuation task. We show that, while the values of social images vary markedly between individuals and between experimental sessions for the same individual, individuals also differentially value particular categories of social images. Furthermore, we demonstrate covariance between values for image categories within individuals and find evidence suggesting that magnitudes of stimulus values tend to diminish over time. PMID:24062635

Brain segmentation and the generation of cortical surfaces

NASA Technical Reports Server (NTRS)

Joshi, M.; Cui, J.; Doolittle, K.; Joshi, S.; Van Essen, D.; Wang, L.; Miller, M. I.

1999-01-01

This paper describes methods for white matter segmentation in brain images and the generation of cortical surfaces from the segmentations. We have developed a system that allows a user to start with a brain volume, obtained by modalities such as MRI or cryosection, and constructs a complete digital representation of the cortical surface. The methodology consists of three basic components: local parametric modeling and Bayesian segmentation; surface generation and local quadratic coordinate fitting; and surface editing. Segmentations are computed by parametrically fitting known density functions to the histogram of the image using the expectation maximization algorithm [DLR77]. The parametric fits are obtained locally rather than globally over the whole volume to overcome local variations in gray levels. To represent the boundary of the gray and white matter we use triangulated meshes generated using isosurface generation algorithms [GH95]. A complete system of local parametric quadratic charts [JWM+95] is superimposed on the triangulated graph to facilitate smoothing and geodesic curve tracking. Algorithms for surface editing include extraction of the largest closed surface. Results for several macaque brains are presented comparing automated and hand surface generation. Copyright 1999 Academic Press.

Prior expectations facilitate metacognition for perceptual decision.

PubMed

Sherman, M T; Seth, A K; Barrett, A B; Kanai, R

2015-09-01

The influential framework of 'predictive processing' suggests that prior probabilistic expectations influence, or even constitute, perceptual contents. This notion is evidenced by the facilitation of low-level perceptual processing by expectations. However, whether expectations can facilitate high-level components of perception remains unclear. We addressed this question by considering the influence of expectations on perceptual metacognition. To isolate the effects of expectation from those of attention we used a novel factorial design: expectation was manipulated by changing the probability that a Gabor target would be presented; attention was manipulated by instructing participants to perform or ignore a concurrent visual search task. We found that, independently of attention, metacognition improved when yes/no responses were congruent with expectations of target presence/absence. Results were modeled under a novel Bayesian signal detection theoretic framework which integrates bottom-up signal propagation with top-down influences, to provide a unified description of the mechanisms underlying perceptual decision and metacognition. Copyright © 2015 Elsevier Inc. All rights reserved.

A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

NASA Astrophysics Data System (ADS)

Gopalan, Giri; Hrafnkelsson, Birgir; Aðalgeirsdóttir, Guðfinna; Jarosch, Alexander H.; Pálsson, Finnur

2018-03-01

Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier.

Genetic Structure in a Small Pelagic Fish Coincides with a Marine Protected Area: Seascape Genetics in Patagonian Fjords.

PubMed

Canales-Aguirre, Cristian B; Ferrada-Fuentes, Sandra; Galleguillos, Ricardo; Hernández, Cristián E

2016-01-01

Marine environmental variables can play an important role in promoting population genetic differentiation in marine organisms. Although fjord ecosystems have attracted much attention due to the great oscillation of environmental variables that produce heterogeneous habitats, species inhabiting this kind of ecosystem have received less attention. In this study, we used Sprattus fuegensis, a small pelagic species that populates the inner waters of the continental shelf, channels and fjords of Chilean Patagonia and Argentina, as a model species to test whether environmental variables of fjords relate to population genetic structure. A total of 282 individuals were analyzed from Chilean Patagonia with eight microsatellite loci. Bayesian and non-Bayesian analyses were conducted to describe the genetic variability of S. fuegensis and whether it shows spatial genetic structure. Results showed two well-differentiated genetic clusters along the Chilean Patagonia distribution (i.e. inside the embayment area called TicToc, and the rest of the fjords), but no spatial isolation by distance (IBD) pattern was found with a Mantel test analysis. Temperature and nitrate were correlated to the expected heterozygosities and explained the allelic frequency variation of data in the redundancy analyses. These results suggest that the singular genetic differences found in S. fuegensis from inside TicToc Bay (East of the Corcovado Gulf) are the result of larvae retention bya combination of oceanographic mesoscale processes (i.e. the west wind drift current reaches the continental shelf exactly in this zone), and the local geographical configuration (i.e. embayment area, islands, archipelagos). We propose that these features generated an isolated area in the Patagonian fjords that promoted genetic differentiation by drift and a singular biodiversity, adding support to the existence of the largest marine protected area (MPA) of continental Chile, which is the Tic-Toc MPA.

A hybrid expectation maximisation and MCMC sampling algorithm to implement Bayesian mixture model based genomic prediction and QTL mapping.

PubMed

Wang, Tingting; Chen, Yi-Ping Phoebe; Bowman, Phil J; Goddard, Michael E; Hayes, Ben J

2016-09-21

Bayesian mixture models in which the effects of SNP are assumed to come from normal distributions with different variances are attractive for simultaneous genomic prediction and QTL mapping. These models are usually implemented with Monte Carlo Markov Chain (MCMC) sampling, which requires long compute times with large genomic data sets. Here, we present an efficient approach (termed HyB_BR), which is a hybrid of an Expectation-Maximisation algorithm, followed by a limited number of MCMC without the requirement for burn-in. To test prediction accuracy from HyB_BR, dairy cattle and human disease trait data were used. In the dairy cattle data, there were four quantitative traits (milk volume, protein kg, fat% in milk and fertility) measured in 16,214 cattle from two breeds genotyped for 632,002 SNPs. Validation of genomic predictions was in a subset of cattle either from the reference set or in animals from a third breeds that were not in the reference set. In all cases, HyB_BR gave almost identical accuracies to Bayesian mixture models implemented with full MCMC, however computational time was reduced by up to 1/17 of that required by full MCMC. The SNPs with high posterior probability of a non-zero effect were also very similar between full MCMC and HyB_BR, with several known genes affecting milk production in this category, as well as some novel genes. HyB_BR was also applied to seven human diseases with 4890 individuals genotyped for around 300 K SNPs in a case/control design, from the Welcome Trust Case Control Consortium (WTCCC). In this data set, the results demonstrated again that HyB_BR performed as well as Bayesian mixture models with full MCMC for genomic predictions and genetic architecture inference while reducing the computational time from 45 h with full MCMC to 3 h with HyB_BR. The results for quantitative traits in cattle and disease in humans demonstrate that HyB_BR can perform equally well as Bayesian mixture models implemented with full MCMC in terms of prediction accuracy, but with up to 17 times faster than the full MCMC implementations. The HyB_BR algorithm makes simultaneous genomic prediction, QTL mapping and inference of genetic architecture feasible in large genomic data sets.

A probabilistic model framework for evaluating year-to-year variation in crop productivity

NASA Astrophysics Data System (ADS)

Yokozawa, M.; Iizumi, T.; Tao, F.

2008-12-01

Most models describing the relation between crop productivity and weather condition have so far been focused on mean changes of crop yield. For keeping stable food supply against abnormal weather as well as climate change, evaluating the year-to-year variations in crop productivity rather than the mean changes is more essential. We here propose a new framework of probabilistic model based on Bayesian inference and Monte Carlo simulation. As an example, we firstly introduce a model on paddy rice production in Japan. It is called PRYSBI (Process- based Regional rice Yield Simulator with Bayesian Inference; Iizumi et al., 2008). The model structure is the same as that of SIMRIW, which was developed and used widely in Japan. The model includes three sub- models describing phenological development, biomass accumulation and maturing of rice crop. These processes are formulated to include response nature of rice plant to weather condition. This model inherently was developed to predict rice growth and yield at plot paddy scale. We applied it to evaluate the large scale rice production with keeping the same model structure. Alternatively, we assumed the parameters as stochastic variables. In order to let the model catch up actual yield at larger scale, model parameters were determined based on agricultural statistical data of each prefecture of Japan together with weather data averaged over the region. The posterior probability distribution functions (PDFs) of parameters included in the model were obtained using Bayesian inference. The MCMC (Markov Chain Monte Carlo) algorithm was conducted to numerically solve the Bayesian theorem. For evaluating the year-to-year changes in rice growth/yield under this framework, we firstly iterate simulations with set of parameter values sampled from the estimated posterior PDF of each parameter and then take the ensemble mean weighted with the posterior PDFs. We will also present another example for maize productivity in China. The framework proposed here provides us information on uncertainties, possibilities and limitations on future improvements in crop model as well.

Bayesian population receptive field modelling.

PubMed

Zeidman, Peter; Silson, Edward Harry; Schwarzkopf, Dietrich Samuel; Baker, Chris Ian; Penny, Will

2017-09-08

We introduce a probabilistic (Bayesian) framework and associated software toolbox for mapping population receptive fields (pRFs) based on fMRI data. This generic approach is intended to work with stimuli of any dimension and is demonstrated and validated in the context of 2D retinotopic mapping. The framework enables the experimenter to specify generative (encoding) models of fMRI timeseries, in which experimental stimuli enter a pRF model of neural activity, which in turns drives a nonlinear model of neurovascular coupling and Blood Oxygenation Level Dependent (BOLD) response. The neuronal and haemodynamic parameters are estimated together on a voxel-by-voxel or region-of-interest basis using a Bayesian estimation algorithm (variational Laplace). This offers several novel contributions to receptive field modelling. The variance/covariance of parameters are estimated, enabling receptive fields to be plotted while properly representing uncertainty about pRF size and location. Variability in the haemodynamic response across the brain is accounted for. Furthermore, the framework introduces formal hypothesis testing to pRF analysis, enabling competing models to be evaluated based on their log model evidence (approximated by the variational free energy), which represents the optimal tradeoff between accuracy and complexity. Using simulations and empirical data, we found that parameters typically used to represent pRF size and neuronal scaling are strongly correlated, which is taken into account by the Bayesian methods we describe when making inferences. We used the framework to compare the evidence for six variants of pRF model using 7 T functional MRI data and we found a circular Difference of Gaussians (DoG) model to be the best explanation for our data overall. We hope this framework will prove useful for mapping stimulus spaces with any number of dimensions onto the anatomy of the brain. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

Calculation of Crystallographic Texture of BCC Steels During Cold Rolling

NASA Astrophysics Data System (ADS)

Das, Arpan

2017-05-01

BCC alloys commonly tend to develop strong fibre textures and often represent as isointensity diagrams in φ 1 sections or by fibre diagrams. Alpha fibre in bcc steels is generally characterised by <110> crystallographic axis parallel to the rolling direction. The objective of present research is to correlate carbon content, carbide dispersion, rolling reduction, Euler angles (ϕ) (when φ 1 = 0° and φ 2 = 45° along alpha fibre) and the resulting alpha fibre texture orientation intensity. In the present research, Bayesian neural computation has been employed to correlate these and compare with the existing feed-forward neural network model comprehensively. Excellent match to the measured texture data within the bounding box of texture training data set has been already predicted through the feed-forward neural network model by other researchers. Feed-forward neural network prediction outside the bounds of training texture data showed deviations from the expected values. Currently, Bayesian computation has been similarly applied to confirm that the predictions are reasonable in the context of basic metallurgical principles, and matched better outside the bounds of training texture data set than the reported feed-forward neural network. Bayesian computation puts error bars on predicted values and allows significance of each individual parameters to be estimated. Additionally, it is also possible by Bayesian computation to estimate the isolated influence of particular variable such as carbon concentration, which exactly cannot in practice be varied independently. This shows the ability of the Bayesian neural network to examine the new phenomenon in situations where the data cannot be accessed through experiments.

Bayesian Inference of Allele-Specific Gene Expression Indicates Abundant Cis-Regulatory Variation in Natural Flycatcher Populations

PubMed Central

Wang, Mi

2017-01-01

Abstract Polymorphism in cis-regulatory sequences can lead to different levels of expression for the two alleles of a gene, providing a starting point for the evolution of gene expression. Little is known about the genome-wide abundance of genetic variation in gene regulation in natural populations but analysis of allele-specific expression (ASE) provides a means for investigating such variation. We performed RNA-seq of multiple tissues from population samples of two closely related flycatcher species and developed a Bayesian algorithm that maximizes data usage by borrowing information from the whole data set and combines several SNPs per transcript to detect ASE. Of 2,576 transcripts analyzed in collared flycatcher, ASE was detected in 185 (7.2%) and a similar frequency was seen in the pied flycatcher. Transcripts with statistically significant ASE commonly showed the major allele in >90% of the reads, reflecting that power was highest when expression was heavily biased toward one of the alleles. This would suggest that the observed frequencies of ASE likely are underestimates. The proportion of ASE transcripts varied among tissues, being lowest in testis and highest in muscle. Individuals often showed ASE of particular transcripts in more than one tissue (73.4%), consistent with a genetic basis for regulation of gene expression. The results suggest that genetic variation in regulatory sequences commonly affects gene expression in natural populations and that it provides a seedbed for phenotypic evolution via divergence in gene expression. PMID:28453623

A Bayesian model for quantifying the change in mortality associated with future ozone exposures under climate change.

PubMed

Alexeeff, Stacey E; Pfister, Gabriele G; Nychka, Doug

2016-03-01

Climate change is expected to have many impacts on the environment, including changes in ozone concentrations at the surface level. A key public health concern is the potential increase in ozone-related summertime mortality if surface ozone concentrations rise in response to climate change. Although ozone formation depends partly on summertime weather, which exhibits considerable inter-annual variability, previous health impact studies have not incorporated the variability of ozone into their prediction models. A major source of uncertainty in the health impacts is the variability of the modeled ozone concentrations. We propose a Bayesian model and Monte Carlo estimation method for quantifying health effects of future ozone. An advantage of this approach is that we include the uncertainty in both the health effect association and the modeled ozone concentrations. Using our proposed approach, we quantify the expected change in ozone-related summertime mortality in the contiguous United States between 2000 and 2050 under a changing climate. The mortality estimates show regional patterns in the expected degree of impact. We also illustrate the results when using a common technique in previous work that averages ozone to reduce the size of the data, and contrast these findings with our own. Our analysis yields more realistic inferences, providing clearer interpretation for decision making regarding the impacts of climate change. © 2015, The International Biometric Society.

Bayesian Estimation of Random Coefficient Dynamic Factor Models

ERIC Educational Resources Information Center

Song, Hairong; Ferrer, Emilio

2012-01-01

Dynamic factor models (DFMs) have typically been applied to multivariate time series data collected from a single unit of study, such as a single individual or dyad. The goal of DFMs application is to capture dynamics of multivariate systems. When multiple units are available, however, DFMs are not suited to capture variations in dynamics across…

Rage against the Machine: Evaluation Metrics in the 21st Century

ERIC Educational Resources Information Center

Yang, Charles

2017-01-01

I review the classic literature in generative grammar and Marr's three-level program for cognitive science to defend the Evaluation Metric as a psychological theory of language learning. Focusing on well-established facts of language variation, change, and use, I argue that optimal statistical principles embodied in Bayesian inference models are…

A Bayesian hierarchical model of environmental impact on human mortality and its spatial variation in the United States 2000-2005

EPA Science Inventory

Background/Question/Methods Many environmental factors influence human mortality simultaneously. However, assessing their cumulative effects remains a challenging task. In this study we used the Environmental Quality Index (EQI), developed by the U.S. EPA, as a measure of overall...

A Tutorial on Multiple Testing: False Discovery Control

NASA Astrophysics Data System (ADS)

Chatelain, F.

2016-09-01

This paper presents an overview of criteria and methods in multiple testing, with an emphasis on the false discovery rate control. The popular Benjamini and Hochberg procedure is described. The rationale for this approach is explained through a simple Bayesian interpretation. Some state-of-the-art variations and extensions are also presented.

Building Models to Predict Hint-or-Attempt Actions of Students

ERIC Educational Resources Information Center

Castro, Francisco Enrique Vicente; Adjei, Seth; Colombo, Tyler; Heffernan, Neil

2015-01-01

A great deal of research in educational data mining is geared towards predicting student performance. Bayesian Knowledge Tracing, Performance Factors Analysis, and the different variations of these have been introduced and have had some success at predicting student knowledge. It is worth noting, however, that very little has been done to…

Genetic architechture and biological basis for feed efficiency in dairy cattle

USDA-ARS?s Scientific Manuscript database

The genetic architecture of residual feed intake (RFI) and related traits was evaluated using a dataset of 2,894 cows. A Bayesian analysis estimated that markers accounted for 14% of the variance in RFI, and that RFI had considerable genetic variation. Effects of marker windows were small, but QTL p...

Methods for identifying SNP interactions: a review on variations of Logic Regression, Random Forest and Bayesian logistic regression.

PubMed

Chen, Carla Chia-Ming; Schwender, Holger; Keith, Jonathan; Nunkesser, Robin; Mengersen, Kerrie; Macrossan, Paula

2011-01-01

Due to advancements in computational ability, enhanced technology and a reduction in the price of genotyping, more data are being generated for understanding genetic associations with diseases and disorders. However, with the availability of large data sets comes the inherent challenges of new methods of statistical analysis and modeling. Considering a complex phenotype may be the effect of a combination of multiple loci, various statistical methods have been developed for identifying genetic epistasis effects. Among these methods, logic regression (LR) is an intriguing approach incorporating tree-like structures. Various methods have built on the original LR to improve different aspects of the model. In this study, we review four variations of LR, namely Logic Feature Selection, Monte Carlo Logic Regression, Genetic Programming for Association Studies, and Modified Logic Regression-Gene Expression Programming, and investigate the performance of each method using simulated and real genotype data. We contrast these with another tree-like approach, namely Random Forests, and a Bayesian logistic regression with stochastic search variable selection.

Algorithmic procedures for Bayesian MEG/EEG source reconstruction in SPM☆

PubMed Central

López, J.D.; Litvak, V.; Espinosa, J.J.; Friston, K.; Barnes, G.R.

2014-01-01

The MEG/EEG inverse problem is ill-posed, giving different source reconstructions depending on the initial assumption sets. Parametric Empirical Bayes allows one to implement most popular MEG/EEG inversion schemes (Minimum Norm, LORETA, etc.) within the same generic Bayesian framework. It also provides a cost-function in terms of the variational Free energy—an approximation to the marginal likelihood or evidence of the solution. In this manuscript, we revisit the algorithm for MEG/EEG source reconstruction with a view to providing a didactic and practical guide. The aim is to promote and help standardise the development and consolidation of other schemes within the same framework. We describe the implementation in the Statistical Parametric Mapping (SPM) software package, carefully explaining each of its stages with the help of a simple simulated data example. We focus on the Multiple Sparse Priors (MSP) model, which we compare with the well-known Minimum Norm and LORETA models, using the negative variational Free energy for model comparison. The manuscript is accompanied by Matlab scripts to allow the reader to test and explore the underlying algorithm. PMID:24041874

Hierarchical Bayesian modeling of ionospheric TEC disturbances as non-stationary processes

NASA Astrophysics Data System (ADS)

Seid, Abdu Mohammed; Berhane, Tesfahun; Roininen, Lassi; Nigussie, Melessew

2018-03-01

We model regular and irregular variation of ionospheric total electron content as stationary and non-stationary processes, respectively. We apply the method developed to SCINDA GPS data set observed at Bahir Dar, Ethiopia (11.6 °N, 37.4 °E) . We use hierarchical Bayesian inversion with Gaussian Markov random process priors, and we model the prior parameters in the hyperprior. We use Matérn priors via stochastic partial differential equations, and use scaled Inv -χ2 hyperpriors for the hyperparameters. For drawing posterior estimates, we use Markov Chain Monte Carlo methods: Gibbs sampling and Metropolis-within-Gibbs for parameter and hyperparameter estimations, respectively. This allows us to quantify model parameter estimation uncertainties as well. We demonstrate the applicability of the method proposed using a synthetic test case. Finally, we apply the method to real GPS data set, which we decompose to regular and irregular variation components. The result shows that the approach can be used as an accurate ionospheric disturbance characterization technique that quantifies the total electron content variability with corresponding error uncertainties.

Efficient Bayesian experimental design for contaminant source identification

NASA Astrophysics Data System (ADS)

Zhang, Jiangjiang; Zeng, Lingzao; Chen, Cheng; Chen, Dingjiang; Wu, Laosheng

2015-01-01

In this study, an efficient full Bayesian approach is developed for the optimal sampling well location design and source parameters identification of groundwater contaminants. An information measure, i.e., the relative entropy, is employed to quantify the information gain from concentration measurements in identifying unknown parameters. In this approach, the sampling locations that give the maximum expected relative entropy are selected as the optimal design. After the sampling locations are determined, a Bayesian approach based on Markov Chain Monte Carlo (MCMC) is used to estimate unknown parameters. In both the design and estimation, the contaminant transport equation is required to be solved many times to evaluate the likelihood. To reduce the computational burden, an interpolation method based on the adaptive sparse grid is utilized to construct a surrogate for the contaminant transport equation. The approximated likelihood can be evaluated directly from the surrogate, which greatly accelerates the design and estimation process. The accuracy and efficiency of our approach are demonstrated through numerical case studies. It is shown that the methods can be used to assist in both single sampling location and monitoring network design for contaminant source identifications in groundwater.

Collinear Latent Variables in Multilevel Confirmatory Factor Analysis: A Comparison of Maximum Likelihood and Bayesian Estimations.

PubMed

Can, Seda; van de Schoot, Rens; Hox, Joop

2015-06-01

Because variables may be correlated in the social and behavioral sciences, multicollinearity might be problematic. This study investigates the effect of collinearity manipulated in within and between levels of a two-level confirmatory factor analysis by Monte Carlo simulation. Furthermore, the influence of the size of the intraclass correlation coefficient (ICC) and estimation method; maximum likelihood estimation with robust chi-squares and standard errors and Bayesian estimation, on the convergence rate are investigated. The other variables of interest were rate of inadmissible solutions and the relative parameter and standard error bias on the between level. The results showed that inadmissible solutions were obtained when there was between level collinearity and the estimation method was maximum likelihood. In the within level multicollinearity condition, all of the solutions were admissible but the bias values were higher compared with the between level collinearity condition. Bayesian estimation appeared to be robust in obtaining admissible parameters but the relative bias was higher than for maximum likelihood estimation. Finally, as expected, high ICC produced less biased results compared to medium ICC conditions.

Topics in Computational Bayesian Statistics With Applications to Hierarchical Models in Astronomy and Sociology

NASA Astrophysics Data System (ADS)

Sahai, Swupnil

This thesis includes three parts. The overarching theme is how to analyze structured hierarchical data, with applications to astronomy and sociology. The first part discusses how expectation propagation can be used to parallelize the computation when fitting big hierarchical bayesian models. This methodology is then used to fit a novel, nonlinear mixture model to ultraviolet radiation from various regions of the observable universe. The second part discusses how the Stan probabilistic programming language can be used to numerically integrate terms in a hierarchical bayesian model. This technique is demonstrated on supernovae data to significantly speed up convergence to the posterior distribution compared to a previous study that used a Gibbs-type sampler. The third part builds a formal latent kernel representation for aggregate relational data as a way to more robustly estimate the mixing characteristics of agents in a network. In particular, the framework is applied to sociology surveys to estimate, as a function of ego age, the age and sex composition of the personal networks of individuals in the United States.

Application of Bayesian inference to the study of hierarchical organization in self-organized complex adaptive systems

NASA Astrophysics Data System (ADS)

Knuth, K. H.

2001-05-01

We consider the application of Bayesian inference to the study of self-organized structures in complex adaptive systems. In particular, we examine the distribution of elements, agents, or processes in systems dominated by hierarchical structure. We demonstrate that results obtained by Caianiello [1] on Hierarchical Modular Systems (HMS) can be found by applying Jaynes' Principle of Group Invariance [2] to a few key assumptions about our knowledge of hierarchical organization. Subsequent application of the Principle of Maximum Entropy allows inferences to be made about specific systems. The utility of the Bayesian method is considered by examining both successes and failures of the hierarchical model. We discuss how Caianiello's original statements suffer from the Mind Projection Fallacy [3] and we restate his assumptions thus widening the applicability of the HMS model. The relationship between inference and statistical physics, described by Jaynes [4], is reiterated with the expectation that this realization will aid the field of complex systems research by moving away from often inappropriate direct application of statistical mechanics to a more encompassing inferential methodology.

Incorporating prior knowledge induced from stochastic differential equations in the classification of stochastic observations.

PubMed

Zollanvari, Amin; Dougherty, Edward R

2016-12-01

In classification, prior knowledge is incorporated in a Bayesian framework by assuming that the feature-label distribution belongs to an uncertainty class of feature-label distributions governed by a prior distribution. A posterior distribution is then derived from the prior and the sample data. An optimal Bayesian classifier (OBC) minimizes the expected misclassification error relative to the posterior distribution. From an application perspective, prior construction is critical. The prior distribution is formed by mapping a set of mathematical relations among the features and labels, the prior knowledge, into a distribution governing the probability mass across the uncertainty class. In this paper, we consider prior knowledge in the form of stochastic differential equations (SDEs). We consider a vector SDE in integral form involving a drift vector and dispersion matrix. Having constructed the prior, we develop the optimal Bayesian classifier between two models and examine, via synthetic experiments, the effects of uncertainty in the drift vector and dispersion matrix. We apply the theory to a set of SDEs for the purpose of differentiating the evolutionary history between two species.

Hierarchical Bayesian Logistic Regression to forecast metabolic control in type 2 DM patients.

PubMed

Dagliati, Arianna; Malovini, Alberto; Decata, Pasquale; Cogni, Giulia; Teliti, Marsida; Sacchi, Lucia; Cerra, Carlo; Chiovato, Luca; Bellazzi, Riccardo

2016-01-01

In this work we present our efforts in building a model able to forecast patients' changes in clinical conditions when repeated measurements are available. In this case the available risk calculators are typically not applicable. We propose a Hierarchical Bayesian Logistic Regression model, which allows taking into account individual and population variability in model parameters estimate. The model is used to predict metabolic control and its variation in type 2 diabetes mellitus. In particular we have analyzed a population of more than 1000 Italian type 2 diabetic patients, collected within the European project Mosaic. The results obtained in terms of Matthews Correlation Coefficient are significantly better than the ones gathered with standard logistic regression model, based on data pooling.

Deep Learning with Hierarchical Convolutional Factor Analysis

PubMed Central

Chen, Bo; Polatkan, Gungor; Sapiro, Guillermo; Blei, David; Dunson, David; Carin, Lawrence

2013-01-01

Unsupervised multi-layered (“deep”) models are considered for general data, with a particular focus on imagery. The model is represented using a hierarchical convolutional factor-analysis construction, with sparse factor loadings and scores. The computation of layer-dependent model parameters is implemented within a Bayesian setting, employing a Gibbs sampler and variational Bayesian (VB) analysis, that explicitly exploit the convolutional nature of the expansion. In order to address large-scale and streaming data, an online version of VB is also developed. The number of basis functions or dictionary elements at each layer is inferred from the data, based on a beta-Bernoulli implementation of the Indian buffet process. Example results are presented for several image-processing applications, with comparisons to related models in the literature. PMID:23787342

Collaborative autonomous sensing with Bayesians in the loop

NASA Astrophysics Data System (ADS)

Ahmed, Nisar

2016-10-01

There is a strong push to develop intelligent unmanned autonomy that complements human reasoning for applications as diverse as wilderness search and rescue, military surveillance, and robotic space exploration. More than just replacing humans for `dull, dirty and dangerous' work, autonomous agents are expected to cope with a whole host of uncertainties while working closely together with humans in new situations. The robotics revolution firmly established the primacy of Bayesian algorithms for tackling challenging perception, learning and decision-making problems. Since the next frontier of autonomy demands the ability to gather information across stretches of time and space that are beyond the reach of a single autonomous agent, the next generation of Bayesian algorithms must capitalize on opportunities to draw upon the sensing and perception abilities of humans-in/on-the-loop. This work summarizes our recent research toward harnessing `human sensors' for information gathering tasks. The basic idea behind is to allow human end users (i.e. non-experts in robotics, statistics, machine learning, etc.) to directly `talk to' the information fusion engine and perceptual processes aboard any autonomous agent. Our approach is grounded in rigorous Bayesian modeling and fusion of flexible semantic information derived from user-friendly interfaces, such as natural language chat and locative hand-drawn sketches. This naturally enables `plug and play' human sensing with existing probabilistic algorithms for planning and perception, and has been successfully demonstrated with human-robot teams in target localization applications.

Estimation of completeness magnitude with a Bayesian modeling of daily and weekly variations in earthquake detectability

NASA Astrophysics Data System (ADS)

Iwata, T.

2014-12-01

In the analysis of seismic activity, assessment of earthquake detectability of a seismic network is a fundamental issue. For this assessment, the completeness magnitude Mc, the minimum magnitude above which all earthquakes are recorded, is frequently estimated. In most cases, Mc is estimated for an earthquake catalog of duration longer than several weeks. However, owing to human activity, noise level in seismic data is higher on weekdays than on weekends, so that earthquake detectability has a weekly variation [e.g., Atef et al., 2009, BSSA]; the consideration of such a variation makes a significant contribution to the precise assessment of earthquake detectability and Mc. For a quantitative evaluation of the weekly variation, we introduced the statistical model of a magnitude-frequency distribution of earthquakes covering an entire magnitude range [Ogata & Katsura, 1993, GJI]. The frequency distribution is represented as the product of the Gutenberg-Richter law and a detection rate function. Then, the weekly variation in one of the model parameters, which corresponds to the magnitude where the detection rate of earthquakes is 50%, was estimated. Because earthquake detectability also have a daily variation [e.g., Iwata, 2013, GJI], and the weekly and daily variations were estimated simultaneously by adopting a modification of a Bayesian smoothing spline method for temporal change in earthquake detectability developed in Iwata [2014, Aust. N. Z. J. Stat.]. Based on the estimated variations in the parameter, the value of Mc was estimated. In this study, the Japan Meteorological Agency catalog from 2006 to 2010 was analyzed; this dataset is the same as analyzed in Iwata [2013] where only the daily variation in earthquake detectability was considered in the estimation of Mc. A rectangular grid with 0.1° intervals covering in and around Japan was deployed, and the value of Mc was estimated for each gridpoint. Consequently, a clear weekly variation was revealed; the detectability is better on Sundays than on the other days. The estimated spatial variation in Mc was compared with that estimated in Iwata [2013]; the maximum difference between Mc values with and without considering the weekly variation approximately equals to 0.2, suggesting the importance of accounting for the weekly variation in the estimation of Mc.

Probabilistic mapping of descriptive health status responses onto health state utilities using Bayesian networks: an empirical analysis converting SF-12 into EQ-5D utility index in a national US sample.

PubMed

Le, Quang A; Doctor, Jason N

2011-05-01

As quality-adjusted life years have become the standard metric in health economic evaluations, mapping health-profile or disease-specific measures onto preference-based measures to obtain quality-adjusted life years has become a solution when health utilities are not directly available. However, current mapping methods are limited due to their predictive validity, reliability, and/or other methodological issues. We employ probability theory together with a graphical model, called a Bayesian network, to convert health-profile measures into preference-based measures and to compare the results to those estimated with current mapping methods. A sample of 19,678 adults who completed both the 12-item Short Form Health Survey (SF-12v2) and EuroQoL 5D (EQ-5D) questionnaires from the 2003 Medical Expenditure Panel Survey was split into training and validation sets. Bayesian networks were constructed to explore the probabilistic relationships between each EQ-5D domain and 12 items of the SF-12v2. The EQ-5D utility scores were estimated on the basis of the predicted probability of each response level of the 5 EQ-5D domains obtained from the Bayesian inference process using the following methods: Monte Carlo simulation, expected utility, and most-likely probability. Results were then compared with current mapping methods including multinomial logistic regression, ordinary least squares, and censored least absolute deviations. The Bayesian networks consistently outperformed other mapping models in the overall sample (mean absolute error=0.077, mean square error=0.013, and R overall=0.802), in different age groups, number of chronic conditions, and ranges of the EQ-5D index. Bayesian networks provide a new robust and natural approach to map health status responses into health utility measures for health economic evaluations.

Analysis of the Bayesian Cramér-Rao lower bound in astrometry. Studying the impact of prior information in the location of an object

NASA Astrophysics Data System (ADS)

Echeverria, Alex; Silva, Jorge F.; Mendez, Rene A.; Orchard, Marcos

2016-10-01

Context. The best precision that can be achieved to estimate the location of a stellar-like object is a topic of permanent interest in the astrometric community. Aims: We analyze bounds for the best position estimation of a stellar-like object on a CCD detector array in a Bayesian setting where the position is unknown, but where we have access to a prior distribution. In contrast to a parametric setting where we estimate a parameter from observations, the Bayesian approach estimates a random object (I.e., the position is a random variable) from observations that are statistically dependent on the position. Methods: We characterize the Bayesian Cramér-Rao (CR) that bounds the minimum mean square error (MMSE) of the best estimator of the position of a point source on a linear CCD-like detector, as a function of the properties of detector, the source, and the background. Results: We quantify and analyze the increase in astrometric performance from the use of a prior distribution of the object position, which is not available in the classical parametric setting. This gain is shown to be significant for various observational regimes, in particular in the case of faint objects or when the observations are taken under poor conditions. Furthermore, we present numerical evidence that the MMSE estimator of this problem tightly achieves the Bayesian CR bound. This is a remarkable result, demonstrating that all the performance gains presented in our analysis can be achieved with the MMSE estimator. Conclusions: The Bayesian CR bound can be used as a benchmark indicator of the expected maximum positional precision of a set of astrometric measurements in which prior information can be incorporated. This bound can be achieved through the conditional mean estimator, in contrast to the parametric case where no unbiased estimator precisely reaches the CR bound.

Genet-specific DNA methylation probabilities detected in a spatial epigenetic analysis of a clonal plant population.

PubMed

Araki, Kiwako S; Kubo, Takuya; Kudoh, Hiroshi

2017-01-01

In sessile organisms such as plants, spatial genetic structures of populations show long-lasting patterns. These structures have been analyzed across diverse taxa to understand the processes that determine the genetic makeup of organismal populations. For many sessile organisms that mainly propagate via clonal spread, epigenetic status can vary between clonal individuals in the absence of genetic changes. However, fewer previous studies have explored the epigenetic properties in comparison to the genetic properties of natural plant populations. Here, we report the simultaneous evaluation of the spatial structure of genetic and epigenetic variation in a natural population of the clonal plant Cardamine leucantha. We applied a hierarchical Bayesian model to evaluate the effects of membership of a genet (a group of individuals clonally derived from a single seed) and vegetation cover on the epigenetic variation between ramets (clonal plants that are physiologically independent individuals). We sampled 332 ramets in a 20 m × 20 m study plot that contained 137 genets (identified using eight SSR markers). We detected epigenetic variation in DNA methylation at 24 methylation-sensitive amplified fragment length polymorphism (MS-AFLP) loci. There were significant genet effects at all 24 MS-AFLP loci in the distribution of subepiloci. Vegetation cover had no statistically significant effect on variation in the majority of MS-AFLP loci. The spatial aggregation of epigenetic variation is therefore largely explained by the aggregation of ramets that belong to the same genets. By applying hierarchical Bayesian analyses, we successfully identified a number of genet-specific changes in epigenetic status within a natural plant population in a complex context, where genotypes and environmental factors are unevenly distributed. This finding suggests that it requires further studies on the spatial epigenetic structure of natural populations of diverse organisms, particularly for sessile clonal species.

Applying spatio-temporal models to assess variations across health care areas and regions: Lessons from the decentralized Spanish National Health System.

PubMed

Librero, Julián; Ibañez, Berta; Martínez-Lizaga, Natalia; Peiró, Salvador; Bernal-Delgado, Enrique

2017-01-01

To illustrate the ability of hierarchical Bayesian spatio-temporal models in capturing different geo-temporal structures in order to explain hospital risk variations using three different conditions: Percutaneous Coronary Intervention (PCI), Colectomy in Colorectal Cancer (CCC) and Chronic Obstructive Pulmonary Disease (COPD). This is an observational population-based spatio-temporal study, from 2002 to 2013, with a two-level geographical structure, Autonomous Communities (AC) and Health Care Areas (HA). The Spanish National Health System, a quasi-federal structure with 17 regional governments (AC) with full responsibility in planning and financing, and 203 HA providing hospital and primary care to a defined population. A poisson-log normal mixed model in the Bayesian framework was fitted using the INLA efficient estimation procedure. The spatio-temporal hospitalization relative risks, the evolution of their variation, and the relative contribution (fraction of variation) of each of the model components (AC, HA, year and interaction AC-year). Following PCI-CCC-CODP order, the three conditions show differences in the initial hospitalization rates (from 4 to 21 per 10,000 person-years) and in their trends (upward, inverted V shape, downward). Most of the risk variation is captured by phenomena occurring at the HA level (fraction variance: 51.6, 54.7 and 56.9%). At AC level, the risk of PCI hospitalization follow a heterogeneous ascending dynamic (interaction AC-year: 17.7%), whereas in COPD the AC role is more homogenous and important (37%). In a system where the decisions loci are differentiated, the spatio-temporal modeling allows to assess the dynamic relative role of different levels of decision and their influence on health outcomes.

Inter-Ethnic/Racial Facial Variations: A Systematic Review and Bayesian Meta-Analysis of Photogrammetric Studies

PubMed Central

Wen, Yi Feng; Wong, Hai Ming; Lin, Ruitao; Yin, Guosheng; McGrath, Colman

2015-01-01

Background Numerous facial photogrammetric studies have been published around the world. We aimed to critically review these studies so as to establish population norms for various angular and linear facial measurements; and to determine inter-ethnic/racial facial variations. Methods and Findings A comprehensive and systematic search of PubMed, ISI Web of Science, Embase, and Scopus was conducted to identify facial photogrammetric studies published before December, 2014. Subjects of eligible studies were either Africans, Asians or Caucasians. A Bayesian hierarchical random effects model was developed to estimate posterior means and 95% credible intervals (CrI) for each measurement by ethnicity/race. Linear contrasts were constructed to explore inter-ethnic/racial facial variations. We identified 38 eligible studies reporting 11 angular and 18 linear facial measurements. Risk of bias of the studies ranged from 0.06 to 0.66. At the significance level of 0.05, African males were found to have smaller nasofrontal angle (posterior mean difference: 8.1°, 95% CrI: 2.2°–13.5°) compared to Caucasian males and larger nasofacial angle (7.4°, 0.1°–13.2°) compared to Asian males. Nasolabial angle was more obtuse in Caucasian females than in African (17.4°, 0.2°–35.3°) and Asian (9.1°, 0.4°–17.3°) females. Additional inter-ethnic/racial variations were revealed when the level of statistical significance was set at 0.10. Conclusions A comprehensive database for angular and linear facial measurements was established from existing studies using the statistical model and inter-ethnic/racial variations of facial features were observed. The results have implications for clinical practice and highlight the need and value for high quality photogrammetric studies. PMID:26247212

Inter-Ethnic/Racial Facial Variations: A Systematic Review and Bayesian Meta-Analysis of Photogrammetric Studies.

PubMed

Wen, Yi Feng; Wong, Hai Ming; Lin, Ruitao; Yin, Guosheng; McGrath, Colman

2015-01-01

Numerous facial photogrammetric studies have been published around the world. We aimed to critically review these studies so as to establish population norms for various angular and linear facial measurements; and to determine inter-ethnic/racial facial variations. A comprehensive and systematic search of PubMed, ISI Web of Science, Embase, and Scopus was conducted to identify facial photogrammetric studies published before December, 2014. Subjects of eligible studies were either Africans, Asians or Caucasians. A Bayesian hierarchical random effects model was developed to estimate posterior means and 95% credible intervals (CrI) for each measurement by ethnicity/race. Linear contrasts were constructed to explore inter-ethnic/racial facial variations. We identified 38 eligible studies reporting 11 angular and 18 linear facial measurements. Risk of bias of the studies ranged from 0.06 to 0.66. At the significance level of 0.05, African males were found to have smaller nasofrontal angle (posterior mean difference: 8.1°, 95% CrI: 2.2°-13.5°) compared to Caucasian males and larger nasofacial angle (7.4°, 0.1°-13.2°) compared to Asian males. Nasolabial angle was more obtuse in Caucasian females than in African (17.4°, 0.2°-35.3°) and Asian (9.1°, 0.4°-17.3°) females. Additional inter-ethnic/racial variations were revealed when the level of statistical significance was set at 0.10. A comprehensive database for angular and linear facial measurements was established from existing studies using the statistical model and inter-ethnic/racial variations of facial features were observed. The results have implications for clinical practice and highlight the need and value for high quality photogrammetric studies.

Self-optimized construction of transition rate matrices from accelerated atomistic simulations with Bayesian uncertainty quantification

NASA Astrophysics Data System (ADS)

Swinburne, Thomas D.; Perez, Danny

2018-05-01

A massively parallel method to build large transition rate matrices from temperature-accelerated molecular dynamics trajectories is presented. Bayesian Markov model analysis is used to estimate the expected residence time in the known state space, providing crucial uncertainty quantification for higher-scale simulation schemes such as kinetic Monte Carlo or cluster dynamics. The estimators are additionally used to optimize where exploration is performed and the degree of temperature acceleration on the fly, giving an autonomous, optimal procedure to explore the state space of complex systems. The method is tested against exactly solvable models and used to explore the dynamics of C15 interstitial defects in iron. Our uncertainty quantification scheme allows for accurate modeling of the evolution of these defects over timescales of several seconds.

Bayesian Inference of Natural Rankings in Incomplete Competition Networks

PubMed Central

Park, Juyong; Yook, Soon-Hyung

2014-01-01

Competition between a complex system's constituents and a corresponding reward mechanism based on it have profound influence on the functioning, stability, and evolution of the system. But determining the dominance hierarchy or ranking among the constituent parts from the strongest to the weakest – essential in determining reward and penalty – is frequently an ambiguous task due to the incomplete (partially filled) nature of competition networks. Here we introduce the “Natural Ranking,” an unambiguous ranking method applicable to a round robin tournament, and formulate an analytical model based on the Bayesian formula for inferring the expected mean and error of the natural ranking of nodes from an incomplete network. We investigate its potential and uses in resolving important issues of ranking by applying it to real-world competition networks. PMID:25163528

Validating Bayesian truth serum in large-scale online human experiments.

PubMed

Frank, Morgan R; Cebrian, Manuel; Pickard, Galen; Rahwan, Iyad

2017-01-01

Bayesian truth serum (BTS) is an exciting new method for improving honesty and information quality in multiple-choice survey, but, despite the method's mathematical reliance on large sample sizes, existing literature about BTS only focuses on small experiments. Combined with the prevalence of online survey platforms, such as Amazon's Mechanical Turk, which facilitate surveys with hundreds or thousands of participants, BTS must be effective in large-scale experiments for BTS to become a readily accepted tool in real-world applications. We demonstrate that BTS quantifiably improves honesty in large-scale online surveys where the "honest" distribution of answers is known in expectation on aggregate. Furthermore, we explore a marketing application where "honest" answers cannot be known, but find that BTS treatment impacts the resulting distributions of answers.

Assessing Requirements Volatility and Risk Using Bayesian Networks

NASA Technical Reports Server (NTRS)

Russell, Michael S.

2010-01-01

There are many factors that affect the level of requirements volatility a system experiences over its lifecycle and the risk that volatility imparts. Improper requirements generation, undocumented user expectations, conflicting design decisions, and anticipated / unanticipated world states are representative of these volatility factors. Combined, these volatility factors can increase programmatic risk and adversely affect successful system development. This paper proposes that a Bayesian Network can be used to support reasonable judgments concerning the most likely sources and types of requirements volatility a developing system will experience prior to starting development and by doing so it is possible to predict the level of requirements volatility the system will experience over its lifecycle. This assessment offers valuable insight to the system's developers, particularly by providing a starting point for risk mitigation planning and execution.

Trust from the past: Bayesian Personalized Ranking based Link Prediction in Knowledge Graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Baichuan; Choudhury, Sutanay; Al-Hasan, Mohammad

2016-02-01

Estimating the confidence for a link is a critical task for Knowledge Graph construction. Link prediction, or predicting the likelihood of a link in a knowledge graph based on prior state is a key research direction within this area. We propose a Latent Feature Embedding based link recommendation model for prediction task and utilize Bayesian Personalized Ranking based optimization technique for learning models for each predicate. Experimental results on large-scale knowledge bases such as YAGO2 show that our approach achieves substantially higher performance than several state-of-art approaches. Furthermore, we also study the performance of the link prediction algorithm in termsmore » of topological properties of the Knowledge Graph and present a linear regression model to reason about its expected level of accuracy.« less

Validating Bayesian truth serum in large-scale online human experiments

PubMed Central

Frank, Morgan R.; Cebrian, Manuel; Pickard, Galen; Rahwan, Iyad

2017-01-01

Bayesian truth serum (BTS) is an exciting new method for improving honesty and information quality in multiple-choice survey, but, despite the method’s mathematical reliance on large sample sizes, existing literature about BTS only focuses on small experiments. Combined with the prevalence of online survey platforms, such as Amazon’s Mechanical Turk, which facilitate surveys with hundreds or thousands of participants, BTS must be effective in large-scale experiments for BTS to become a readily accepted tool in real-world applications. We demonstrate that BTS quantifiably improves honesty in large-scale online surveys where the “honest” distribution of answers is known in expectation on aggregate. Furthermore, we explore a marketing application where “honest” answers cannot be known, but find that BTS treatment impacts the resulting distributions of answers. PMID:28494000

Bayesian Inference of Natural Rankings in Incomplete Competition Networks

NASA Astrophysics Data System (ADS)

Park, Juyong; Yook, Soon-Hyung

2014-08-01

Competition between a complex system's constituents and a corresponding reward mechanism based on it have profound influence on the functioning, stability, and evolution of the system. But determining the dominance hierarchy or ranking among the constituent parts from the strongest to the weakest - essential in determining reward and penalty - is frequently an ambiguous task due to the incomplete (partially filled) nature of competition networks. Here we introduce the ``Natural Ranking,'' an unambiguous ranking method applicable to a round robin tournament, and formulate an analytical model based on the Bayesian formula for inferring the expected mean and error of the natural ranking of nodes from an incomplete network. We investigate its potential and uses in resolving important issues of ranking by applying it to real-world competition networks.

Rate variation and estimation of divergence times using strict and relaxed clocks.

PubMed

Brown, Richard P; Yang, Ziheng

2011-09-26

Understanding causes of biological diversity may be greatly enhanced by knowledge of divergence times. Strict and relaxed clock models are used in Bayesian estimation of divergence times. We examined whether: i) strict clock models are generally more appropriate in shallow phylogenies where rate variation is expected to be low, ii) the likelihood ratio test of the clock (LRT) reliably informs which model is appropriate for dating divergence times. Strict and relaxed models were used to analyse sequences simulated under different levels of rate variation. Published shallow phylogenies (Black bass, Primate-sucking lice, Podarcis lizards, Gallotiinae lizards, and Caprinae mammals) were also analysed to determine natural levels of rate variation relative to the performance of the different models. Strict clock analyses performed well on data simulated under the independent rates model when the standard deviation of log rate on branches, σ, was low (≤ 0.1), but were inappropriate when σ>0.1 (95% of rates fall within 0.0082-0.0121 subs/site/Ma when σ = 0.1, for a mean rate of 0.01). The independent rates relaxed clock model performed well at all levels of rate variation, although posterior intervals on times were significantly wider than for the strict clock. The strict clock is therefore superior when rate variation is low. The performance of a correlated rates relaxed clock model was similar to the strict clock. Increased numbers of independent loci led to slightly narrower posteriors under the relaxed clock while older root ages provided proportionately narrower posteriors. The LRT had low power for σ = 0.01-0.1, but high power for σ = 0.5-2.0. Posterior means of σ2 were useful for assessing rate variation in published datasets. Estimates of natural levels of rate variation ranged from 0.05-3.38 for different partitions. Differences in divergence times between relaxed and strict clock analyses were greater in two datasets with higher σ2 for one or more partitions, supporting the simulation results. The strict clock can be superior for trees with shallow roots because of low levels of rate variation between branches. The LRT allows robust assessment of suitability of the clock model as does examination of posteriors on σ2.

Bayesian Mapping Reveals That Attention Boosts Neural Responses to Predicted and Unpredicted Stimuli.

PubMed

Garrido, Marta I; Rowe, Elise G; Halász, Veronika; Mattingley, Jason B

2018-05-01

Predictive coding posits that the human brain continually monitors the environment for regularities and detects inconsistencies. It is unclear, however, what effect attention has on expectation processes, as there have been relatively few studies and the results of these have yielded contradictory findings. Here, we employed Bayesian model comparison to adjudicate between 2 alternative computational models. The "Opposition" model states that attention boosts neural responses equally to predicted and unpredicted stimuli, whereas the "Interaction" model assumes that attentional boosting of neural signals depends on the level of predictability. We designed a novel, audiospatial attention task that orthogonally manipulated attention and prediction by playing oddball sequences in either the attended or unattended ear. We observed sensory prediction error responses, with electroencephalography, across all attentional manipulations. Crucially, posterior probability maps revealed that, overall, the Opposition model better explained scalp and source data, suggesting that attention boosts responses to predicted and unpredicted stimuli equally. Furthermore, Dynamic Causal Modeling showed that these Opposition effects were expressed in plastic changes within the mismatch negativity network. Our findings provide empirical evidence for a computational model of the opposing interplay of attention and expectation in the brain.

Evidence of major genes affecting resistance to bacterial cold water disease in rainbow trout using Bayesian methods of segregation analysis

USDA-ARS?s Scientific Manuscript database

Bacterial cold water disease (BCWD) causes significant economic loss in salmonid aquaculture. We previously detected genetic variation for BCWD resistance in our rainbow trout population, and a family-based selection program to improve resistance was initiated at the National Center for Cool and Col...

Whole genome analysis using Bayesian models to identify candidate genes for immune response to vaccination

USDA-ARS?s Scientific Manuscript database

This study identified genome regions associated with variation in immune response to vaccination against bovine viral diarrhea virus type 2 (BVDV 2) in American Angus calves. Calves were born in the spring or fall of 2006-2008 (n = 620). Two doses of modified live vaccine were administered three wee...

Evidence of major genes affecting bacterial cold water disease resistance in rainbow trout using Bayesian methods of complex segregation analysis

USDA-ARS?s Scientific Manuscript database

Bacterial cold water disease (BCWD) causes significant economic loss in salmonid aquaculture. We previously detected genetic variation for BCWD resistance in our rainbow trout population, and a family-based selection program to improve resistance was initiated at the NCCCWA in 2005. The main objec...

A novel Bayesian approach to quantify clinical variables and to determine their spectroscopic counterparts in 1H NMR metabonomic data

PubMed Central

Vehtari, Aki; Mäkinen, Ville-Petteri; Soininen, Pasi; Ingman, Petri; Mäkelä, Sanna M; Savolainen, Markku J; Hannuksela, Minna L; Kaski, Kimmo; Ala-Korpela, Mika

2007-01-01

Background A key challenge in metabonomics is to uncover quantitative associations between multidimensional spectroscopic data and biochemical measures used for disease risk assessment and diagnostics. Here we focus on clinically relevant estimation of lipoprotein lipids by 1H NMR spectroscopy of serum. Results A Bayesian methodology, with a biochemical motivation, is presented for a real 1H NMR metabonomics data set of 75 serum samples. Lipoprotein lipid concentrations were independently obtained for these samples via ultracentrifugation and specific biochemical assays. The Bayesian models were constructed by Markov chain Monte Carlo (MCMC) and they showed remarkably good quantitative performance, the predictive R-values being 0.985 for the very low density lipoprotein triglycerides (VLDL-TG), 0.787 for the intermediate, 0.943 for the low, and 0.933 for the high density lipoprotein cholesterol (IDL-C, LDL-C and HDL-C, respectively). The modelling produced a kernel-based reformulation of the data, the parameters of which coincided with the well-known biochemical characteristics of the 1H NMR spectra; particularly for VLDL-TG and HDL-C the Bayesian methodology was able to clearly identify the most characteristic resonances within the heavily overlapping information in the spectra. For IDL-C and LDL-C the resulting model kernels were more complex than those for VLDL-TG and HDL-C, probably reflecting the severe overlap of the IDL and LDL resonances in the 1H NMR spectra. Conclusion The systematic use of Bayesian MCMC analysis is computationally demanding. Nevertheless, the combination of high-quality quantification and the biochemical rationale of the resulting models is expected to be useful in the field of metabonomics. PMID:17493257

Fine-scale genetic population structure in a mobile marine mammal: inshore bottlenose dolphins in Moreton Bay, Australia.

PubMed

Ansmann, Ina C; Parra, Guido J; Lanyon, Janet M; Seddon, Jennifer M

2012-09-01

Highly mobile marine species in areas with no obvious geographic barriers are expected to show low levels of genetic differentiation. However, small-scale variation in habitat may lead to resource polymorphisms and drive local differentiation by adaptive divergence. Using nuclear microsatellite genotyping at 20 loci, and mitochondrial control region sequencing, we investigated fine-scale population structuring of inshore bottlenose dolphins (Tursiops aduncus) inhabiting a range of habitats in and around Moreton Bay, Australia. Bayesian structure analysis identified two genetic clusters within Moreton Bay, with evidence of admixture between them (F(ST) = 0.05, P = 0.001). There was only weak isolation by distance but one cluster of dolphins was more likely to be found in shallow southern areas and the other in the deeper waters of the central northern bay. In further analysis removing admixed individuals, southern dolphins appeared genetically restricted with lower levels of variation (AR = 3.252, π = 0.003) and high mean relatedness (r = 0.239) between individuals. In contrast, northern dolphins were more diverse (AR = 4.850, π = 0.009) and were mixing with a group of dolphins outside the bay (microsatellite-based STRUCTURE analysis), which appears to have historically been distinct from the bay dolphins (mtDNA Φ(ST) = 0.272, P < 0.001). This study demonstrates the ability of genetic techniques to expose fine-scale patterns of population structure and explore their origins and mechanisms. A complex variety of inter-related factors including local habitat variation, differential resource use, social behaviour and learning, and anthropogenic disturbances are likely to have played a role in driving fine-scale population structure among bottlenose dolphins in Moreton Bay. © 2012 Blackwell Publishing Ltd.

Probabilistic delay differential equation modeling of event-related potentials.

PubMed

Ostwald, Dirk; Starke, Ludger

2016-08-01

"Dynamic causal models" (DCMs) are a promising approach in the analysis of functional neuroimaging data due to their biophysical interpretability and their consolidation of functional-segregative and functional-integrative propositions. In this theoretical note we are concerned with the DCM framework for electroencephalographically recorded event-related potentials (ERP-DCM). Intuitively, ERP-DCM combines deterministic dynamical neural mass models with dipole-based EEG forward models to describe the event-related scalp potential time-series over the entire electrode space. Since its inception, ERP-DCM has been successfully employed to capture the neural underpinnings of a wide range of neurocognitive phenomena. However, in spite of its empirical popularity, the technical literature on ERP-DCM remains somewhat patchy. A number of previous communications have detailed certain aspects of the approach, but no unified and coherent documentation exists. With this technical note, we aim to close this gap and to increase the technical accessibility of ERP-DCM. Specifically, this note makes the following novel contributions: firstly, we provide a unified and coherent review of the mathematical machinery of the latent and forward models constituting ERP-DCM by formulating the approach as a probabilistic latent delay differential equation model. Secondly, we emphasize the probabilistic nature of the model and its variational Bayesian inversion scheme by explicitly deriving the variational free energy function in terms of both the likelihood expectation and variance parameters. Thirdly, we detail and validate the estimation of the model with a special focus on the explicit form of the variational free energy function and introduce a conventional nonlinear optimization scheme for its maximization. Finally, we identify and discuss a number of computational issues which may be addressed in the future development of the approach. Copyright © 2016 Elsevier Inc. All rights reserved.

Effect of database profile variation on drug safety assessment: an analysis of spontaneous adverse event reports of Japanese cases

PubMed Central

Nomura, Kaori; Takahashi, Kunihiko; Hinomura, Yasushi; Kawaguchi, Genta; Matsushita, Yasuyuki; Marui, Hiroko; Anzai, Tatsuhiko; Hashiguchi, Masayuki; Mochizuki, Mayumi

2015-01-01

Background The use of a statistical approach to analyze cumulative adverse event (AE) reports has been encouraged by regulatory authorities. However, data variations affect statistical analyses (eg, signal detection). Further, differences in regulations, social issues, and health care systems can cause variations in AE data. The present study examined similarities and differences between two publicly available databases, ie, the Japanese Adverse Drug Event Report (JADER) database and the US Food and Drug Administration Adverse Event Reporting System (FAERS), and how they affect signal detection. Methods Two AE data sources from 2010 were examined, ie, JADER cases (JP) and Japanese cases extracted from the FAERS (FAERS-JP). Three methods for signals of disproportionate reporting, ie, the reporting odds ratio, Bayesian confidence propagation neural network, and Gamma Poisson Shrinker (GPS), were used on drug-event combinations for three substances frequently recorded in both systems. Results The two databases showed similar elements of AE reports, but no option was provided for a shareable case identifier. The average number of AEs per case was 1.6±1.3 (maximum 37) in the JP and 3.3±3.5 (maximum 62) in the FAERS-JP. Between 5% and 57% of all AEs were signaled by three quantitative methods for etanercept, infliximab, and paroxetine. Signals identified by GPS for the JP and FAERS-JP, as referenced by Japanese labeling, showed higher positive sensitivity than was expected. Conclusion The FAERS-JP was different from the JADER. Signals derived from both datasets identified different results, but shared certain signals. Discrepancies in type of AEs, drugs reported, and average number of AEs per case were potential contributing factors. This study will help those concerned with pharmacovigilance better understand the use and pitfalls of using spontaneous AE data. PMID:26109846

Experimental design and Bayesian networks for enhancement of delta-endotoxin production by Bacillus thuringiensis.

PubMed

Ennouri, Karim; Ayed, Rayda Ben; Hassen, Hanen Ben; Mazzarello, Maura; Ottaviani, Ennio

2015-12-01

Bacillus thuringiensis (Bt) is a Gram-positive bacterium. The entomopathogenic activity of Bt is related to the existence of the crystal consisting of protoxins, also called delta-endotoxins. In order to optimize and explain the production of delta-endotoxins of Bacillus thuringiensis kurstaki, we studied seven medium components: soybean meal, starch, KH₂PO₄, K₂HPO₄, FeSO₄, MnSO₄, and MgSO₄and their relationships with the concentration of delta-endotoxins using an experimental design (Plackett-Burman design) and Bayesian networks modelling. The effects of the ingredients of the culture medium on delta-endotoxins production were estimated. The developed model showed that different medium components are important for the Bacillus thuringiensis fermentation. The most important factors influenced the production of delta-endotoxins are FeSO₄, K2HPO₄, starch and soybean meal. Indeed, it was found that soybean meal, K₂HPO₄, KH₂PO₄and starch also showed positive effect on the delta-endotoxins production. However, FeSO4 and MnSO4 expressed opposite effect. The developed model, based on Bayesian techniques, can automatically learn emerging models in data to serve in the prediction of delta-endotoxins concentrations. The constructed model in the present study implies that experimental design (Plackett-Burman design) joined with Bayesian networks method could be used for identification of effect variables on delta-endotoxins variation.

Genetic variation and structure in remnant population of critically endangered Melicope zahlbruckneri

USGS Publications Warehouse

Raji, J. A.; Atkinson, Carter T.

2016-01-01

The distribution and amount of genetic variation within and between populations of plant species are important for their adaptability to future habitat changes and also critical for their restoration and overall management. This study was initiated to assess the genetic status of the remnant population of Melicope zahlbruckneri–a critically endangered species in Hawaii, and determine the extent of genetic variation and diversity in order to propose valuable conservation approaches. Estimated genetic structure of individuals based on molecular marker allele frequencies identified genetic groups with low overall differentiation but identified the most genetically diverse individuals within the population. Analysis of Amplified Fragment Length Polymorphic (AFLP) marker loci in the population based on Bayesian model and multivariate statistics classified the population into four subgroups. We inferred a mixed species population structure based on Bayesian clustering and frequency of unique alleles. The percentage of Polymorphic Fragment (PPF) ranged from 18.8 to 64.6% for all marker loci with an average of 54.9% within the population. Inclusion of all surviving M. zahlbruckneri trees in future restorative planting at new sites are suggested, and approaches for longer term maintenance of genetic variability are discussed. To our knowledge, this study represents the first report of molecular genetic analysis of the remaining population of M. zahlbruckneri and also illustrates the importance of genetic variability for conservation of a small endangered population.

Novel health economic evaluation of a vaccination strategy to prevent HPV-related diseases: the BEST study.

PubMed

Favato, Giampiero; Baio, Gianluca; Capone, Alessandro; Marcellusi, Andrea; Costa, Silvano; Garganese, Giorgia; Picardo, Mauro; Drummond, Mike; Jonsson, Bengt; Scambia, Giovanni; Zweifel, Peter; Mennini, Francesco S

2012-12-01

The development of human papillomavirus (HPV)-related diseases is not understood perfectly and uncertainties associated with commonly utilized probabilistic models must be considered. The study assessed the cost-effectiveness of a quadrivalent-based multicohort HPV vaccination strategy within a Bayesian framework. A full Bayesian multicohort Markov model was used, in which all unknown quantities were associated with suitable probability distributions reflecting the state of currently available knowledge. These distributions were informed by observed data or expert opinion. The model cycle lasted 1 year, whereas the follow-up time horizon was 90 years. Precancerous cervical lesions, cervical cancers, and anogenital warts were considered as outcomes. The base case scenario (2 cohorts of girls aged 12 and 15 y) and other multicohort vaccination strategies (additional cohorts aged 18 and 25 y) were cost-effective, with a discounted cost per quality-adjusted life-year gained that corresponded to €12,013, €13,232, and €15,890 for vaccination programs based on 2, 3, and 4 cohorts, respectively. With multicohort vaccination strategies, the reduction in the number of HPV-related events occurred earlier (range, 3.8-6.4 y) when compared with a single cohort. The analysis of the expected value of information showed that the results of the model were subject to limited uncertainty (cost per patient = €12.6). This methodological approach is designed to incorporate the uncertainty associated with HPV vaccination. Modeling the cost-effectiveness of a multicohort vaccination program with Bayesian statistics confirmed the value for money of quadrivalent-based HPV vaccination. The expected value of information gave the most appropriate and feasible representation of the true value of this program.

Bayesian assessment of the expected data impact on prediction confidence in optimal sampling design

NASA Astrophysics Data System (ADS)

Leube, P. C.; Geiges, A.; Nowak, W.

2012-02-01

Incorporating hydro(geo)logical data, such as head and tracer data, into stochastic models of (subsurface) flow and transport helps to reduce prediction uncertainty. Because of financial limitations for investigation campaigns, information needs toward modeling or prediction goals should be satisfied efficiently and rationally. Optimal design techniques find the best one among a set of investigation strategies. They optimize the expected impact of data on prediction confidence or related objectives prior to data collection. We introduce a new optimal design method, called PreDIA(gnosis) (Preposterior Data Impact Assessor). PreDIA derives the relevant probability distributions and measures of data utility within a fully Bayesian, generalized, flexible, and accurate framework. It extends the bootstrap filter (BF) and related frameworks to optimal design by marginalizing utility measures over the yet unknown data values. PreDIA is a strictly formal information-processing scheme free of linearizations. It works with arbitrary simulation tools, provides full flexibility concerning measurement types (linear, nonlinear, direct, indirect), allows for any desired task-driven formulations, and can account for various sources of uncertainty (e.g., heterogeneity, geostatistical assumptions, boundary conditions, measurement values, model structure uncertainty, a large class of model errors) via Bayesian geostatistics and model averaging. Existing methods fail to simultaneously provide these crucial advantages, which our method buys at relatively higher-computational costs. We demonstrate the applicability and advantages of PreDIA over conventional linearized methods in a synthetic example of subsurface transport. In the example, we show that informative data is often invisible for linearized methods that confuse zero correlation with statistical independence. Hence, PreDIA will often lead to substantially better sampling designs. Finally, we extend our example to specifically highlight the consideration of conceptual model uncertainty.

Neural Mechanisms of Updating under Reducible and Irreducible Uncertainty.

PubMed

Kobayashi, Kenji; Hsu, Ming

2017-07-19

Adaptive decision making depends on an agent's ability to use environmental signals to reduce uncertainty. However, because of multiple types of uncertainty, agents must take into account not only the extent to which signals violate prior expectations but also whether uncertainty can be reduced in the first place. Here we studied how human brains of both sexes respond to signals under conditions of reducible and irreducible uncertainty. We show behaviorally that subjects' value updating was sensitive to the reducibility of uncertainty, and could be quantitatively characterized by a Bayesian model where agents ignore expectancy violations that do not update beliefs or values. Using fMRI, we found that neural processes underlying belief and value updating were separable from responses to expectancy violation, and that reducibility of uncertainty in value modulated connections from belief-updating regions to value-updating regions. Together, these results provide insights into how agents use knowledge about uncertainty to make better decisions while ignoring mere expectancy violation. SIGNIFICANCE STATEMENT To make good decisions, a person must observe the environment carefully, and use these observations to reduce uncertainty about consequences of actions. Importantly, uncertainty should not be reduced purely based on how surprising the observations are, particularly because in some cases uncertainty is not reducible. Here we show that the human brain indeed reduces uncertainty adaptively by taking into account the nature of uncertainty and ignoring mere surprise. Behaviorally, we show that human subjects reduce uncertainty in a quasioptimal Bayesian manner. Using fMRI, we characterize brain regions that may be involved in uncertainty reduction, as well as the network they constitute, and dissociate them from brain regions that respond to mere surprise. Copyright © 2017 the authors 0270-6474/17/376972-11$15.00/0.

Neural Mechanisms of Updating under Reducible and Irreducible Uncertainty

PubMed Central

2017-01-01

Adaptive decision making depends on an agent's ability to use environmental signals to reduce uncertainty. However, because of multiple types of uncertainty, agents must take into account not only the extent to which signals violate prior expectations but also whether uncertainty can be reduced in the first place. Here we studied how human brains of both sexes respond to signals under conditions of reducible and irreducible uncertainty. We show behaviorally that subjects' value updating was sensitive to the reducibility of uncertainty, and could be quantitatively characterized by a Bayesian model where agents ignore expectancy violations that do not update beliefs or values. Using fMRI, we found that neural processes underlying belief and value updating were separable from responses to expectancy violation, and that reducibility of uncertainty in value modulated connections from belief-updating regions to value-updating regions. Together, these results provide insights into how agents use knowledge about uncertainty to make better decisions while ignoring mere expectancy violation. SIGNIFICANCE STATEMENT To make good decisions, a person must observe the environment carefully, and use these observations to reduce uncertainty about consequences of actions. Importantly, uncertainty should not be reduced purely based on how surprising the observations are, particularly because in some cases uncertainty is not reducible. Here we show that the human brain indeed reduces uncertainty adaptively by taking into account the nature of uncertainty and ignoring mere surprise. Behaviorally, we show that human subjects reduce uncertainty in a quasioptimal Bayesian manner. Using fMRI, we characterize brain regions that may be involved in uncertainty reduction, as well as the network they constitute, and dissociate them from brain regions that respond to mere surprise. PMID:28626019

Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies.

PubMed

Chen, Bo; Chen, Minhua; Paisley, John; Zaas, Aimee; Woods, Christopher; Ginsburg, Geoffrey S; Hero, Alfred; Lucas, Joseph; Dunson, David; Carin, Lawrence

2010-11-09

Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data.

Prediction and assimilation of surf-zone processes using a Bayesian network: Part II: Inverse models

USGS Publications Warehouse

Plant, Nathaniel G.; Holland, K. Todd

2011-01-01

A Bayesian network model has been developed to simulate a relatively simple problem of wave propagation in the surf zone (detailed in Part I). Here, we demonstrate that this Bayesian model can provide both inverse modeling and data-assimilation solutions for predicting offshore wave heights and depth estimates given limited wave-height and depth information from an onshore location. The inverse method is extended to allow data assimilation using observational inputs that are not compatible with deterministic solutions of the problem. These inputs include sand bar positions (instead of bathymetry) and estimates of the intensity of wave breaking (instead of wave-height observations). Our results indicate that wave breaking information is essential to reduce prediction errors. In many practical situations, this information could be provided from a shore-based observer or from remote-sensing systems. We show that various combinations of the assimilated inputs significantly reduce the uncertainty in the estimates of water depths and wave heights in the model domain. Application of the Bayesian network model to new field data demonstrated significant predictive skill (R2 = 0.7) for the inverse estimate of a month-long time series of offshore wave heights. The Bayesian inverse results include uncertainty estimates that were shown to be most accurate when given uncertainty in the inputs (e.g., depth and tuning parameters). Furthermore, the inverse modeling was extended to directly estimate tuning parameters associated with the underlying wave-process model. The inverse estimates of the model parameters not only showed an offshore wave height dependence consistent with results of previous studies but the uncertainty estimates of the tuning parameters also explain previously reported variations in the model parameters.

King eider use an income strategy for egg production: a case study for incorporating individual dietary variation into nutrient allocation research

USGS Publications Warehouse

Oppel, Steffen; Powell, Abby N.; O'Brien, Diane M.

2010-01-01

The use of stored nutrients for reproduction represents an important component of life-history variation. Recent studies from several species have used stable isotopes to estimate the reliance on stored body reserves in reproduction. Such approaches rely on population-level dietary endpoints to characterize stored reserves (“capital”) and current diet (“income”). Individual variation in diet choice has so far not been incorporated in such approaches, but is crucial for assessing variation in nutrient allocation strategies. We investigated nutrient allocation to egg production in a large-bodied sea duck in northern Alaska, the king eider (Somateria spectabilis). We first used Bayesian isotopic mixing models to quantify at the population level the amount of endogenous carbon and nitrogen invested into egg proteins based on carbon and nitrogen isotope ratios. We then defined the isotopic signature of the current diet of every nesting female based on isotope ratios of eggshell membranes, because diets varied isotopically among individual king eiders on breeding grounds. We used these individual-based dietary isotope signals to characterize nutrient allocation for each female in the study population. At the population level, the Bayesian and the individual-based approaches yielded identical results, and showed that king eiders used an income strategy for the synthesis of egg proteins. The majority of the carbon and nitrogen in albumen (C: 86 ± 18%, N: 99 ± 1%) and the nitrogen in lipid-free yolk (90 ± 15%) were derived from food consumed on breeding grounds. Carbon in lipid-free yolk derived evenly from endogenous sources and current diet (exogenous C: 54 ± 24%), but source contribution was highly variable among individual females. These results suggest that even large-bodied birds traditionally viewed as capital breeders use exogenous nutrients for reproduction. We recommend that investigations of nutrient allocation should incorporate individual variation into mixing models to reveal intraspecific variation in reproductive strategies.

Biogeographic discordance of molecular phylogenetic and phenotypic variation in a continental archipelago radiation of land snails.

PubMed

Stankowski, Sean; Johnson, Michael S

2014-01-07

In island archipelagos, where islands have experienced repeated periods of fragmentation and connection through cyclic changes in sea level, complex among-island distributions might reflect historical distributional changes or local evolution. We test the relative importance of these mechanisms in an endemic radiation of Rhagada land snails in the Dampier Archipelago, a continental archipelago off the coast of Western Australia, where ten morphospecies have complex, overlapping distributions. We obtained partial mtDNA sequence (COI) for 1015 snails collected from 213 locations across 30 Islands, and used Bayesian phylogenetic analysis and Analysis of Molecular Variance (AMOVA) to determine whether geography or the morphological taxonomy best explains the pattern of molecular evolution. Rather than forming distinct monophyletic groups, as would be expected if they had single, independent origins, all of the widely distributed morphospecies were polyphyletic, distributed among several well-supported clades, each of which included several morphospecies. Each mitochondrial clade had a clear, cohesive geographic distribution, together forming a series of parapatric replacements separated by narrow contact zones. AMOVA revealed further incongruence between mtDNA diversity and morphological variation within clades, as the taxonomic hypothesis always explained a low or non-significant proportion of the molecular variation. In contrast, the pattern of mtDNA evolution closely reflected contemporary and historical marine barriers. Despite opportunities for distributional changes during periods when the islands were connected, there is no evidence that dispersal has contributed to the geographic variation of shell form at the broad scale. Based on an estimate of dispersal made previously for Rhagada, we conclude that the periods of connection have been too short in duration to allow for extensive overland dispersal or deep mitochondrial introgression. The result is a sharp and resilient phylogeographic pattern. The distribution of morphotypes among clades and distant islands is explained most simply by their parallel evolution.

Biogeographic discordance of molecular phylogenetic and phenotypic variation in a continental archipelago radiation of land snails

PubMed Central

2014-01-01

Background In island archipelagos, where islands have experienced repeated periods of fragmentation and connection through cyclic changes in sea level, complex among-island distributions might reflect historical distributional changes or local evolution. We test the relative importance of these mechanisms in an endemic radiation of Rhagada land snails in the Dampier Archipelago, a continental archipelago off the coast of Western Australia, where ten morphospecies have complex, overlapping distributions. Results We obtained partial mtDNA sequence (COI) for 1015 snails collected from 213 locations across 30 Islands, and used Bayesian phylogenetic analysis and Analysis of Molecular Variance (AMOVA) to determine whether geography or the morphological taxonomy best explains the pattern of molecular evolution. Rather than forming distinct monophyletic groups, as would be expected if they had single, independent origins, all of the widely distributed morphospecies were polyphyletic, distributed among several well-supported clades, each of which included several morphospecies. Each mitochondrial clade had a clear, cohesive geographic distribution, together forming a series of parapatric replacements separated by narrow contact zones. AMOVA revealed further incongruence between mtDNA diversity and morphological variation within clades, as the taxonomic hypothesis always explained a low or non-significant proportion of the molecular variation. In contrast, the pattern of mtDNA evolution closely reflected contemporary and historical marine barriers. Conclusions Despite opportunities for distributional changes during periods when the islands were connected, there is no evidence that dispersal has contributed to the geographic variation of shell form at the broad scale. Based on an estimate of dispersal made previously for Rhagada, we conclude that the periods of connection have been too short in duration to allow for extensive overland dispersal or deep mitochondrial introgression. The result is a sharp and resilient phylogeographic pattern. The distribution of morphotypes among clades and distant islands is explained most simply by their parallel evolution. PMID:24393567

Robust cue integration: a Bayesian model and evidence from cue-conflict studies with stereoscopic and figure cues to slant.

PubMed

Knill, David C

2007-05-23

Most research on depth cue integration has focused on stimulus regimes in which stimuli contain the small cue conflicts that one might expect to normally arise from sensory noise. In these regimes, linear models for cue integration provide a good approximation to system performance. This article focuses on situations in which large cue conflicts can naturally occur in stimuli. We describe a Bayesian model for nonlinear cue integration that makes rational inferences about scenes across the entire range of possible cue conflicts. The model derives from the simple intuition that multiple properties of scenes or causal factors give rise to the image information associated with most cues. To make perceptual inferences about one property of a scene, an ideal observer must necessarily take into account the possible contribution of these other factors to the information provided by a cue. In the context of classical depth cues, large cue conflicts most commonly arise when one or another cue is generated by an object or scene that violates the strongest form of constraint that makes the cue informative. For example, when binocularly viewing a slanted trapezoid, the slant interpretation of the figure derived by assuming that the figure is rectangular may conflict greatly with the slant suggested by stereoscopic disparities. An optimal Bayesian estimator incorporates the possibility that different constraints might apply to objects in the world and robustly integrates cues with large conflicts by effectively switching between different internal models of the prior constraints underlying one or both cues. We performed two experiments to test the predictions of the model when applied to estimating surface slant from binocular disparities and the compression cue (the aspect ratio of figures in an image). The apparent weight that subjects gave to the compression cue decreased smoothly as a function of the conflict between the cues but did not shrink to zero; that is, subjects did not fully veto the compression cue at large cue conflicts. A Bayesian model that assumes a mixed prior distribution of figure shapes in the world, with a large proportion being very regular and a smaller proportion having random shapes, provides a good quantitative fit for subjects' performance. The best fitting model parameters are consistent with the sensory noise to be expected in measurements of figure shape, further supporting the Bayesian model as an account of robust cue integration.

Bayesian Model Averaging of Artificial Intelligence Models for Hydraulic Conductivity Estimation

NASA Astrophysics Data System (ADS)

Nadiri, A.; Chitsazan, N.; Tsai, F. T.; Asghari Moghaddam, A.

2012-12-01

This research presents a Bayesian artificial intelligence model averaging (BAIMA) method that incorporates multiple artificial intelligence (AI) models to estimate hydraulic conductivity and evaluate estimation uncertainties. Uncertainty in the AI model outputs stems from error in model input as well as non-uniqueness in selecting different AI methods. Using one single AI model tends to bias the estimation and underestimate uncertainty. BAIMA employs Bayesian model averaging (BMA) technique to address the issue of using one single AI model for estimation. BAIMA estimates hydraulic conductivity by averaging the outputs of AI models according to their model weights. In this study, the model weights were determined using the Bayesian information criterion (BIC) that follows the parsimony principle. BAIMA calculates the within-model variances to account for uncertainty propagation from input data to AI model output. Between-model variances are evaluated to account for uncertainty due to model non-uniqueness. We employed Takagi-Sugeno fuzzy logic (TS-FL), artificial neural network (ANN) and neurofuzzy (NF) to estimate hydraulic conductivity for the Tasuj plain aquifer, Iran. BAIMA combined three AI models and produced better fitting than individual models. While NF was expected to be the best AI model owing to its utilization of both TS-FL and ANN models, the NF model is nearly discarded by the parsimony principle. The TS-FL model and the ANN model showed equal importance although their hydraulic conductivity estimates were quite different. This resulted in significant between-model variances that are normally ignored by using one AI model.

Inferring the most probable maps of underground utilities using Bayesian mapping model

NASA Astrophysics Data System (ADS)

Bilal, Muhammad; Khan, Wasiq; Muggleton, Jennifer; Rustighi, Emiliano; Jenks, Hugo; Pennock, Steve R.; Atkins, Phil R.; Cohn, Anthony

2018-03-01

Mapping the Underworld (MTU), a major initiative in the UK, is focused on addressing social, environmental and economic consequences raised from the inability to locate buried underground utilities (such as pipes and cables) by developing a multi-sensor mobile device. The aim of MTU device is to locate different types of buried assets in real time with the use of automated data processing techniques and statutory records. The statutory records, even though typically being inaccurate and incomplete, provide useful prior information on what is buried under the ground and where. However, the integration of information from multiple sensors (raw data) with these qualitative maps and their visualization is challenging and requires the implementation of robust machine learning/data fusion approaches. An approach for automated creation of revised maps was developed as a Bayesian Mapping model in this paper by integrating the knowledge extracted from sensors raw data and available statutory records. The combination of statutory records with the hypotheses from sensors was for initial estimation of what might be found underground and roughly where. The maps were (re)constructed using automated image segmentation techniques for hypotheses extraction and Bayesian classification techniques for segment-manhole connections. The model consisting of image segmentation algorithm and various Bayesian classification techniques (segment recognition and expectation maximization (EM) algorithm) provided robust performance on various simulated as well as real sites in terms of predicting linear/non-linear segments and constructing refined 2D/3D maps.

On estimating the accuracy of monitoring methods using Bayesian error propagation technique

NASA Astrophysics Data System (ADS)

Zonta, Daniele; Bruschetta, Federico; Cappello, Carlo; Zandonini, R.; Pozzi, Matteo; Wang, Ming; Glisic, B.; Inaudi, D.; Posenato, D.; Zhao, Y.

2014-04-01

This paper illustrates an application of Bayesian logic to monitoring data analysis and structural condition state inference. The case study is a 260 m long cable-stayed bridge spanning the Adige River 10 km north of the town of Trento, Italy. This is a statically indeterminate structure, having a composite steel-concrete deck, supported by 12 stay cables. Structural redundancy, possible relaxation losses and an as-built condition differing from design, suggest that long-term load redistribution between cables can be expected. To monitor load redistribution, the owner decided to install a monitoring system which combines built-on-site elasto-magnetic and fiber-optic sensors. In this note, we discuss a rational way to improve the accuracy of the load estimate from the EM sensors taking advantage of the FOS information. More specifically, we use a multi-sensor Bayesian data fusion approach which combines the information from the two sensing systems with the prior knowledge, including design information and the outcomes of laboratory calibration. Using the data acquired to date, we demonstrate that combining the two measurements allows a more accurate estimate of the cable load, to better than 50 kN.

Hierarchical Commensurate and Power Prior Models for Adaptive Incorporation of Historical Information in Clinical Trials

PubMed Central

Hobbs, Brian P.; Carlin, Bradley P.; Mandrekar, Sumithra J.; Sargent, Daniel J.

2011-01-01

Summary Bayesian clinical trial designs offer the possibility of a substantially reduced sample size, increased statistical power, and reductions in cost and ethical hazard. However when prior and current information conflict, Bayesian methods can lead to higher than expected Type I error, as well as the possibility of a costlier and lengthier trial. This motivates an investigation of the feasibility of hierarchical Bayesian methods for incorporating historical data that are adaptively robust to prior information that reveals itself to be inconsistent with the accumulating experimental data. In this paper, we present several models that allow for the commensurability of the information in the historical and current data to determine how much historical information is used. A primary tool is elaborating the traditional power prior approach based upon a measure of commensurability for Gaussian data. We compare the frequentist performance of several methods using simulations, and close with an example of a colon cancer trial that illustrates a linear models extension of our adaptive borrowing approach. Our proposed methods produce more precise estimates of the model parameters, in particular conferring statistical significance to the observed reduction in tumor size for the experimental regimen as compared to the control regimen. PMID:21361892

Bayesian Inference for Generalized Linear Models for Spiking Neurons

PubMed Central

Gerwinn, Sebastian; Macke, Jakob H.; Bethge, Matthias

2010-01-01

Generalized Linear Models (GLMs) are commonly used statistical methods for modelling the relationship between neural population activity and presented stimuli. When the dimension of the parameter space is large, strong regularization has to be used in order to fit GLMs to datasets of realistic size without overfitting. By imposing properly chosen priors over parameters, Bayesian inference provides an effective and principled approach for achieving regularization. Here we show how the posterior distribution over model parameters of GLMs can be approximated by a Gaussian using the Expectation Propagation algorithm. In this way, we obtain an estimate of the posterior mean and posterior covariance, allowing us to calculate Bayesian confidence intervals that characterize the uncertainty about the optimal solution. From the posterior we also obtain a different point estimate, namely the posterior mean as opposed to the commonly used maximum a posteriori estimate. We systematically compare the different inference techniques on simulated as well as on multi-electrode recordings of retinal ganglion cells, and explore the effects of the chosen prior and the performance measure used. We find that good performance can be achieved by choosing an Laplace prior together with the posterior mean estimate. PMID:20577627

"Contrasting patterns of selection at Pinus pinaster Ait. Drought stress candidate genes as revealed by genetic differentiation analyses".

PubMed

Eveno, Emmanuelle; Collada, Carmen; Guevara, M Angeles; Léger, Valérie; Soto, Alvaro; Díaz, Luis; Léger, Patrick; González-Martínez, Santiago C; Cervera, M Teresa; Plomion, Christophe; Garnier-Géré, Pauline H

2008-02-01

The importance of natural selection for shaping adaptive trait differentiation among natural populations of allogamous tree species has long been recognized. Determining the molecular basis of local adaptation remains largely unresolved, and the respective roles of selection and demography in shaping population structure are actively debated. Using a multilocus scan that aims to detect outliers from simulated neutral expectations, we analyzed patterns of nucleotide diversity and genetic differentiation at 11 polymorphic candidate genes for drought stress tolerance in phenotypically contrasted Pinus pinaster Ait. populations across its geographical range. We compared 3 coalescent-based methods: 2 frequentist-like, including 1 approach specifically developed for biallelic single nucleotide polymorphisms (SNPs) here and 1 Bayesian. Five genes showed outlier patterns that were robust across methods at the haplotype level for 2 of them. Two genes presented higher F(ST) values than expected (PR-AGP4 and erd3), suggesting that they could have been affected by the action of diversifying selection among populations. In contrast, 3 genes presented lower F(ST) values than expected (dhn-1, dhn2, and lp3-1), which could represent signatures of homogenizing selection among populations. A smaller proportion of outliers were detected at the SNP level suggesting the potential functional significance of particular combinations of sites in drought-response candidate genes. The Bayesian method appeared robust to low sample sizes, flexible to assumptions regarding migration rates, and powerful for detecting selection at the haplotype level, but the frequentist-like method adapted to SNPs was more efficient for the identification of outlier SNPs showing low differentiation. Population-specific effects estimated in the Bayesian method also revealed populations with lower immigration rates, which could have led to favorable situations for local adaptation. Outlier patterns are discussed in relation to the different genes' putative involvement in drought tolerance responses, from published results in transcriptomics and association mapping in P. pinaster and other related species. These genes clearly constitute relevant candidates for future association studies in P. pinaster.

Practical considerations in Bayesian fusion of point sensors

NASA Astrophysics Data System (ADS)

Johnson, Kevin; Minor, Christian

2012-06-01

Sensor data fusion is and has been a topic of considerable research, but rigorous and quantitative understanding of the benefits of fusing specific types of sensor data remains elusive. Often, sensor fusion is performed on an ad hoc basis with the assumption that overall detection capabilities will improve, only to discover later, after expensive and time consuming laboratory and/or field testing that little advantage was gained. The work presented here will discuss these issues with theoretical and practical considerations in the context of fusing chemical sensors with binary outputs. Results are given for the potential performance gains one could expect with such systems, as well as the practical difficulties involved in implementing an optimal Bayesian fusion strategy with realistic scenarios. Finally, a discussion of the biases that inaccurate statistical estimates introduce into the results and their consequences is presented.

A Bayesian method for inferring transmission chains in a partially observed epidemic.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marzouk, Youssef M.; Ray, Jaideep

2008-10-01

We present a Bayesian approach for estimating transmission chains and rates in the Abakaliki smallpox epidemic of 1967. The epidemic affected 30 individuals in a community of 74; only the dates of appearance of symptoms were recorded. Our model assumes stochastic transmission of the infections over a social network. Distinct binomial random graphs model intra- and inter-compound social connections, while disease transmission over each link is treated as a Poisson process. Link probabilities and rate parameters are objects of inference. Dates of infection and recovery comprise the remaining unknowns. Distributions for smallpox incubation and recovery periods are obtained from historicalmore » data. Using Markov chain Monte Carlo, we explore the joint posterior distribution of the scalar parameters and provide an expected connectivity pattern for the social graph and infection pathway.« less

Bayesian Optimization Under Mixed Constraints with A Slack-Variable Augmented Lagrangian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Picheny, Victor; Gramacy, Robert B.; Wild, Stefan M.

An augmented Lagrangian (AL) can convert a constrained optimization problem into a sequence of simpler (e.g., unconstrained) problems, which are then usually solved with local solvers. Recently, surrogate-based Bayesian optimization (BO) sub-solvers have been successfully deployed in the AL framework for a more global search in the presence of inequality constraints; however, a drawback was that expected improvement (EI) evaluations relied on Monte Carlo. Here we introduce an alternative slack variable AL, and show that in this formulation the EI may be evaluated with library routines. The slack variables furthermore facilitate equality as well as inequality constraints, and mixtures thereof.more » We show our new slack “ALBO” compares favorably to the original. Its superiority over conventional alternatives is reinforced on several mixed constraint examples.« less

Maximum entropy perception-action space: a Bayesian model of eye movement selection

NASA Astrophysics Data System (ADS)

Colas, Francis; Bessière, Pierre; Girard, Benoît

2011-03-01

In this article, we investigate the issue of the selection of eye movements in a free-eye Multiple Object Tracking task. We propose a Bayesian model of retinotopic maps with a complex logarithmic mapping. This model is structured in two parts: a representation of the visual scene, and a decision model based on the representation. We compare different decision models based on different features of the representation and we show that taking into account uncertainty helps predict the eye movements of subjects recorded in a psychophysics experiment. Finally, based on experimental data, we postulate that the complex logarithmic mapping has a functional relevance, as the density of objects in this space in more uniform than expected. This may indicate that the representation space and control strategies are such that the object density is of maximum entropy.

A Hierarchical Modeling Approach to Data Analysis and Study Design in a Multi-Site Experimental fMRI Study

ERIC Educational Resources Information Center

Zhou, Bo; Konstorum, Anna; Duong, Thao; Tieu, Kinh H.; Wells, William M.; Brown, Gregory G.; Stern, Hal S.; Shahbaba, Babak

2013-01-01

We propose a hierarchical Bayesian model for analyzing multi-site experimental fMRI studies. Our method takes the hierarchical structure of the data (subjects are nested within sites, and there are multiple observations per subject) into account and allows for modeling between-site variation. Using posterior predictive model checking and model…

Uncertainties in Parameters Estimated with Neural Networks: Application to Strong Gravitational Lensing

NASA Astrophysics Data System (ADS)

Perreault Levasseur, Laurence; Hezaveh, Yashar D.; Wechsler, Risa H.

2017-11-01

In Hezaveh et al. we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational-lensing systems. Here we demonstrate a method for obtaining the uncertainties of these parameters. We review the framework of variational inference to obtain approximate posteriors of Bayesian neural networks and apply it to a network trained to estimate the parameters of the Singular Isothermal Ellipsoid plus external shear and total flux magnification. We show that the method can capture the uncertainties due to different levels of noise in the input data, as well as training and architecture-related errors made by the network. To evaluate the accuracy of the resulting uncertainties, we calculate the coverage probabilities of marginalized distributions for each lensing parameter. By tuning a single variational parameter, the dropout rate, we obtain coverage probabilities approximately equal to the confidence levels for which they were calculated, resulting in accurate and precise uncertainty estimates. Our results suggest that the application of approximate Bayesian neural networks to astrophysical modeling problems can be a fast alternative to Monte Carlo Markov Chains, allowing orders of magnitude improvement in speed.

Variational Gaussian approximation for Poisson data

NASA Astrophysics Data System (ADS)

Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

2018-02-01

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

Algorithmic procedures for Bayesian MEG/EEG source reconstruction in SPM.

PubMed

López, J D; Litvak, V; Espinosa, J J; Friston, K; Barnes, G R

2014-01-01

The MEG/EEG inverse problem is ill-posed, giving different source reconstructions depending on the initial assumption sets. Parametric Empirical Bayes allows one to implement most popular MEG/EEG inversion schemes (Minimum Norm, LORETA, etc.) within the same generic Bayesian framework. It also provides a cost-function in terms of the variational Free energy-an approximation to the marginal likelihood or evidence of the solution. In this manuscript, we revisit the algorithm for MEG/EEG source reconstruction with a view to providing a didactic and practical guide. The aim is to promote and help standardise the development and consolidation of other schemes within the same framework. We describe the implementation in the Statistical Parametric Mapping (SPM) software package, carefully explaining each of its stages with the help of a simple simulated data example. We focus on the Multiple Sparse Priors (MSP) model, which we compare with the well-known Minimum Norm and LORETA models, using the negative variational Free energy for model comparison. The manuscript is accompanied by Matlab scripts to allow the reader to test and explore the underlying algorithm. © 2013. Published by Elsevier Inc. All rights reserved.

Estimating the periodic components of a biomedical signal through inverse problem modelling and Bayesian inference with sparsity enforcing prior

NASA Astrophysics Data System (ADS)

Dumitru, Mircea; Djafari, Ali-Mohammad

2015-01-01

The recent developments in chronobiology need a periodic components variation analysis for the signals expressing the biological rhythms. A precise estimation of the periodic components vector is required. The classical approaches, based on FFT methods, are inefficient considering the particularities of the data (short length). In this paper we propose a new method, using the sparsity prior information (reduced number of non-zero values components). The considered law is the Student-t distribution, viewed as a marginal distribution of a Infinite Gaussian Scale Mixture (IGSM) defined via a hidden variable representing the inverse variances and modelled as a Gamma Distribution. The hyperparameters are modelled using the conjugate priors, i.e. using Inverse Gamma Distributions. The expression of the joint posterior law of the unknown periodic components vector, hidden variables and hyperparameters is obtained and then the unknowns are estimated via Joint Maximum A Posteriori (JMAP) and Posterior Mean (PM). For the PM estimator, the expression of the posterior law is approximated by a separable one, via the Bayesian Variational Approximation (BVA), using the Kullback-Leibler (KL) divergence. Finally we show the results on synthetic data in cancer treatment applications.

Approximate method of variational Bayesian matrix factorization/completion with sparse prior

NASA Astrophysics Data System (ADS)

Kawasumi, Ryota; Takeda, Koujin

2018-05-01

We derive the analytical expression of a matrix factorization/completion solution by the variational Bayes method, under the assumption that the observed matrix is originally the product of low-rank, dense and sparse matrices with additive noise. We assume the prior of a sparse matrix is a Laplace distribution by taking matrix sparsity into consideration. Then we use several approximations for the derivation of a matrix factorization/completion solution. By our solution, we also numerically evaluate the performance of a sparse matrix reconstruction in matrix factorization, and completion of a missing matrix element in matrix completion.

A pleiotropy-informed Bayesian false discovery rate adapted to a shared control design finds new disease associations from GWAS summary statistics.

PubMed

Liley, James; Wallace, Chris

2015-02-01

Genome-wide association studies (GWAS) have been successful in identifying single nucleotide polymorphisms (SNPs) associated with many traits and diseases. However, at existing sample sizes, these variants explain only part of the estimated heritability. Leverage of GWAS results from related phenotypes may improve detection without the need for larger datasets. The Bayesian conditional false discovery rate (cFDR) constitutes an upper bound on the expected false discovery rate (FDR) across a set of SNPs whose p values for two diseases are both less than two disease-specific thresholds. Calculation of the cFDR requires only summary statistics and have several advantages over traditional GWAS analysis. However, existing methods require distinct control samples between studies. Here, we extend the technique to allow for some or all controls to be shared, increasing applicability. Several different SNP sets can be defined with the same cFDR value, and we show that the expected FDR across the union of these sets may exceed expected FDR in any single set. We describe a procedure to establish an upper bound for the expected FDR among the union of such sets of SNPs. We apply our technique to pairwise analysis of p values from ten autoimmune diseases with variable sharing of controls, enabling discovery of 59 SNP-disease associations which do not reach GWAS significance after genomic control in individual datasets. Most of the SNPs we highlight have previously been confirmed using replication studies or larger GWAS, a useful validation of our technique; we report eight SNP-disease associations across five diseases not previously declared. Our technique extends and strengthens the previous algorithm, and establishes robust limits on the expected FDR. This approach can improve SNP detection in GWAS, and give insight into shared aetiology between phenotypically related conditions.

A Multivariate and Probabilistic Assessment of Drought in the Pacific Northwest under Observed and Future Climate.

NASA Astrophysics Data System (ADS)

Mortuza, M. R.; Demissie, Y. K.

2015-12-01

In lieu with the recent and anticipated more server and frequently droughts incidences in Yakima River Basin (YRB), a reliable and comprehensive drought assessment is deemed necessary to avoid major crop production loss and better manage the water right issues in the region during low precipitation and/or snow accumulation years. In this study, we have conducted frequency analysis of hydrological droughts and quantified associated uncertainty in the YRB under both historical and changing climate. Streamflow drought index (SDI) was employed to identify mutually correlated drought characteristics (e.g., severity, duration and peak). The historical and future characteristics of drought were estimated by applying tri-variate copulas probability distribution, which effectively describe the joint distribution and dependence of drought severity, duration, and peak. The associated prediction uncertainty, related to parameters of the joint probability and climate projections, were evaluated using the Bayesian approach with bootstrap resampling. For the climate change scenarios, two future representative pathways (RCP4.5 and RCP8.5) from University of Idaho's Multivariate Adaptive Constructed Analogs (MACA) database were considered. The results from the study are expected to provide useful information towards drought risk management in YRB under anticipated climate changes.

Probabilistic modeling of children's handwriting

NASA Astrophysics Data System (ADS)

Puri, Mukta; Srihari, Sargur N.; Hanson, Lisa

2013-12-01

There is little work done in the analysis of children's handwriting, which can be useful in developing automatic evaluation systems and in quantifying handwriting individuality. We consider the statistical analysis of children's handwriting in early grades. Samples of handwriting of children in Grades 2-4 who were taught the Zaner-Bloser style were considered. The commonly occurring word "and" written in cursive style as well as hand-print were extracted from extended writing. The samples were assigned feature values by human examiners using a truthing tool. The human examiners looked at how the children constructed letter formations in their writing, looking for similarities and differences from the instructions taught in the handwriting copy book. These similarities and differences were measured using a feature space distance measure. Results indicate that the handwriting develops towards more conformity with the class characteristics of the Zaner-Bloser copybook which, with practice, is the expected result. Bayesian networks were learnt from the data to enable answering various probabilistic queries, such as determining students who may continue to produce letter formations as taught during lessons in school and determining the students who will develop a different and/or variation of the those letter formations and the number of different types of letter formations.

Inverse Ising problem in continuous time: A latent variable approach

NASA Astrophysics Data System (ADS)

Donner, Christian; Opper, Manfred

2017-12-01

We consider the inverse Ising problem: the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form which allows for simple iterative inference algorithms with analytical updates. The variables are (1) Poisson variables to linearize an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.

Evaluating the Impact of Genomic Data and Priors on Bayesian Estimates of the Angiosperm Evolutionary Timescale.

PubMed

Foster, Charles S P; Sauquet, Hervê; van der Merwe, Marlien; McPherson, Hannah; Rossetto, Maurizio; Ho, Simon Y W

2017-05-01

The evolutionary timescale of angiosperms has long been a key question in biology. Molecular estimates of this timescale have shown considerable variation, being influenced by differences in taxon sampling, gene sampling, fossil calibrations, evolutionary models, and choices of priors. Here, we analyze a data set comprising 76 protein-coding genes from the chloroplast genomes of 195 taxa spanning 86 families, including novel genome sequences for 11 taxa, to evaluate the impact of models, priors, and gene sampling on Bayesian estimates of the angiosperm evolutionary timescale. Using a Bayesian relaxed molecular-clock method, with a core set of 35 minimum and two maximum fossil constraints, we estimated that crown angiosperms arose 221 (251-192) Ma during the Triassic. Based on a range of additional sensitivity and subsampling analyses, we found that our date estimates were generally robust to large changes in the parameters of the birth-death tree prior and of the model of rate variation across branches. We found an exception to this when we implemented fossil calibrations in the form of highly informative gamma priors rather than as uniform priors on node ages. Under all other calibration schemes, including trials of seven maximum age constraints, we consistently found that the earliest divergences of angiosperm clades substantially predate the oldest fossils that can be assigned unequivocally to their crown group. Overall, our results and experiments with genome-scale data suggest that reliable estimates of the angiosperm crown age will require increased taxon sampling, significant methodological changes, and new information from the fossil record. [Angiospermae, chloroplast, genome, molecular dating, Triassic.]. © The Author(s) 2016. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

The evolution of virulence in primate malaria parasites based on Bayesian reconstructions of ancestral states.

PubMed

Garamszegi, László Zsolt

2011-02-01

Plasmodium parasites, the causative agents of malaria, are generally considered as harmful parasites, but many of them cause mild symptoms. Little is known about the evolutionary history and phylogenetic constraints that generate this interspecific variation in virulence due to uncertainties about the phylogenetic associations of parasites. Here, to account for such phylogenetic uncertainty, phylogenetic methods based on Bayesian statistics were followed in combination with sequence data from five genes to estimate the ancestral state of virulence in primate Plasmodium parasites. When recent parasites were categorised according to the damage caused to the host, Bayesian estimates of ancestral states indicated that the acquisition of a harmful host exploitation strategy is more likely to be a recent evolutionary event than a result of an ancient change in a character state altering virulence. On the contrary, there was more evidence for moderate host exploitation having a deep origin along the phylogenetic tree. Moreover, the evolution of host severity is determined by the phylogenetic relationships of parasites, as severity gains did not appear randomly on the evolutionary tree. Such phylogenetic constraints can be mediated by the acquisition of virulence genes. As the impact of a parasite on a host is the result of both the parasite's investment in reproduction and host sensitivity, virulence was also estimated by calculating peak parasitemia after eliminating host effects. A directional random-walk evolutionary model showed that the ancestral primate malarias reproduced at very low parasitemia in their hosts. Consequently, the extreme variation in the outcome of malaria infection in different host species can be better understood in light of the phylogeny of parasites. Copyright © 2010 Australian Society for Parasitology Inc. Published by Elsevier Ltd. All rights reserved.

Variations in Obesity Rates between US Counties: Impacts of Activity Access, Food Environments, and Settlement Patterns.

PubMed

Congdon, Peter

2017-09-07

There is much ongoing research about the effect of the urban environment as compared with individual behaviour on growing obesity levels, including food environment, settlement patterns (e.g., sprawl, walkability, commuting patterns), and activity access. This paper considers obesity variations between US counties, and delineates the main dimensions of geographic variation in obesity between counties: by urban-rural status, by region, by area poverty status, and by majority ethnic group. Available measures of activity access, food environment, and settlement patterns are then assessed in terms of how far they can account for geographic variation. A county level regression analysis uses a Bayesian methodology that controls for spatial correlation in unmeasured area risk factors. It is found that environmental measures do play a significant role in explaining geographic contrasts in obesity.

Variations in Obesity Rates between US Counties: Impacts of Activity Access, Food Environments, and Settlement Patterns

PubMed Central

2017-01-01

There is much ongoing research about the effect of the urban environment as compared with individual behaviour on growing obesity levels, including food environment, settlement patterns (e.g., sprawl, walkability, commuting patterns), and activity access. This paper considers obesity variations between US counties, and delineates the main dimensions of geographic variation in obesity between counties: by urban-rural status, by region, by area poverty status, and by majority ethnic group. Available measures of activity access, food environment, and settlement patterns are then assessed in terms of how far they can account for geographic variation. A county level regression analysis uses a Bayesian methodology that controls for spatial correlation in unmeasured area risk factors. It is found that environmental measures do play a significant role in explaining geographic contrasts in obesity. PMID:28880209

Bayesian structured additive regression modeling of epidemic data: application to cholera

PubMed Central

2012-01-01

Background A significant interest in spatial epidemiology lies in identifying associated risk factors which enhances the risk of infection. Most studies, however, make no, or limited use of the spatial structure of the data, as well as possible nonlinear effects of the risk factors. Methods We develop a Bayesian Structured Additive Regression model for cholera epidemic data. Model estimation and inference is based on fully Bayesian approach via Markov Chain Monte Carlo (MCMC) simulations. The model is applied to cholera epidemic data in the Kumasi Metropolis, Ghana. Proximity to refuse dumps, density of refuse dumps, and proximity to potential cholera reservoirs were modeled as continuous functions; presence of slum settlers and population density were modeled as fixed effects, whereas spatial references to the communities were modeled as structured and unstructured spatial effects. Results We observe that the risk of cholera is associated with slum settlements and high population density. The risk of cholera is equal and lower for communities with fewer refuse dumps, but variable and higher for communities with more refuse dumps. The risk is also lower for communities distant from refuse dumps and potential cholera reservoirs. The results also indicate distinct spatial variation in the risk of cholera infection. Conclusion The study highlights the usefulness of Bayesian semi-parametric regression model analyzing public health data. These findings could serve as novel information to help health planners and policy makers in making effective decisions to control or prevent cholera epidemics. PMID:22866662

A bayesian analysis for identifying DNA copy number variations using a compound poisson process.

PubMed

Chen, Jie; Yiğiter, Ayten; Wang, Yu-Ping; Deng, Hong-Wen

2010-01-01

To study chromosomal aberrations that may lead to cancer formation or genetic diseases, the array-based Comparative Genomic Hybridization (aCGH) technique is often used for detecting DNA copy number variants (CNVs). Various methods have been developed for gaining CNVs information based on aCGH data. However, most of these methods make use of the log-intensity ratios in aCGH data without taking advantage of other information such as the DNA probe (e.g., biomarker) positions/distances contained in the data. Motivated by the specific features of aCGH data, we developed a novel method that takes into account the estimation of a change point or locus of the CNV in aCGH data with its associated biomarker position on the chromosome using a compound Poisson process. We used a Bayesian approach to derive the posterior probability for the estimation of the CNV locus. To detect loci of multiple CNVs in the data, a sliding window process combined with our derived Bayesian posterior probability was proposed. To evaluate the performance of the method in the estimation of the CNV locus, we first performed simulation studies. Finally, we applied our approach to real data from aCGH experiments, demonstrating its applicability.

A Bayesian framework to estimate diversification rates and their variation through time and space

PubMed Central

2011-01-01

Background Patterns of species diversity are the result of speciation and extinction processes, and molecular phylogenetic data can provide valuable information to derive their variability through time and across clades. Bayesian Markov chain Monte Carlo methods offer a promising framework to incorporate phylogenetic uncertainty when estimating rates of diversification. Results We introduce a new approach to estimate diversification rates in a Bayesian framework over a distribution of trees under various constant and variable rate birth-death and pure-birth models, and test it on simulated phylogenies. Furthermore, speciation and extinction rates and their posterior credibility intervals can be estimated while accounting for non-random taxon sampling. The framework is particularly suitable for hypothesis testing using Bayes factors, as we demonstrate analyzing dated phylogenies of Chondrostoma (Cyprinidae) and Lupinus (Fabaceae). In addition, we develop a model that extends the rate estimation to a meta-analysis framework in which different data sets are combined in a single analysis to detect general temporal and spatial trends in diversification. Conclusions Our approach provides a flexible framework for the estimation of diversification parameters and hypothesis testing while simultaneously accounting for uncertainties in the divergence times and incomplete taxon sampling. PMID:22013891

Framework for network modularization and Bayesian network analysis to investigate the perturbed metabolic network

PubMed Central

2011-01-01

Background Genome-scale metabolic network models have contributed to elucidating biological phenomena, and predicting gene targets to engineer for biotechnological applications. With their increasing importance, their precise network characterization has also been crucial for better understanding of the cellular physiology. Results We herein introduce a framework for network modularization and Bayesian network analysis (FMB) to investigate organism’s metabolism under perturbation. FMB reveals direction of influences among metabolic modules, in which reactions with similar or positively correlated flux variation patterns are clustered, in response to specific perturbation using metabolic flux data. With metabolic flux data calculated by constraints-based flux analysis under both control and perturbation conditions, FMB, in essence, reveals the effects of specific perturbations on the biological system through network modularization and Bayesian network analysis at metabolic modular level. As a demonstration, this framework was applied to the genetically perturbed Escherichia coli metabolism, which is a lpdA gene knockout mutant, using its genome-scale metabolic network model. Conclusions After all, it provides alternative scenarios of metabolic flux distributions in response to the perturbation, which are complementary to the data obtained from conventionally available genome-wide high-throughput techniques or metabolic flux analysis. PMID:22784571

Framework for network modularization and Bayesian network analysis to investigate the perturbed metabolic network.

PubMed

Kim, Hyun Uk; Kim, Tae Yong; Lee, Sang Yup

2011-01-01

Genome-scale metabolic network models have contributed to elucidating biological phenomena, and predicting gene targets to engineer for biotechnological applications. With their increasing importance, their precise network characterization has also been crucial for better understanding of the cellular physiology. We herein introduce a framework for network modularization and Bayesian network analysis (FMB) to investigate organism's metabolism under perturbation. FMB reveals direction of influences among metabolic modules, in which reactions with similar or positively correlated flux variation patterns are clustered, in response to specific perturbation using metabolic flux data. With metabolic flux data calculated by constraints-based flux analysis under both control and perturbation conditions, FMB, in essence, reveals the effects of specific perturbations on the biological system through network modularization and Bayesian network analysis at metabolic modular level. As a demonstration, this framework was applied to the genetically perturbed Escherichia coli metabolism, which is a lpdA gene knockout mutant, using its genome-scale metabolic network model. After all, it provides alternative scenarios of metabolic flux distributions in response to the perturbation, which are complementary to the data obtained from conventionally available genome-wide high-throughput techniques or metabolic flux analysis.

A Bayesian analysis of HAT-P-7b using the EXONEST algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Placek, Ben; Knuth, Kevin H.

2015-01-13

The study of exoplanets (planets orbiting other stars) is revolutionizing the way we view our universe. High-precision photometric data provided by the Kepler Space Telescope (Kepler) enables not only the detection of such planets, but also their characterization. This presents a unique opportunity to apply Bayesian methods to better characterize the multitude of previously confirmed exoplanets. This paper focuses on applying the EXONEST algorithm to characterize the transiting short-period-hot-Jupiter, HAT-P-7b (also referred to as Kepler-2b). EXONEST evaluates a suite of exoplanet photometric models by applying Bayesian Model Selection, which is implemented with the MultiNest algorithm. These models take into accountmore » planetary effects, such as reflected light and thermal emissions, as well as the effect of the planetary motion on the host star, such as Doppler beaming, or boosting, of light from the reflex motion of the host star, and photometric variations due to the planet-induced ellipsoidal shape of the host star. By calculating model evidences, one can determine which model best describes the observed data, thus identifying which effects dominate the planetary system. Presented are parameter estimates and model evidences for HAT-P-7b.« less

Genetic diversity of calcareous grassland plant species depends on historical landscape configuration.

PubMed

Reisch, Christoph; Schmidkonz, Sonja; Meier, Katrin; Schöpplein, Quirin; Meyer, Carina; Hums, Christian; Putz, Christina; Schmid, Christoph

2017-04-24

Habitat fragmentation is considered to be a main reason for decreasing genetic diversity of plant species. However, the results of many fragmentation studies are inconsistent. This may be due to the influence of habitat conditions, having an indirect effect on genetic variation via reproduction. Consequently we took a comparative approach to analyse the impact of habitat fragmentation and habitat conditions on the genetic diversity of calcareous grassland species in this study. We selected five typical grassland species (Primula veris, Dianthus carthusianorum, Medicago falcata, Polygala comosa and Salvia pratensis) occurring in 18 fragments of calcareous grasslands in south eastern Germany. We sampled 1286 individuals in 87 populations and analysed genetic diversity using amplified fragment length polymorphisms. Additionally, we collected data concerning habitat fragmentation (historical and present landscape structure) and habitat conditions (vegetation structure, soil conditions) of the selected study sites. The whole data set was analysed using Bayesian multiple regressions. Our investigation indicated a habitat loss of nearly 80% and increasing isolation between grasslands since 1830. Bayesian analysis revealed a significant impact of the historical landscape structure, whereas habitat conditions played no important role for the present-day genetic variation of the studied plant species. Our study indicates that the historical landscape structure may be more important for genetic diversity than present habitat conditions. Populations persisting in abandoned grassland fragments may contribute significantly to the species' variability even under deteriorating habitat conditions. Therefore, these populations should be included in approaches to preserve the genetic variation of calcareous grassland species.

Novel patterns of historical isolation, dispersal, and secondary contact across Baja California in the Rosy Boa (Lichanura trivirgata).

PubMed

Wood, Dustin A; Fisher, Robert N; Reeder, Tod W

2008-02-01

Mitochondrial DNA (mtDNA) sequence variation was examined in 131 individuals of the Rosy Boa (Lichanura trivirgata) from across the species range in southwestern North America. Bayesian inference and nested clade phylogeographic analyses (NCPA) were used to estimate relationships and infer evolutionary processes. These patterns were evaluated as they relate to previously hypothesized vicariant events and new insights are provided into the biogeographic and evolutionary processes important in Baja California and surrounding North American deserts. Three major lineages (Lineages A, B, and C) are revealed with very little overlap. Lineage A and B are predominately separated along the Colorado River and are found primarily within California and Arizona (respectively), while Lineage C consists of disjunct groups distributed along the Baja California peninsula as well as south-central Arizona, southward along the coastal regions of Sonora, Mexico. Estimated divergence time points (using a Bayesian relaxed molecular clock) and geographic congruence with postulated vicariant events suggest early extensions of the Gulf of California and subsequent development of the Colorado River during the Late Miocene-Pliocene led to the formation of these mtDNA lineages. Our results also suggest that vicariance hypotheses alone do not fully explain patterns of genetic variation. Therefore, we highlight the importance of dispersal to explain these patterns and current distribution of populations. We also compare the mtDNA lineages with those based on morphological variation and evaluate their implications for taxonomy.

Novel patterns of historical isolation, dispersal, and secondary contact across Baja California in the Rosy Boa (Lichanura trivirgata)

USGS Publications Warehouse

Wood, D.A.; Fisher, R.N.; Reeder, T.W.

2008-01-01

Mitochondrial DNA (mtDNA) sequence variation was examined in 131 individuals of the Rosy Boa (Lichanura trivirgata) from across the species range in southwestern North America. Bayesian inference and nested clade phylogeographic analyses (NCPA) were used to estimate relationships and infer evolutionary processes. These patterns were evaluated as they relate to previously hypothesized vicariant events and new insights are provided into the biogeographic and evolutionary processes important in Baja California and surrounding North American deserts. Three major lineages (Lineages A, B, and C) are revealed with very little overlap. Lineage A and B are predominately separated along the Colorado River and are found primarily within California and Arizona (respectively), while Lineage C consists of disjunct groups distributed along the Baja California peninsula as well as south-central Arizona, southward along the coastal regions of Sonora, Mexico. Estimated divergence time points (using a Bayesian relaxed molecular clock) and geographic congruence with postulated vicariant events suggest early extensions of the Gulf of California and subsequent development of the Colorado River during the Late Miocene-Pliocene led to the formation of these mtDNA lineages. Our results also suggest that vicariance hypotheses alone do not fully explain patterns of genetic variation. Therefore, we highlight the importance of dispersal to explain these patterns and current distribution of populations. We also compare the mtDNA lineages with those based on morphological variation and evaluate their implications for taxonomy. ?? 2007 Elsevier Inc. All rights reserved.

The double slit experiment and the time reversed fire alarm

NASA Astrophysics Data System (ADS)

Halabi, Tarek

2011-03-01

When both slits of the double slit experiment are open, closing one paradoxically increases the detection rate at some points on the detection screen. Feynman famously warned that temptation to "understand" such a puzzling feature only draws us into blind alleys. Nevertheless, we gain insight into this feature by drawing an analogy between the double slit experiment and a time reversed fire alarm. Much as closing the slit increases probability of a future detection, ruling out fire drill scenarios, having heard the fire alarm, increases probability of a past fire (using Bayesian inference). Classically, Bayesian inference is associated with computing probabilities of past events. We therefore identify this feature of the double slit experiment with a time reversed thermodynamic arrow. We believe that much of the enigma of quantum mechanics is simply due to some variation of time's arrow.

Analyses of amplified fragment length polymorphisms (AFLP) indicate rapid radiation of Diospyros species (Ebenaceae) endemic to New Caledonia

PubMed Central

2013-01-01

Background Radiation in some plant groups has occurred on islands and due to the characteristic rapid pace of phenotypic evolution, standard molecular markers often provide insufficient variation for phylogenetic reconstruction. To resolve relationships within a clade of 21 closely related New Caledonian Diospyros species and evaluate species boundaries we analysed genome-wide DNA variation via amplified fragment length polymorphisms (AFLP). Results A neighbour-joining (NJ) dendrogram based on Dice distances shows all species except D. minimifolia, D. parviflora and D. vieillardii to form unique clusters of genetically similar accessions. However, there was little variation between these species clusters, resulting in unresolved species relationships and a star-like general NJ topology. Correspondingly, analyses of molecular variance showed more variation within species than between them. A Bayesian analysis with BEAST produced a similar result. Another Bayesian method, this time a clustering method, Structure, demonstrated the presence of two groups, highly congruent with those observed in a principal coordinate analysis (PCO). Molecular divergence between the two groups is low and does not correspond to any hypothesised taxonomic, ecological or geographical patterns. Conclusions We hypothesise that such a pattern could have been produced by rapid and complex evolution involving a widespread progenitor for which an initial split into two groups was followed by subsequent fragmentation into many diverging populations, which was followed by range expansion of then divergent entities. Overall, this process resulted in an opportunistic pattern of phenotypic diversification. The time since divergence was probably insufficient for some species to become genetically well-differentiated, resulting in progenitor/derivative relationships being exhibited in a few cases. In other cases, our analyses may have revealed evidence for the existence of cryptic species, for which more study of morphology and ecology are now required. PMID:24330478

Stochastic extreme downscaling model for an assessment of changes in rainfall intensity-duration-frequency curves over South Korea using multiple regional climate models

NASA Astrophysics Data System (ADS)

So, Byung-Jin; Kim, Jin-Young; Kwon, Hyun-Han; Lima, Carlos H. R.

2017-10-01

A conditional copula function based downscaling model in a fully Bayesian framework is developed in this study to evaluate future changes in intensity-duration frequency (IDF) curves in South Korea. The model incorporates a quantile mapping approach for bias correction while integrated Bayesian inference allows accounting for parameter uncertainties. The proposed approach is used to temporally downscale expected changes in daily rainfall, inferred from multiple CORDEX-RCMs based on Representative Concentration Pathways (RCPs) 4.5 and 8.5 scenarios, into sub-daily temporal scales. Among the CORDEX-RCMs, a noticeable increase in rainfall intensity is observed in the HadGem3-RA (9%), RegCM (28%), and SNU_WRF (13%) on average, whereas no noticeable changes are observed in the GRIMs (-2%) for the period 2020-2050. More specifically, a 5-30% increase in rainfall intensity is expected in all of the CORDEX-RCMs for 50-year return values under the RCP 8.5 scenario. Uncertainty in simulated rainfall intensity gradually decreases toward the longer durations, which is largely associated with the enhanced strength of the relationship with the 24-h annual maximum rainfalls (AMRs). A primary advantage of the proposed model is that projected changes in future rainfall intensities are well preserved.

Bayesian cross-entropy methodology for optimal design of validation experiments

NASA Astrophysics Data System (ADS)

Jiang, X.; Mahadevan, S.

2006-07-01

An important concern in the design of validation experiments is how to incorporate the mathematical model in the design in order to allow conclusive comparisons of model prediction with experimental output in model assessment. The classical experimental design methods are more suitable for phenomena discovery and may result in a subjective, expensive, time-consuming and ineffective design that may adversely impact these comparisons. In this paper, an integrated Bayesian cross-entropy methodology is proposed to perform the optimal design of validation experiments incorporating the computational model. The expected cross entropy, an information-theoretic distance between the distributions of model prediction and experimental observation, is defined as a utility function to measure the similarity of two distributions. A simulated annealing algorithm is used to find optimal values of input variables through minimizing or maximizing the expected cross entropy. The measured data after testing with the optimum input values are used to update the distribution of the experimental output using Bayes theorem. The procedure is repeated to adaptively design the required number of experiments for model assessment, each time ensuring that the experiment provides effective comparison for validation. The methodology is illustrated for the optimal design of validation experiments for a three-leg bolted joint structure and a composite helicopter rotor hub component.

Allele frequency changes due to hitch-hiking in genomic selection programs

PubMed Central

2014-01-01

Background Genomic selection makes it possible to reduce pedigree-based inbreeding over best linear unbiased prediction (BLUP) by increasing emphasis on own rather than family information. However, pedigree inbreeding might not accurately reflect loss of genetic variation and the true level of inbreeding due to changes in allele frequencies and hitch-hiking. This study aimed at understanding the impact of using long-term genomic selection on changes in allele frequencies, genetic variation and level of inbreeding. Methods Selection was performed in simulated scenarios with a population of 400 animals for 25 consecutive generations. Six genetic models were considered with different heritabilities and numbers of QTL (quantitative trait loci) affecting the trait. Four selection criteria were used, including selection on own phenotype and on estimated breeding values (EBV) derived using phenotype-BLUP, genomic BLUP and Bayesian Lasso. Changes in allele frequencies at QTL, markers and linked neutral loci were investigated for the different selection criteria and different scenarios, along with the loss of favourable alleles and the rate of inbreeding measured by pedigree and runs of homozygosity. Results For each selection criterion, hitch-hiking in the vicinity of the QTL appeared more extensive when accuracy of selection was higher and the number of QTL was lower. When inbreeding was measured by pedigree information, selection on genomic BLUP EBV resulted in lower levels of inbreeding than selection on phenotype BLUP EBV, but this did not always apply when inbreeding was measured by runs of homozygosity. Compared to genomic BLUP, selection on EBV from Bayesian Lasso led to less genetic drift, reduced loss of favourable alleles and more effectively controlled the rate of both pedigree and genomic inbreeding in all simulated scenarios. In addition, selection on EBV from Bayesian Lasso showed a higher selection differential for mendelian sampling terms than selection on genomic BLUP EBV. Conclusions Neutral variation can be shaped to a great extent by the hitch-hiking effects associated with selection, rather than just by genetic drift. When implementing long-term genomic selection, strategies for genomic control of inbreeding are essential, due to a considerable hitch-hiking effect, regardless of the method that is used for prediction of EBV. PMID:24495634

Sensitivity analyses for sparse-data problems-using weakly informative bayesian priors.

PubMed

Hamra, Ghassan B; MacLehose, Richard F; Cole, Stephen R

2013-03-01

Sparse-data problems are common, and approaches are needed to evaluate the sensitivity of parameter estimates based on sparse data. We propose a Bayesian approach that uses weakly informative priors to quantify sensitivity of parameters to sparse data. The weakly informative prior is based on accumulated evidence regarding the expected magnitude of relationships using relative measures of disease association. We illustrate the use of weakly informative priors with an example of the association of lifetime alcohol consumption and head and neck cancer. When data are sparse and the observed information is weak, a weakly informative prior will shrink parameter estimates toward the prior mean. Additionally, the example shows that when data are not sparse and the observed information is not weak, a weakly informative prior is not influential. Advancements in implementation of Markov Chain Monte Carlo simulation make this sensitivity analysis easily accessible to the practicing epidemiologist.

Sensitivity Analyses for Sparse-Data Problems—Using Weakly Informative Bayesian Priors

PubMed Central

Hamra, Ghassan B.; MacLehose, Richard F.; Cole, Stephen R.

2013-01-01

Sparse-data problems are common, and approaches are needed to evaluate the sensitivity of parameter estimates based on sparse data. We propose a Bayesian approach that uses weakly informative priors to quantify sensitivity of parameters to sparse data. The weakly informative prior is based on accumulated evidence regarding the expected magnitude of relationships using relative measures of disease association. We illustrate the use of weakly informative priors with an example of the association of lifetime alcohol consumption and head and neck cancer. When data are sparse and the observed information is weak, a weakly informative prior will shrink parameter estimates toward the prior mean. Additionally, the example shows that when data are not sparse and the observed information is not weak, a weakly informative prior is not influential. Advancements in implementation of Markov Chain Monte Carlo simulation make this sensitivity analysis easily accessible to the practicing epidemiologist. PMID:23337241

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pichara, Karim; Protopapas, Pavlos

We present an automatic classification method for astronomical catalogs with missing data. We use Bayesian networks and a probabilistic graphical model that allows us to perform inference to predict missing values given observed data and dependency relationships between variables. To learn a Bayesian network from incomplete data, we use an iterative algorithm that utilizes sampling methods and expectation maximization to estimate the distributions and probabilistic dependencies of variables from data with missing values. To test our model, we use three catalogs with missing data (SAGE, Two Micron All Sky Survey, and UBVI) and one complete catalog (MACHO). We examine howmore » classification accuracy changes when information from missing data catalogs is included, how our method compares to traditional missing data approaches, and at what computational cost. Integrating these catalogs with missing data, we find that classification of variable objects improves by a few percent and by 15% for quasar detection while keeping the computational cost the same.« less

Optimal execution in high-frequency trading with Bayesian learning

NASA Astrophysics Data System (ADS)

Du, Bian; Zhu, Hongliang; Zhao, Jingdong

2016-11-01

We consider optimal trading strategies in which traders submit bid and ask quotes to maximize the expected quadratic utility of total terminal wealth in a limit order book. The trader's bid and ask quotes will be changed by the Poisson arrival of market orders. Meanwhile, the trader may update his estimate of other traders' target sizes and directions by Bayesian learning. The solution of optimal execution in the limit order book is a two-step procedure. First, we model an inactive trading with no limit order in the market. The dealer simply holds dollars and shares of stocks until terminal time. Second, he calibrates his bid and ask quotes to the limit order book. The optimal solutions are given by dynamic programming and in fact they are globally optimal. We also give numerical simulation to the value function and optimal quotes at the last part of the article.

Correcting Satellite Image Derived Surface Model for Atmospheric Effects

NASA Technical Reports Server (NTRS)

Emery, William; Baldwin, Daniel

1998-01-01

This project was a continuation of the project entitled "Resolution Earth Surface Features from Repeat Moderate Resolution Satellite Imagery". In the previous study, a Bayesian Maximum Posterior Estimate (BMPE) algorithm was used to obtain a composite series of repeat imagery from the Advanced Very High Resolution Radiometer (AVHRR). The spatial resolution of the resulting composite was significantly greater than the 1 km resolution of the individual AVHRR images. The BMPE algorithm utilized a simple, no-atmosphere geometrical model for the short-wave radiation budget at the Earth's surface. A necessary assumption of the algorithm is that all non geometrical parameters remain static over the compositing period. This assumption is of course violated by temporal variations in both the surface albedo and the atmospheric medium. The effect of the albedo variations is expected to be minimal since the variations are on a fairly long time scale compared to the compositing period, however, the atmospheric variability occurs on a relatively short time scale and can be expected to cause significant errors in the surface reconstruction. The current project proposed to incorporate an atmospheric correction into the BMPE algorithm for the purpose of investigating the effects of a variable atmosphere on the surface reconstructions. Once the atmospheric effects were determined, the investigation could be extended to include corrections various cloud effects, including short wave radiation through thin cirrus clouds. The original proposal was written for a three year project, funded one year at a time. The first year of the project focused on developing an understanding of atmospheric corrections and choosing an appropriate correction model. Several models were considered and the list was narrowed to the two best suited. These were the 5S and 6S shortwave radiation models developed at NASA/GODDARD and tested extensively with data from the AVHRR instrument. Although the 6S model was a successor to the 5S and slightly more advanced, the 5S was selected because outputs from the individual components comprising the short-wave radiation budget were more easily separated. The separation was necessary since both the 5S and 6S did not include geometrical corrections for terrain, a fundamental constituent of the BMPE algorithm. The 5S correction code was incorporated into the BMPE algorithm and many sensitivity studies were performed.

Understanding sport continuation: an integration of the theories of planned behaviour and basic psychological needs.

PubMed

Gucciardi, Daniel F; Jackson, Ben

2015-01-01

Fostering individuals' long-term participation in activities that promote positive development such as organised sport is an important agenda for research and practice. We integrated the theories of planned behaviour (TPB) and basic psychological needs (BPN) to identify factors associated with young adults' continuation in organised sport over a 12-month period. Prospective study, including an online psycho-social assessment at Time 1 and an assessment of continuation in sport approximately 12 months later. Participants (N=292) aged between 17 and 21 years (M=18.03; SD=1.29) completed an online survey assessing the theories of planned behaviour and basic psychological needs constructs. Bayesian structural equation modelling (BSEM) was employed to test the hypothesised theoretical sequence, using informative priors for structural relations based on empirical and theoretical expectations. The analyses revealed support for the robustness of the hypothesised theoretical model in terms of the pattern of relations as well as the direction and strength of associations among the constructs derived from quantitative summaries of existing research and theoretical expectations. The satisfaction of basic psychological needs was associated with more positive attitudes, higher levels of perceived behavioural control, and more favourable subjective norms; positive attitudes and perceived behavioural control were associated with higher behavioural intentions; and both intentions and perceived behavioural control predicted sport continuation. This study demonstrated the utility of Bayesian structural equation modelling for testing the robustness of an integrated theoretical model, which is informed by empirical evidence from meta-analyses and theoretical expectations, for understanding sport continuation. Crown Copyright © 2013. Published by Elsevier Ltd. All rights reserved.

Approximate likelihood calculation on a phylogeny for Bayesian estimation of divergence times.

PubMed

dos Reis, Mario; Yang, Ziheng

2011-07-01

The molecular clock provides a powerful way to estimate species divergence times. If information on some species divergence times is available from the fossil or geological record, it can be used to calibrate a phylogeny and estimate divergence times for all nodes in the tree. The Bayesian method provides a natural framework to incorporate different sources of information concerning divergence times, such as information in the fossil and molecular data. Current models of sequence evolution are intractable in a Bayesian setting, and Markov chain Monte Carlo (MCMC) is used to generate the posterior distribution of divergence times and evolutionary rates. This method is computationally expensive, as it involves the repeated calculation of the likelihood function. Here, we explore the use of Taylor expansion to approximate the likelihood during MCMC iteration. The approximation is much faster than conventional likelihood calculation. However, the approximation is expected to be poor when the proposed parameters are far from the likelihood peak. We explore the use of parameter transforms (square root, logarithm, and arcsine) to improve the approximation to the likelihood curve. We found that the new methods, particularly the arcsine-based transform, provided very good approximations under relaxed clock models and also under the global clock model when the global clock is not seriously violated. The approximation is poorer for analysis under the global clock when the global clock is seriously wrong and should thus not be used. The results suggest that the approximate method may be useful for Bayesian dating analysis using large data sets.

Social deprivation and population density are not associated with small area risk of amyotrophic lateral sclerosis.

PubMed

Rooney, James P K; Tobin, Katy; Crampsie, Arlene; Vajda, Alice; Heverin, Mark; McLaughlin, Russell; Staines, Anthony; Hardiman, Orla

2015-10-01

Evidence of an association between areal ALS risk and population density has been previously reported. We aim to examine ALS spatial incidence in Ireland using small areas, to compare this analysis with our previous analysis of larger areas and to examine the associations between population density, social deprivation and ALS incidence. Residential area social deprivation has not been previously investigated as a risk factor for ALS. Using the Irish ALS register, we included all cases of ALS diagnosed in Ireland from 1995-2013. 2006 census data was used to calculate age and sex standardised expected cases per small area. Social deprivation was assessed using the pobalHP deprivation index. Bayesian smoothing was used to calculate small area relative risk for ALS, whilst cluster analysis was performed using SaTScan. The effects of population density and social deprivation were tested in two ways: (1) as covariates in the Bayesian spatial model; (2) via post-Bayesian regression. 1701 cases were included. Bayesian smoothed maps of relative risk at small area resolution matched closely to our previous analysis at a larger area resolution. Cluster analysis identified two areas of significant low risk. These areas did not correlate with population density or social deprivation indices. Two areas showing low frequency of ALS have been identified in the Republic of Ireland. These areas do not correlate with population density or residential area social deprivation, indicating that other reasons, such as genetic admixture may account for the observed findings. Copyright © 2015 Elsevier Inc. All rights reserved.

Attention in a Bayesian Framework

PubMed Central

Whiteley, Louise; Sahani, Maneesh

2012-01-01

The behavioral phenomena of sensory attention are thought to reflect the allocation of a limited processing resource, but there is little consensus on the nature of the resource or why it should be limited. Here we argue that a fundamental bottleneck emerges naturally within Bayesian models of perception, and use this observation to frame a new computational account of the need for, and action of, attention – unifying diverse attentional phenomena in a way that goes beyond previous inferential, probabilistic and Bayesian models. Attentional effects are most evident in cluttered environments, and include both selective phenomena, where attention is invoked by cues that point to particular stimuli, and integrative phenomena, where attention is invoked dynamically by endogenous processing. However, most previous Bayesian accounts of attention have focused on describing relatively simple experimental settings, where cues shape expectations about a small number of upcoming stimuli and thus convey “prior” information about clearly defined objects. While operationally consistent with the experiments it seeks to describe, this view of attention as prior seems to miss many essential elements of both its selective and integrative roles, and thus cannot be easily extended to complex environments. We suggest that the resource bottleneck stems from the computational intractability of exact perceptual inference in complex settings, and that attention reflects an evolved mechanism for approximate inference which can be shaped to refine the local accuracy of perception. We show that this approach extends the simple picture of attention as prior, so as to provide a unified and computationally driven account of both selective and integrative attentional phenomena. PMID:22712010

The future of life expectancy and life expectancy inequalities in England and Wales: Bayesian spatiotemporal forecasting

PubMed Central

Bennett, James E; Li, Guangquan; Foreman, Kyle; Best, Nicky; Kontis, Vasilis; Pearson, Clare; Hambly, Peter; Ezzati, Majid

2015-01-01

Summary Background To plan for pensions and health and social services, future mortality and life expectancy need to be forecast. Consistent forecasts for all subnational units within a country are very rare. Our aim was to forecast mortality and life expectancy for England and Wales' districts. Methods We developed Bayesian spatiotemporal models for forecasting of age-specific mortality and life expectancy at a local, small-area level. The models included components that accounted for mortality in relation to age, birth cohort, time, and space. We used geocoded mortality and population data between 1981 and 2012 from the Office for National Statistics together with the model with the smallest error to forecast age-specific death rates and life expectancy to 2030 for 375 of England and Wales' 376 districts. We measured model performance by withholding recent data and comparing forecasts with this withheld data. Findings Life expectancy at birth in England and Wales was 79·5 years (95% credible interval 79·5–79·6) for men and 83·3 years (83·3–83·4) for women in 2012. District life expectancies ranged between 75·2 years (74·9–75·6) and 83·4 years (82·1–84·8) for men and between 80·2 years (79·8–80·5) and 87·3 years (86·0–88·8) for women. Between 1981 and 2012, life expectancy increased by 8·2 years for men and 6·0 years for women, closing the female–male gap from 6·0 to 3·8 years. National life expectancy in 2030 is expected to reach 85·7 (84·2–87·4) years for men and 87·6 (86·7–88·9) years for women, further reducing the female advantage to 1·9 years. Life expectancy will reach or surpass 81·4 years for men and reach or surpass 84·5 years for women in every district by 2030. Longevity inequality across districts, measured as the difference between the 1st and 99th percentiles of district life expectancies, has risen since 1981, and is forecast to rise steadily to 8·3 years (6·8–9·7) for men and 8·3 years (7·1–9·4) for women by 2030. Interpretation Present forecasts underestimate the expected rise in life expectancy, especially for men, and hence the need to provide improved health and social services and pensions for elderly people in England and Wales. Health and social policies are needed to curb widening life expectancy inequalities, help deprived districts catch up in longevity gains, and avoid a so-called grand divergence in health and longevity. Funding UK Medical Research Council and Public Health England. PMID:25935825

Spatio Temporal EEG Source Imaging with the Hierarchical Bayesian Elastic Net and Elitist Lasso Models

PubMed Central

Paz-Linares, Deirel; Vega-Hernández, Mayrim; Rojas-López, Pedro A.; Valdés-Hernández, Pedro A.; Martínez-Montes, Eduardo; Valdés-Sosa, Pedro A.

2017-01-01

The estimation of EEG generating sources constitutes an Inverse Problem (IP) in Neuroscience. This is an ill-posed problem due to the non-uniqueness of the solution and regularization or prior information is needed to undertake Electrophysiology Source Imaging. Structured Sparsity priors can be attained through combinations of (L1 norm-based) and (L2 norm-based) constraints such as the Elastic Net (ENET) and Elitist Lasso (ELASSO) models. The former model is used to find solutions with a small number of smooth nonzero patches, while the latter imposes different degrees of sparsity simultaneously along different dimensions of the spatio-temporal matrix solutions. Both models have been addressed within the penalized regression approach, where the regularization parameters are selected heuristically, leading usually to non-optimal and computationally expensive solutions. The existing Bayesian formulation of ENET allows hyperparameter learning, but using the computationally intensive Monte Carlo/Expectation Maximization methods, which makes impractical its application to the EEG IP. While the ELASSO have not been considered before into the Bayesian context. In this work, we attempt to solve the EEG IP using a Bayesian framework for ENET and ELASSO models. We propose a Structured Sparse Bayesian Learning algorithm based on combining the Empirical Bayes and the iterative coordinate descent procedures to estimate both the parameters and hyperparameters. Using realistic simulations and avoiding the inverse crime we illustrate that our methods are able to recover complicated source setups more accurately and with a more robust estimation of the hyperparameters and behavior under different sparsity scenarios than classical LORETA, ENET and LASSO Fusion solutions. We also solve the EEG IP using data from a visual attention experiment, finding more interpretable neurophysiological patterns with our methods. The Matlab codes used in this work, including Simulations, Methods, Quality Measures and Visualization Routines are freely available in a public website. PMID:29200994

Spatio Temporal EEG Source Imaging with the Hierarchical Bayesian Elastic Net and Elitist Lasso Models.

PubMed

Paz-Linares, Deirel; Vega-Hernández, Mayrim; Rojas-López, Pedro A; Valdés-Hernández, Pedro A; Martínez-Montes, Eduardo; Valdés-Sosa, Pedro A

2017-01-01

The estimation of EEG generating sources constitutes an Inverse Problem (IP) in Neuroscience. This is an ill-posed problem due to the non-uniqueness of the solution and regularization or prior information is needed to undertake Electrophysiology Source Imaging. Structured Sparsity priors can be attained through combinations of (L1 norm-based) and (L2 norm-based) constraints such as the Elastic Net (ENET) and Elitist Lasso (ELASSO) models. The former model is used to find solutions with a small number of smooth nonzero patches, while the latter imposes different degrees of sparsity simultaneously along different dimensions of the spatio-temporal matrix solutions. Both models have been addressed within the penalized regression approach, where the regularization parameters are selected heuristically, leading usually to non-optimal and computationally expensive solutions. The existing Bayesian formulation of ENET allows hyperparameter learning, but using the computationally intensive Monte Carlo/Expectation Maximization methods, which makes impractical its application to the EEG IP. While the ELASSO have not been considered before into the Bayesian context. In this work, we attempt to solve the EEG IP using a Bayesian framework for ENET and ELASSO models. We propose a Structured Sparse Bayesian Learning algorithm based on combining the Empirical Bayes and the iterative coordinate descent procedures to estimate both the parameters and hyperparameters. Using realistic simulations and avoiding the inverse crime we illustrate that our methods are able to recover complicated source setups more accurately and with a more robust estimation of the hyperparameters and behavior under different sparsity scenarios than classical LORETA, ENET and LASSO Fusion solutions. We also solve the EEG IP using data from a visual attention experiment, finding more interpretable neurophysiological patterns with our methods. The Matlab codes used in this work, including Simulations, Methods, Quality Measures and Visualization Routines are freely available in a public website.

Genomic prediction using an iterative conditional expectation algorithm for a fast BayesC-like model.

PubMed

Dong, Linsong; Wang, Zhiyong

2018-06-11

Genomic prediction is feasible for estimating genomic breeding values because of dense genome-wide markers and credible statistical methods, such as Genomic Best Linear Unbiased Prediction (GBLUP) and various Bayesian methods. Compared with GBLUP, Bayesian methods propose more flexible assumptions for the distributions of SNP effects. However, most Bayesian methods are performed based on Markov chain Monte Carlo (MCMC) algorithms, leading to computational efficiency challenges. Hence, some fast Bayesian approaches, such as fast BayesB (fBayesB), were proposed to speed up the calculation. This study proposed another fast Bayesian method termed fast BayesC (fBayesC). The prior distribution of fBayesC assumes that a SNP with probability γ has a non-zero effect which comes from a normal density with a common variance. The simulated data from QTLMAS XII workshop and actual data on large yellow croaker were used to compare the predictive results of fBayesB, fBayesC and (MCMC-based) BayesC. The results showed that when γ was set as a small value, such as 0.01 in the simulated data or 0.001 in the actual data, fBayesB and fBayesC yielded lower prediction accuracies (abilities) than BayesC. In the actual data, fBayesC could yield very similar predictive abilities as BayesC when γ ≥ 0.01. When γ = 0.01, fBayesB could also yield similar results as fBayesC and BayesC. However, fBayesB could not yield an explicit result when γ ≥ 0.1, but a similar situation was not observed for fBayesC. Moreover, the computational speed of fBayesC was significantly faster than that of BayesC, making fBayesC a promising method for genomic prediction.

Bayesian regression discontinuity designs: incorporating clinical knowledge in the causal analysis of primary care data.

PubMed

Geneletti, Sara; O'Keeffe, Aidan G; Sharples, Linda D; Richardson, Sylvia; Baio, Gianluca

2015-07-10

The regression discontinuity (RD) design is a quasi-experimental design that estimates the causal effects of a treatment by exploiting naturally occurring treatment rules. It can be applied in any context where a particular treatment or intervention is administered according to a pre-specified rule linked to a continuous variable. Such thresholds are common in primary care drug prescription where the RD design can be used to estimate the causal effect of medication in the general population. Such results can then be contrasted to those obtained from randomised controlled trials (RCTs) and inform prescription policy and guidelines based on a more realistic and less expensive context. In this paper, we focus on statins, a class of cholesterol-lowering drugs, however, the methodology can be applied to many other drugs provided these are prescribed in accordance to pre-determined guidelines. Current guidelines in the UK state that statins should be prescribed to patients with 10-year cardiovascular disease risk scores in excess of 20%. If we consider patients whose risk scores are close to the 20%  risk score threshold, we find that there is an element of random variation in both the risk score itself and its measurement. We can therefore consider the threshold as a randomising device that assigns statin prescription to individuals just above the threshold and withholds it from those just below. Thus, we are effectively replicating the conditions of an RCT in the area around the threshold, removing or at least mitigating confounding. We frame the RD design in the language of conditional independence, which clarifies the assumptions necessary to apply an RD design to data, and which makes the links with instrumental variables clear. We also have context-specific knowledge about the expected sizes of the effects of statin prescription and are thus able to incorporate this into Bayesian models by formulating informative priors on our causal parameters. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Drought-Adaptation Potential in Fagus sylvatica: Linking Moisture Availability with Genetic Diversity and Dendrochronology

PubMed Central

Pluess, Andrea R.; Weber, Pascale

2012-01-01

Background Microevolution is essential for species persistence especially under anticipated climate change scenarios. Species distribution projection models suggested that the dominant tree species of lowland forests in Switzerland, European beech (Fagus sylvatica L.), might disappear from most areas due to expected longer dry periods. However, if genotypes at the moisture boundary of the species climatic envelope are adapted to lower moisture availability, they can serve as seed source for the continuation of beech forests under changing climates. Methodology/Principal Findings With an AFLP genome scan approach, we studied neutral and potentially adaptive genetic variation in Fagus sylvatica in three regions containing a dry and a mesic site each (n ind. = 241, n markers = 517). We linked this dataset with dendrochronological growth measures and local moisture availabilities based on precipitation and soil characteristics. Genetic diversity decreased slightly at dry sites. Overall genetic differentiation was low (F st = 0.028) and Bayesian cluster analysis grouped all populations together suggesting high (historical) gene flow. The Bayesian outlier analyses indicated 13 markers with three markers differing between all dry and mesic sites and the others between the contrasting sites within individual regions. A total of 41 markers, including seven outlier loci, changed their frequency with local moisture availability. Tree height and median basal growth increments were reduced at dry sites, but marker presence/absence was not related to dendrochronological characteristics. Conclusion and Their Significance The outlier alleles and the makers with changing frequencies in relation to moisture availability indicate microevolutionary processes occurring within short geographic distances. The general genetic similarity among sites suggests that ‘preadaptive’ genes can easily spread across the landscape. Yet, due to the long live span of trees, fostering saplings originating from dry sites and grown within mesic sites might increase resistance of beech forests during the anticipated longer dry periods. PMID:22448260

Drought-adaptation potential in Fagus sylvatica: linking moisture availability with genetic diversity and dendrochronology.

PubMed

Pluess, Andrea R; Weber, Pascale

2012-01-01

Microevolution is essential for species persistence especially under anticipated climate change scenarios. Species distribution projection models suggested that the dominant tree species of lowland forests in Switzerland, European beech (Fagus sylvatica L.), might disappear from most areas due to expected longer dry periods. However, if genotypes at the moisture boundary of the species climatic envelope are adapted to lower moisture availability, they can serve as seed source for the continuation of beech forests under changing climates. With an AFLP genome scan approach, we studied neutral and potentially adaptive genetic variation in Fagus sylvatica in three regions containing a dry and a mesic site each (n(ind.) = 241, n(markers) = 517). We linked this dataset with dendrochronological growth measures and local moisture availabilities based on precipitation and soil characteristics. Genetic diversity decreased slightly at dry sites. Overall genetic differentiation was low (F(st) = 0.028) and Bayesian cluster analysis grouped all populations together suggesting high (historical) gene flow. The Bayesian outlier analyses indicated 13 markers with three markers differing between all dry and mesic sites and the others between the contrasting sites within individual regions. A total of 41 markers, including seven outlier loci, changed their frequency with local moisture availability. Tree height and median basal growth increments were reduced at dry sites, but marker presence/absence was not related to dendrochronological characteristics. CONCLUSION AND THEIR SIGNIFICANCE: The outlier alleles and the makers with changing frequencies in relation to moisture availability indicate microevolutionary processes occurring within short geographic distances. The general genetic similarity among sites suggests that 'preadaptive' genes can easily spread across the landscape. Yet, due to the long live span of trees, fostering saplings originating from dry sites and grown within mesic sites might increase resistance of beech forests during the anticipated longer dry periods.

Genetic Structure in a Small Pelagic Fish Coincides with a Marine Protected Area: Seascape Genetics in Patagonian Fjords

PubMed Central

Ferrada-Fuentes, Sandra; Galleguillos, Ricardo; Hernández, Cristián E.

2016-01-01

Marine environmental variables can play an important role in promoting population genetic differentiation in marine organisms. Although fjord ecosystems have attracted much attention due to the great oscillation of environmental variables that produce heterogeneous habitats, species inhabiting this kind of ecosystem have received less attention. In this study, we used Sprattus fuegensis, a small pelagic species that populates the inner waters of the continental shelf, channels and fjords of Chilean Patagonia and Argentina, as a model species to test whether environmental variables of fjords relate to population genetic structure. A total of 282 individuals were analyzed from Chilean Patagonia with eight microsatellite loci. Bayesian and non-Bayesian analyses were conducted to describe the genetic variability of S. fuegensis and whether it shows spatial genetic structure. Results showed two well-differentiated genetic clusters along the Chilean Patagonia distribution (i.e. inside the embayment area called TicToc, and the rest of the fjords), but no spatial isolation by distance (IBD) pattern was found with a Mantel test analysis. Temperature and nitrate were correlated to the expected heterozygosities and explained the allelic frequency variation of data in the redundancy analyses. These results suggest that the singular genetic differences found in S. fuegensis from inside TicToc Bay (East of the Corcovado Gulf) are the result of larvae retention bya combination of oceanographic mesoscale processes (i.e. the west wind drift current reaches the continental shelf exactly in this zone), and the local geographical configuration (i.e. embayment area, islands, archipelagos). We propose that these features generated an isolated area in the Patagonian fjords that promoted genetic differentiation by drift and a singular biodiversity, adding support to the existence of the largest marine protected area (MPA) of continental Chile, which is the Tic-Toc MPA. PMID:27505009

Bayesian deconvolution and quantification of metabolites in complex 1D NMR spectra using BATMAN.

PubMed

Hao, Jie; Liebeke, Manuel; Astle, William; De Iorio, Maria; Bundy, Jacob G; Ebbels, Timothy M D

2014-01-01

Data processing for 1D NMR spectra is a key bottleneck for metabolomic and other complex-mixture studies, particularly where quantitative data on individual metabolites are required. We present a protocol for automated metabolite deconvolution and quantification from complex NMR spectra by using the Bayesian automated metabolite analyzer for NMR (BATMAN) R package. BATMAN models resonances on the basis of a user-controllable set of templates, each of which specifies the chemical shifts, J-couplings and relative peak intensities for a single metabolite. Peaks are allowed to shift position slightly between spectra, and peak widths are allowed to vary by user-specified amounts. NMR signals not captured by the templates are modeled non-parametrically by using wavelets. The protocol covers setting up user template libraries, optimizing algorithmic input parameters, improving prior information on peak positions, quality control and evaluation of outputs. The outputs include relative concentration estimates for named metabolites together with associated Bayesian uncertainty estimates, as well as the fit of the remainder of the spectrum using wavelets. Graphical diagnostics allow the user to examine the quality of the fit for multiple spectra simultaneously. This approach offers a workflow to analyze large numbers of spectra and is expected to be useful in a wide range of metabolomics studies.

Application of Bayesian configural frequency analysis (BCFA) to determine characteristics user and non-user motor X

NASA Astrophysics Data System (ADS)

Mawardi, Muhamad Iqbal; Padmadisastra, Septiadi; Tantular, Bertho

2018-03-01

Configural Frequency Analysis is a method for cell-wise testing in contingency tables for exploratory search type and antitype, that can see the existence of discrepancy on the model by existence of a significant difference between the frequency of observation and frequency of expectation. This analysis focuses on whether or not the interaction among categories from different variables, and not the interaction among variables. One of the extensions of CFA method is Bayesian CFA, this alternative method pursue the same goal as frequentist version of CFA with the advantage that adjustment of the experiment-wise significance level α is not necessary and test whether groups of types and antitypes form composite types or composite antitypes. Hence, this research will present the concept of the Bayesian CFA and how it works for the real data. The data on this paper is based on case studies in a company about decrease Brand Awareness & Image motor X on Top Of Mind Unit indicator in Cirebon City for user 30.8% and non user 9.8%. From the result of B-CFA have four characteristics from deviation, one of the four characteristics above that is the configuration 2212 need more attention by company to determine promotion strategy to maintain and improve Top Of Mind Unit in Cirebon City.

Exploring the Specifications of Spatial Adjacencies and Weights in Bayesian Spatial Modeling with Intrinsic Conditional Autoregressive Priors in a Small-area Study of Fall Injuries

PubMed Central

Law, Jane

2016-01-01

Intrinsic conditional autoregressive modeling in a Bayeisan hierarchical framework has been increasingly applied in small-area ecological studies. This study explores the specifications of spatial structure in this Bayesian framework in two aspects: adjacency, i.e., the set of neighbor(s) for each area; and (spatial) weight for each pair of neighbors. Our analysis was based on a small-area study of falling injuries among people age 65 and older in Ontario, Canada, that was aimed to estimate risks and identify risk factors of such falls. In the case study, we observed incorrect adjacencies information caused by deficiencies in the digital map itself. Further, when equal weights was replaced by weights based on a variable of expected count, the range of estimated risks increased, the number of areas with probability of estimated risk greater than one at different probability thresholds increased, and model fit improved. More importantly, significance of a risk factor diminished. Further research to thoroughly investigate different methods of variable weights; quantify the influence of specifications of spatial weights; and develop strategies for better defining spatial structure of a map in small-area analysis in Bayesian hierarchical spatial modeling is recommended. PMID:29546147

Tidally induced variations in vertical and horizontal motion on Rutford Ice Stream, West Antarctica, inferred from remotely sensed observations

NASA Astrophysics Data System (ADS)

Minchew, B. M.; Simons, M.; Riel, B.; Milillo, P.

2017-01-01

To better understand the influence of stress changes over floating ice shelves on grounded ice streams, we develop a Bayesian method for inferring time-dependent 3-D surface velocity fields from synthetic aperture radar (SAR) and optical remote sensing data. Our specific goal is to observe ocean tide-induced variability in vertical ice shelf position and horizontal ice stream flow. Thus, we consider the special case where observed surface displacement at a given location can be defined by a 3-D secular velocity vector, a family of 3-D sinusoidal functions, and a correction to the digital elevation model used to process the SAR data. Using nearly 9 months of SAR data collected from multiple satellite viewing geometries with the COSMO-SkyMed 4-satellite constellation, we infer the spatiotemporal response of Rutford Ice Stream, West Antarctica, to ocean tidal forcing. Consistent with expected tidal uplift, inferred vertical motion over the ice shelf is dominated by semidiurnal and diurnal tidal constituents. Horizontal ice flow variability, on the other hand, occurs primarily at the fortnightly spring-neap tidal period (Msf). We propose that periodic grounding of the ice shelf is the primary mechanism for translating vertical tidal motion into horizontal flow variability, causing ice flow to accelerate first and most strongly over the ice shelf. Flow variations then propagate through the grounded ice stream at a mean rate of ˜29 km/d and decay quasi-linearly with distance over ˜85 km upstream of the grounding zone.

Field heritability of a plant adaptation to fire in heterogeneous landscapes.

PubMed

Castellanos, M C; González-Martínez, S C; Pausas, J G

2015-11-01

The strong association observed between fire regimes and variation in plant adaptations to fire suggests a rapid response to fire as an agent of selection. It also suggests that fire-related traits are heritable, a precondition for evolutionary change. One example is serotiny, the accumulation of seeds in unopened fruits or cones until the next fire, an important strategy for plant population persistence in fire-prone ecosystems. Here, we evaluate the potential of this trait to respond to natural selection in its natural setting. For this, we use a SNP marker approach to estimate genetic variance and heritability of serotiny directly in the field for two Mediterranean pine species. Study populations were large and heterogeneous in climatic conditions and fire regime. We first estimated the realized relatedness among trees from genotypes, and then partitioned the phenotypic variance in serotiny using Bayesian animal models that incorporated environmental predictors. As expected, field heritability was smaller (around 0.10 for both species) than previous estimates under common garden conditions (0.20). An estimate on a subset of stands with more homogeneous environmental conditions was not different from that in the complete set of stands, suggesting that our models correctly captured the environmental variation at the spatial scale of the study. Our results highlight the importance of measuring quantitative genetic parameters in natural populations, where environmental heterogeneity is a critical aspect. The heritability of serotiny, although not high, combined with high phenotypic variance within populations, confirms the potential of this fire-related trait for evolutionary change in the wild. © 2015 John Wiley & Sons Ltd.

Lateral Variations of the Behavior of the North Anatolian Fault from the Marmara Sea to the Karliova Triple Junction Using Geodetic Data

NASA Astrophysics Data System (ADS)

Masson, F.; Klein, E.; Rembert, F.; Peyret, M.; Duputel, Z.; Yavasoglu, H.; Ulrich, P.

2017-12-01

The North Anatolian Fault (NAF) is the major transform system that accommodates the westward movement of the relatively rigid Anatolian block with respect to Eurasia. Mitigating the hazard associated with devastating earthquakes requires understanding how the NAF accumulates and releases the stored elastic strain energy both in space and in time. In this study, we present new results obtained from re-analyzed geodetic data sets: 1- along the offshore segment of the NAF through the Marmara Sea and 2- along the whole onshore NAF from Ismetpaça to Karliova. To study the Marmara sea segments, we analyze GPS and InSAR data from Istanbul to Tekirdag and propose a new interpretation of the velocity field in the area. The results indicate large east-west variations in the behavior of the fault that are modeled using a Bayesian approach. Some parts of the fault are probably creeping at shallow depth, inducing a lower strain accumulation than expected if the fault is fully locked. Along the NAF from Ismetpaça to Karliova, we use a synthesis of the velocities provided by Kreemer et al. (2014), updated with the new data provided by Aktug et al. (2015). The main results indicate (1) a contrasted behavior between eastern and western segments of the fault, the eastern part being fully locked while the western part is only partially coupled and (2) the existence of compressional and extensional segments that are well-correlated with pull-apart basins and mountain ranges respectively.

How Many Batches Are Needed for Process Validation under the New FDA Guidance?

PubMed

Yang, Harry

2013-01-01

The newly updated FDA Guidance for Industry on Process Validation: General Principles and Practices ushers in a life cycle approach to process validation. While the guidance no longer considers the use of traditional three-batch validation appropriate, it does not prescribe the number of validation batches for a prospective validation protocol, nor does it provide specific methods to determine it. This potentially could leave manufacturers in a quandary. In this paper, I develop a Bayesian method to address the issue. By combining process knowledge gained from Stage 1 Process Design (PD) with expected outcomes of Stage 2 Process Performance Qualification (PPQ), the number of validation batches for PPQ is determined to provide a high level of assurance that the process will consistently produce future batches meeting quality standards. Several examples based on simulated data are presented to illustrate the use of the Bayesian method in helping manufacturers make risk-based decisions for Stage 2 PPQ, and they highlight the advantages of the method over traditional Frequentist approaches. The discussions in the paper lend support for a life cycle and risk-based approach to process validation recommended in the new FDA guidance. The newly updated FDA Guidance for Industry on Process Validation: General Principles and Practices ushers in a life cycle approach to process validation. While the guidance no longer considers the use of traditional three-batch validation appropriate, it does not prescribe the number of validation batches for a prospective validation protocol, nor does it provide specific methods to determine it. This potentially could leave manufacturers in a quandary. In this paper, I develop a Bayesian method to address the issue. By combining process knowledge gained from Stage 1 Process Design (PD) with expected outcomes of Stage 2 Process Performance Qualification (PPQ), the number of validation batches for PPQ is determined to provide a high level of assurance that the process will consistently produce future batches meeting quality standards. Several examples based on simulated data are presented to illustrate the use of the Bayesian method in helping manufacturers make risk-based decisions for Stage 2 PPQ, and THEY highlight the advantages of the method over traditional Frequentist approaches. The discussions in the paper lend support for a life cycle and risk-based approach to process validation recommended in the new FDA guidance.

Protein degradation rate is the dominant mechanism accounting for the differences in protein abundance of basal p53 in a human breast and colorectal cancer cell line.

PubMed

Lakatos, Eszter; Salehi-Reyhani, Ali; Barclay, Michael; Stumpf, Michael P H; Klug, David R

2017-01-01

We determine p53 protein abundances and cell to cell variation in two human cancer cell lines with single cell resolution, and show that the fractional width of the distributions is the same in both cases despite a large difference in average protein copy number. We developed a computational framework to identify dominant mechanisms controlling the variation of protein abundance in a simple model of gene expression from the summary statistics of single cell steady state protein expression distributions. Our results, based on single cell data analysed in a Bayesian framework, lends strong support to a model in which variation in the basal p53 protein abundance may be best explained by variations in the rate of p53 protein degradation. This is supported by measurements of the relative average levels of mRNA which are very similar despite large variation in the level of protein.

VINE: A Variational Inference -Based Bayesian Neural Network Engine

DTIC Science & Technology

2018-01-01

networks are trained using the same dataset and hyper parameter settings as discussed. Table 1 Performance evaluation of the proposed transfer learning...multiplication/addition/subtraction. These operations can be implemented using nested loops in which various iterations of a loop are independent of...each other. This introduces an opportunity for optimization where a loop may be unrolled fully or partially to increase parallelism at the cost of

Bayesian segmentation of atrium wall using globally-optimal graph cuts on 3D meshes.

PubMed

Veni, Gopalkrishna; Fu, Zhisong; Awate, Suyash P; Whitaker, Ross T

2013-01-01

Efficient segmentation of the left atrium (LA) wall from delayed enhancement MRI is challenging due to inconsistent contrast, combined with noise, and high variation in atrial shape and size. We present a surface-detection method that is capable of extracting the atrial wall by computing an optimal a-posteriori estimate. This estimation is done on a set of nested meshes, constructed from an ensemble of segmented training images, and graph cuts on an associated multi-column, proper-ordered graph. The graph/mesh is a part of a template/model that has an associated set of learned intensity features. When this mesh is overlaid onto a test image, it produces a set of costs which lead to an optimal segmentation. The 3D mesh has an associated weighted, directed multi-column graph with edges that encode smoothness and inter-surface penalties. Unlike previous graph-cut methods that impose hard constraints on the surface properties, the proposed method follows from a Bayesian formulation resulting in soft penalties on spatial variation of the cuts through the mesh. The novelty of this method also lies in the construction of proper-ordered graphs on complex shapes for choosing among distinct classes of base shapes for automatic LA segmentation. We evaluate the proposed segmentation framework on simulated and clinical cardiac MRI.

Possible determinants and spatial patterns of anaemia among young children in Nigeria: a Bayesian semi-parametric modelling.

PubMed

Gayawan, Ezra; Arogundade, Ekundayo D; Adebayo, Samson B

2014-03-01

Anaemia is a global public health problem affecting both developing and developed countries with major consequences for human health and socioeconomic development. This paper examines the possible relationship between Hb concentration and severity of anaemia with individual and household characteristics of children aged 6-59 months in Nigeria; and explores possible geographical variations of these outcome variables. Data on Hb concentration and severity of anaemia in children aged 6-59 months that participated in the 2010 Nigeria Malaria Indicator Survey were analysed. A semi-parametric model using a hierarchical Bayesian approach was adopted to examine the putative relationship of covariates of different types and possible spatial variation. Gaussian, binary and ordinal outcome variables were considered in modelling. Spatial analyses reveal a distinct North-South divide in Hb concentration of the children analysed and that states in Northern Nigeria possess a higher risk of anaemia. Other important risk factors include the household wealth index, sex of the child, whether or not the child had fever or malaria in the 2 weeks preceding the survey, and children under 24 months of age. There is a need for state level implementation of specific programmes that target vulnerable children as this can help in reversing the existing patterns.

Genetic Structure of Bluefin Tuna in the Mediterranean Sea Correlates with Environmental Variables

PubMed Central

Riccioni, Giulia; Stagioni, Marco; Landi, Monica; Ferrara, Giorgia; Barbujani, Guido; Tinti, Fausto

2013-01-01

Background Atlantic Bluefin Tuna (ABFT) shows complex demography and ecological variation in the Mediterranean Sea. Genetic surveys have detected significant, although weak, signals of population structuring; catch series analyses and tagging programs identified complex ABFT spatial dynamics and migration patterns. Here, we tested the hypothesis that the genetic structure of the ABFT in the Mediterranean is correlated with mean surface temperature and salinity. Methodology We used six samples collected from Western and Central Mediterranean integrated with a new sample collected from the recently identified easternmost reproductive area of Levantine Sea. To assess population structure in the Mediterranean we used a multidisciplinary framework combining classical population genetics, spatial and Bayesian clustering methods and a multivariate approach based on factor analysis. Conclusions FST analysis and Bayesian clustering methods detected several subpopulations in the Mediterranean, a result also supported by multivariate analyses. In addition, we identified significant correlations of genetic diversity with mean salinity and surface temperature values revealing that ABFT is genetically structured along two environmental gradients. These results suggest that a preference for some spawning habitat conditions could contribute to shape ABFT genetic structuring in the Mediterranean. However, further studies should be performed to assess to what extent ABFT spawning behaviour in the Mediterranean Sea can be affected by environmental variation. PMID:24260341

A Bayesian Nonparametric Approach to Image Super-Resolution.

PubMed

Polatkan, Gungor; Zhou, Mingyuan; Carin, Lawrence; Blei, David; Daubechies, Ingrid

2015-02-01

Super-resolution methods form high-resolution images from low-resolution images. In this paper, we develop a new Bayesian nonparametric model for super-resolution. Our method uses a beta-Bernoulli process to learn a set of recurring visual patterns, called dictionary elements, from the data. Because it is nonparametric, the number of elements found is also determined from the data. We test the results on both benchmark and natural images, comparing with several other models from the research literature. We perform large-scale human evaluation experiments to assess the visual quality of the results. In a first implementation, we use Gibbs sampling to approximate the posterior. However, this algorithm is not feasible for large-scale data. To circumvent this, we then develop an online variational Bayes (VB) algorithm. This algorithm finds high quality dictionaries in a fraction of the time needed by the Gibbs sampler.

A Bayesian Measurment Error Model for Misaligned Radiographic Data

DOE PAGES

Lennox, Kristin P.; Glascoe, Lee G.

2013-09-06

An understanding of the inherent variability in micro-computed tomography (micro-CT) data is essential to tasks such as statistical process control and the validation of radiographic simulation tools. The data present unique challenges to variability analysis due to the relatively low resolution of radiographs, and also due to minor variations from run to run which can result in misalignment or magnification changes between repeated measurements of a sample. Positioning changes artificially inflate the variability of the data in ways that mask true physical phenomena. We present a novel Bayesian nonparametric regression model that incorporates both additive and multiplicative measurement error inmore » addition to heteroscedasticity to address this problem. We also use this model to assess the effects of sample thickness and sample position on measurement variability for an aluminum specimen. Supplementary materials for this article are available online.« less

Annealed Importance Sampling for Neural Mass Models

PubMed Central

Penny, Will; Sengupta, Biswa

2016-01-01

Neural Mass Models provide a compact description of the dynamical activity of cell populations in neocortical regions. Moreover, models of regional activity can be connected together into networks, and inferences made about the strength of connections, using M/EEG data and Bayesian inference. To date, however, Bayesian methods have been largely restricted to the Variational Laplace (VL) algorithm which assumes that the posterior distribution is Gaussian and finds model parameters that are only locally optimal. This paper explores the use of Annealed Importance Sampling (AIS) to address these restrictions. We implement AIS using proposals derived from Langevin Monte Carlo (LMC) which uses local gradient and curvature information for efficient exploration of parameter space. In terms of the estimation of Bayes factors, VL and AIS agree about which model is best but report different degrees of belief. Additionally, AIS finds better model parameters and we find evidence of non-Gaussianity in their posterior distribution. PMID:26942606

Decision making with epistemic uncertainty under safety constraints: An application to seismic design

USGS Publications Warehouse

Veneziano, D.; Agarwal, A.; Karaca, E.

2009-01-01

The problem of accounting for epistemic uncertainty in risk management decisions is conceptually straightforward, but is riddled with practical difficulties. Simple approximations are often used whereby future variations in epistemic uncertainty are ignored or worst-case scenarios are postulated. These strategies tend to produce sub-optimal decisions. We develop a general framework based on Bayesian decision theory and exemplify it for the case of seismic design of buildings. When temporal fluctuations of the epistemic uncertainties and regulatory safety constraints are included, the optimal level of seismic protection exceeds the normative level at the time of construction. Optimal Bayesian decisions do not depend on the aleatory or epistemic nature of the uncertainties, but only on the total (epistemic plus aleatory) uncertainty and how that total uncertainty varies randomly during the lifetime of the project. ?? 2009 Elsevier Ltd. All rights reserved.

Predicting coastal cliff erosion using a Bayesian probabilistic model

USGS Publications Warehouse

Hapke, Cheryl J.; Plant, Nathaniel G.

2010-01-01

Regional coastal cliff retreat is difficult to model due to the episodic nature of failures and the along-shore variability of retreat events. There is a growing demand, however, for predictive models that can be used to forecast areas vulnerable to coastal erosion hazards. Increasingly, probabilistic models are being employed that require data sets of high temporal density to define the joint probability density function that relates forcing variables (e.g. wave conditions) and initial conditions (e.g. cliff geometry) to erosion events. In this study we use a multi-parameter Bayesian network to investigate correlations between key variables that control and influence variations in cliff retreat processes. The network uses Bayesian statistical methods to estimate event probabilities using existing observations. Within this framework, we forecast the spatial distribution of cliff retreat along two stretches of cliffed coast in Southern California. The input parameters are the height and slope of the cliff, a descriptor of material strength based on the dominant cliff-forming lithology, and the long-term cliff erosion rate that represents prior behavior. The model is forced using predicted wave impact hours. Results demonstrate that the Bayesian approach is well-suited to the forward modeling of coastal cliff retreat, with the correct outcomes forecast in 70–90% of the modeled transects. The model also performs well in identifying specific locations of high cliff erosion, thus providing a foundation for hazard mapping. This approach can be employed to predict cliff erosion at time-scales ranging from storm events to the impacts of sea-level rise at the century-scale.

Uncertainty Analysis and Parameter Estimation For Nearshore Hydrodynamic Models

NASA Astrophysics Data System (ADS)

Ardani, S.; Kaihatu, J. M.

2012-12-01

Numerical models represent deterministic approaches used for the relevant physical processes in the nearshore. Complexity of the physics of the model and uncertainty involved in the model inputs compel us to apply a stochastic approach to analyze the robustness of the model. The Bayesian inverse problem is one powerful way to estimate the important input model parameters (determined by apriori sensitivity analysis) and can be used for uncertainty analysis of the outputs. Bayesian techniques can be used to find the range of most probable parameters based on the probability of the observed data and the residual errors. In this study, the effect of input data involving lateral (Neumann) boundary conditions, bathymetry and off-shore wave conditions on nearshore numerical models are considered. Monte Carlo simulation is applied to a deterministic numerical model (the Delft3D modeling suite for coupled waves and flow) for the resulting uncertainty analysis of the outputs (wave height, flow velocity, mean sea level and etc.). Uncertainty analysis of outputs is performed by random sampling from the input probability distribution functions and running the model as required until convergence to the consistent results is achieved. The case study used in this analysis is the Duck94 experiment, which was conducted at the U.S. Army Field Research Facility at Duck, North Carolina, USA in the fall of 1994. The joint probability of model parameters relevant for the Duck94 experiments will be found using the Bayesian approach. We will further show that, by using Bayesian techniques to estimate the optimized model parameters as inputs and applying them for uncertainty analysis, we can obtain more consistent results than using the prior information for input data which means that the variation of the uncertain parameter will be decreased and the probability of the observed data will improve as well. Keywords: Monte Carlo Simulation, Delft3D, uncertainty analysis, Bayesian techniques, MCMC

Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies

PubMed Central

2010-01-01

Background Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. Results Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. Conclusions Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data. PMID:21062443

Reducing Variation in the Assessment of Student Writing

ERIC Educational Resources Information Center

Hunter, Kerry; Docherty, Peter

2011-01-01

This paper extends the literature on grader variation and the role of moderation and socialisation processes in reducing this variation. It offers a fresh categorisation of academics' assessment beliefs and expectations, and uses this categorisation to analyse the interaction between implicit and explicit expectations in relation to grader…

Migration from new-accession countries and duration expectancy in the EU-15: 2002–2008

PubMed Central

DeWaard, Jack; Ha, Jasmine Trang; Raymer, James; Wiśniowski, Arkadiusz

2016-01-01

European Union (EU) enlargements in 2004 and 2007 were accompanied by increased migration from new-accession to established-member (EU-15) countries. The impacts of these flows depend, in part, on the amount of time that persons from the former countries live in the latter over the life course. In this paper, we develop period estimates of duration expectancy in EU-15 countries among persons from new-accession countries. Using a newly developed set of harmonised Bayesian estimates of migration flows each year from 2002 to 2008 from the Integrated Modelling of European Migration (IMEM) Project, we exploit period age patterns of country-to-country migration and mortality to summarize the average number of years that persons from new-accession countries could be expected to live in EU-15 countries over the life course. In general, the results show that the amount of time that persons from new-accession countries could be expected to live in the EU-15 nearly doubled after 2004. PMID:28286353

A full-Bayesian approach to parameter inference from tracer travel time moments and investigation of scale effects at the Cape Cod experimental site

USGS Publications Warehouse

Woodbury, Allan D.; Rubin, Yoram

2000-01-01

A method for inverting the travel time moments of solutes in heterogeneous aquifers is presented and is based on peak concentration arrival times as measured at various samplers in an aquifer. The approach combines a Lagrangian [Rubin and Dagan, 1992] solute transport framework with full‐Bayesian hydrogeological parameter inference. In the full‐Bayesian approach the noise values in the observed data are treated as hyperparameters, and their effects are removed by marginalization. The prior probability density functions (pdfs) for the model parameters (horizontal integral scale, velocity, and log K variance) and noise values are represented by prior pdfs developed from minimum relative entropy considerations. Analysis of the Cape Cod (Massachusetts) field experiment is presented. Inverse results for the hydraulic parameters indicate an expected value for the velocity, variance of log hydraulic conductivity, and horizontal integral scale of 0.42 m/d, 0.26, and 3.0 m, respectively. While these results are consistent with various direct‐field determinations, the importance of the findings is in the reduction of confidence range about the various expected values. On selected control planes we compare observed travel time frequency histograms with the theoretical pdf, conditioned on the observed travel time moments. We observe a positive skew in the travel time pdf which tends to decrease as the travel time distance grows. We also test the hypothesis that there is no scale dependence of the integral scale λ with the scale of the experiment at Cape Cod. We adopt two strategies. The first strategy is to use subsets of the full data set and then to see if the resulting parameter fits are different as we use different data from control planes at expanding distances from the source. The second approach is from the viewpoint of entropy concentration. No increase in integral scale with distance is inferred from either approach over the range of the Cape Cod tracer experiment.

Bayesian evaluation of budgets for endemic disease control: An example using management changes to reduce milk somatic cell count early in the first lactation of Irish dairy cows.

PubMed

Archer, S C; Mc Coy, F; Wapenaar, W; Green, M J

2014-01-01

The aim of this research was to determine budgets for specific management interventions to control heifer mastitis in Irish dairy herds as an example of evidence synthesis and 1-step Bayesian micro-simulation in a veterinary context. Budgets were determined for different decision makers based on their willingness to pay. Reducing the prevalence of heifers with a high milk somatic cell count (SCC) early in the first lactation could be achieved through herd level management interventions for pre- and peri-partum heifers, however the cost effectiveness of these interventions is unknown. A synthesis of multiple sources of evidence, accounting for variability and uncertainty in the available data is invaluable to inform decision makers around likely economic outcomes of investing in disease control measures. One analytical approach to this is Bayesian micro-simulation, where the trajectory of different individuals undergoing specific interventions is simulated. The classic micro-simulation framework was extended to encompass synthesis of evidence from 2 separate statistical models and previous research, with the outcome for an individual cow or herd assessed in terms of changes in lifetime milk yield, disposal risk, and likely financial returns conditional on the interventions being simultaneously applied. The 3 interventions tested were storage of bedding inside, decreasing transition yard stocking density, and spreading of bedding evenly in the calving area. Budgets for the interventions were determined based on the minimum expected return on investment, and the probability of the desired outcome. Budgets for interventions to control heifer mastitis were highly dependent on the decision maker's willingness to pay, and hence minimum expected return on investment. Understanding the requirements of decision makers and their rational spending limits would be useful for the development of specific interventions for particular farms to control heifer mastitis, and other endemic diseases. Copyright © 2013 The Authors. Published by Elsevier B.V. All rights reserved.

Comparing models of the periodic variations in spin-down and beamwidth for PSR B1828-11

NASA Astrophysics Data System (ADS)

Ashton, G.; Jones, D. I.; Prix, R.

2016-05-01

We build a framework using tools from Bayesian data analysis to evaluate models explaining the periodic variations in spin-down and beamwidth of PSR B1828-11. The available data consist of the time-averaged spin-down rate, which displays a distinctive double-peaked modulation, and measurements of the beamwidth. Two concepts exist in the literature that are capable of explaining these variations; we formulate predictive models from these and quantitatively compare them. The first concept is phenomenological and stipulates that the magnetosphere undergoes periodic switching between two metastable states as first suggested by Lyne et al. The second concept, precession, was first considered as a candidate for the modulation of B1828-11 by Stairs et al. We quantitatively compare models built from these concepts using a Bayesian odds ratio. Because the phenomenological switching model itself was informed by these data in the first place, it is difficult to specify appropriate parameter-space priors that can be trusted for an unbiased model comparison. Therefore, we first perform a parameter estimation using the spin-down data, and then use the resulting posterior distributions as priors for model comparison on the beamwidth data. We find that a precession model with a simple circular Gaussian beam geometry fails to appropriately describe the data, while allowing for a more general beam geometry provides a good fit to the data. The resulting odds between the precession model (with a general beam geometry) and the switching model are estimated as 102.7±0.5 in favour of the precession model.

Improving the quantification of contrast enhanced ultrasound using a Bayesian approach

NASA Astrophysics Data System (ADS)

Rizzo, Gaia; Tonietto, Matteo; Castellaro, Marco; Raffeiner, Bernd; Coran, Alessandro; Fiocco, Ugo; Stramare, Roberto; Grisan, Enrico

2017-03-01

Contrast Enhanced Ultrasound (CEUS) is a sensitive imaging technique to assess tissue vascularity, that can be useful in the quantification of different perfusion patterns. This can be particularly important in the early detection and staging of arthritis. In a recent study we have shown that a Gamma-variate can accurately quantify synovial perfusion and it is flexible enough to describe many heterogeneous patterns. Moreover, we have shown that through a pixel-by-pixel analysis the quantitative information gathered characterizes more effectively the perfusion. However, the SNR ratio of the data and the nonlinearity of the model makes the parameter estimation difficult. Using classical non-linear-leastsquares (NLLS) approach the number of unreliable estimates (those with an asymptotic coefficient of variation greater than a user-defined threshold) is significant, thus affecting the overall description of the perfusion kinetics and of its heterogeneity. In this work we propose to solve the parameter estimation at the pixel level within a Bayesian framework using Variational Bayes (VB), and an automatic and data-driven prior initialization. When evaluating the pixels for which both VB and NLLS provided reliable estimates, we demonstrated that the parameter values provided by the two methods are well correlated (Pearson's correlation between 0.85 and 0.99). Moreover, the mean number of unreliable pixels drastically reduces from 54% (NLLS) to 26% (VB), without increasing the computational time (0.05 s/pixel for NLLS and 0.07 s/pixel for VB). When considering the efficiency of the algorithms as computational time per reliable estimate, VB outperforms NLLS (0.11 versus 0.25 seconds per reliable estimate respectively).

Hierarchical Bayesian modeling of spatio-temporal patterns of lung cancer incidence risk in Georgia, USA: 2000-2007

NASA Astrophysics Data System (ADS)

Yin, Ping; Mu, Lan; Madden, Marguerite; Vena, John E.

2014-10-01

Lung cancer is the second most commonly diagnosed cancer in both men and women in Georgia, USA. However, the spatio-temporal patterns of lung cancer risk in Georgia have not been fully studied. Hierarchical Bayesian models are used here to explore the spatio-temporal patterns of lung cancer incidence risk by race and gender in Georgia for the period of 2000-2007. With the census tract level as the spatial scale and the 2-year period aggregation as the temporal scale, we compare a total of seven Bayesian spatio-temporal models including two under a separate modeling framework and five under a joint modeling framework. One joint model outperforms others based on the deviance information criterion. Results show that the northwest region of Georgia has consistently high lung cancer incidence risk for all population groups during the study period. In addition, there are inverse relationships between the socioeconomic status and the lung cancer incidence risk among all Georgian population groups, and the relationships in males are stronger than those in females. By mapping more reliable variations in lung cancer incidence risk at a relatively fine spatio-temporal scale for different Georgian population groups, our study aims to better support healthcare performance assessment, etiological hypothesis generation, and health policy making.

Bayesian change point analysis of abundance trends for pelagic fishes in the upper San Francisco Estuary.

PubMed

Thomson, James R; Kimmerer, Wim J; Brown, Larry R; Newman, Ken B; Mac Nally, Ralph; Bennett, William A; Feyrer, Frederick; Fleishman, Erica

2010-07-01

We examined trends in abundance of four pelagic fish species (delta smelt, longfin smelt, striped bass, and threadfin shad) in the upper San Francisco Estuary, California, USA, over 40 years using Bayesian change point models. Change point models identify times of abrupt or unusual changes in absolute abundance (step changes) or in rates of change in abundance (trend changes). We coupled Bayesian model selection with linear regression splines to identify biotic or abiotic covariates with the strongest associations with abundances of each species. We then refitted change point models conditional on the selected covariates to explore whether those covariates could explain statistical trends or change points in species abundances. We also fitted a multispecies change point model that identified change points common to all species. All models included hierarchical structures to model data uncertainties, including observation errors and missing covariate values. There were step declines in abundances of all four species in the early 2000s, with a likely common decline in 2002. Abiotic variables, including water clarity, position of the 2 per thousand isohaline (X2), and the volume of freshwater exported from the estuary, explained some variation in species' abundances over the time series, but no selected covariates could explain statistically the post-2000 change points for any species.

Clarifying the debate on population-based screening for breast cancer with mammography

PubMed Central

Chen, Tony Hsiu-Hsi; Yen, Amy Ming-Fang; Fann, Jean Ching-Yuan; Gordon, Paula; Chen, Sam Li-Sheng; Chiu, Sherry Yueh-Hsia; Hsu, Chen-Yang; Chang, King-Jen; Lee, Won-Chul; Yeoh, Khay Guan; Saito, Hiroshi; Promthet, Supannee; Hamashima, Chisato; Maidin, Alimin; Robinson, Fredie; Zhao, Li-Zhong

2017-01-01

Abstract Background: The recent controversy about using mammography to screen for breast cancer based on randomized controlled trials over 3 decades in Western countries has not only eclipsed the paradigm of evidence-based medicine, but also puts health decision-makers in countries where breast cancer screening is still being considered in a dilemma to adopt or abandon such a well-established screening modality. Methods: We reanalyzed the empirical data from the Health Insurance Plan trial in 1963 to the UK age trial in 1991 and their follow-up data published until 2015. We first performed Bayesian conjugated meta-analyses on the heterogeneity of attendance rate, sensitivity, and over-detection and their impacts on advanced stage breast cancer and death from breast cancer across trials using Bayesian Poisson fixed- and random-effect regression model. Bayesian meta-analysis of causal model was then developed to assess a cascade of causal relationships regarding the impact of both attendance and sensitivity on 2 main outcomes. Results: The causes of heterogeneity responsible for the disparities across the trials were clearly manifested in 3 components. The attendance rate ranged from 61.3% to 90.4%. The sensitivity estimates show substantial variation from 57.26% to 87.97% but improved with time from 64% in 1963 to 82% in 1980 when Bayesian conjugated meta-analysis was conducted in chronological order. The percentage of over-detection shows a wide range from 0% to 28%, adjusting for long lead-time. The impacts of the attendance rate and sensitivity on the 2 main outcomes were statistically significant. Causal inference made by linking these causal relationships with emphasis on the heterogeneity of the attendance rate and sensitivity accounted for the variation in the reduction of advanced breast cancer (none-30%) and of mortality (none-31%). We estimated a 33% (95% CI: 24–42%) and 13% (95% CI: 6–20%) breast cancer mortality reduction for the best scenario (90% attendance rate and 95% sensitivity) and the poor scenario (30% attendance rate and 55% sensitivity), respectively. Conclusion: Elucidating the scenarios from high to low performance and learning from the experiences of these trials helps screening policy-makers contemplate on how to avoid errors made in ineffective studies and emulate the effective studies to save women lives. PMID:28099330

Bayesian statistics applied to the location of the source of explosions at Stromboli Volcano, Italy

USGS Publications Warehouse

Saccorotti, G.; Chouet, B.; Martini, M.; Scarpa, R.

1998-01-01

We present a method for determining the location and spatial extent of the source of explosions at Stromboli Volcano, Italy, based on a Bayesian inversion of the slowness vector derived from frequency-slowness analyses of array data. The method searches for source locations that minimize the error between the expected and observed slowness vectors. For a given set of model parameters, the conditional probability density function of slowness vectors is approximated by a Gaussian distribution of expected errors. The method is tested with synthetics using a five-layer velocity model derived for the north flank of Stromboli and a smoothed velocity model derived from a power-law approximation of the layered structure. Application to data from Stromboli allows for a detailed examination of uncertainties in source location due to experimental errors and incomplete knowledge of the Earth model. Although the solutions are not constrained in the radial direction, excellent resolution is achieved in both transverse and depth directions. Under the assumption that the horizontal extent of the source does not exceed the crater dimension, the 90% confidence region in the estimate of the explosive source location corresponds to a small volume extending from a depth of about 100 m to a maximum depth of about 300 m beneath the active vents, with a maximum likelihood source region located in the 120- to 180-m-depth interval.

GAD vaccine reduces insulin loss in recently diagnosed type 1 diabetes: findings from a Bayesian meta-analysis.

PubMed

Beam, Craig A; MacCallum, Colleen; Herold, Kevan C; Wherrett, Diane K; Palmer, Jerry; Ludvigsson, Johnny

2017-01-01

GAD is a major target of the autoimmune response that occurs in type 1 diabetes mellitus. Randomised controlled clinical trials of a GAD + alum vaccine in human participants have so far given conflicting results. In this study, we sought to see whether a clearer answer to the question of whether GAD65 has an effect on C-peptide could be reached by combining individual-level data from the randomised controlled trials using Bayesian meta-analysis to estimate the probability of a positive biological effect (a reduction in C-peptide loss compared with placebo approximately 1 year after the GAD vaccine). We estimate that there is a 98% probability that 20 μg GAD with alum administered twice yields a positive biological effect. The effect is probably a 15-20% reduction in the loss of C-peptide at approximately 1 year after treatment. This translates to an annual expected loss of between -0.250 and -0.235 pmol/ml in treated patients compared with an expected 2 h AUC loss of -0.294 pmol/ml at 1 year for untreated newly diagnosed patients. The biological effect of this vaccination should be developed further in order to reach clinically desirable reductions in insulin loss in patients recently diagnosed with type 1 diabetes.

Reference-dependent risk sensitivity as rational inference.

PubMed

Denrell, Jerker C

2015-07-01

Existing explanations of reference-dependent risk sensitivity attribute it to cognitive imperfections and heuristic choice processes. This article shows that behavior consistent with an S-shaped value function could be an implication of rational inferences about the expected values of alternatives. Theoretically, I demonstrate that even a risk-neutral Bayesian decision maker, who is uncertain about the reliability of observations, should use variability in observed outcomes as a predictor of low expected value for outcomes above a reference level, and as a predictor of high expected value for outcomes below a reference level. Empirically, I show that combining past outcomes using an S-shaped value function leads to accurate predictions about future values. The theory also offers a rationale for why risk sensitivity consistent with an inverse S-shaped value function should occur in experiments on decisions from experience with binary payoff distributions. (c) 2015 APA, all rights reserved).

A Bayesian method for assessing multiscalespecies-habitat relationships

USGS Publications Warehouse

Stuber, Erica F.; Gruber, Lutz F.; Fontaine, Joseph J.

2017-01-01

ContextScientists face several theoretical and methodological challenges in appropriately describing fundamental wildlife-habitat relationships in models. The spatial scales of habitat relationships are often unknown, and are expected to follow a multi-scale hierarchy. Typical frequentist or information theoretic approaches often suffer under collinearity in multi-scale studies, fail to converge when models are complex or represent an intractable computational burden when candidate model sets are large.ObjectivesOur objective was to implement an automated, Bayesian method for inference on the spatial scales of habitat variables that best predict animal abundance.MethodsWe introduce Bayesian latent indicator scale selection (BLISS), a Bayesian method to select spatial scales of predictors using latent scale indicator variables that are estimated with reversible-jump Markov chain Monte Carlo sampling. BLISS does not suffer from collinearity, and substantially reduces computation time of studies. We present a simulation study to validate our method and apply our method to a case-study of land cover predictors for ring-necked pheasant (Phasianus colchicus) abundance in Nebraska, USA.ResultsOur method returns accurate descriptions of the explanatory power of multiple spatial scales, and unbiased and precise parameter estimates under commonly encountered data limitations including spatial scale autocorrelation, effect size, and sample size. BLISS outperforms commonly used model selection methods including stepwise and AIC, and reduces runtime by 90%.ConclusionsGiven the pervasiveness of scale-dependency in ecology, and the implications of mismatches between the scales of analyses and ecological processes, identifying the spatial scales over which species are integrating habitat information is an important step in understanding species-habitat relationships. BLISS is a widely applicable method for identifying important spatial scales, propagating scale uncertainty, and testing hypotheses of scaling relationships.

A Bayesian Approach to the Overlap Analysis of Epidemiologically Linked Traits.

PubMed

Asimit, Jennifer L; Panoutsopoulou, Kalliope; Wheeler, Eleanor; Berndt, Sonja I; Cordell, Heather J; Morris, Andrew P; Zeggini, Eleftheria; Barroso, Inês

2015-12-01

Diseases often cooccur in individuals more often than expected by chance, and may be explained by shared underlying genetic etiology. A common approach to genetic overlap analyses is to use summary genome-wide association study data to identify single-nucleotide polymorphisms (SNPs) that are associated with multiple traits at a selected P-value threshold. However, P-values do not account for differences in power, whereas Bayes' factors (BFs) do, and may be approximated using summary statistics. We use simulation studies to compare the power of frequentist and Bayesian approaches with overlap analyses, and to decide on appropriate thresholds for comparison between the two methods. It is empirically illustrated that BFs have the advantage over P-values of a decreasing type I error rate as study size increases for single-disease associations. Consequently, the overlap analysis of traits from different-sized studies encounters issues in fair P-value threshold selection, whereas BFs are adjusted automatically. Extensive simulations show that Bayesian overlap analyses tend to have higher power than those that assess association strength with P-values, particularly in low-power scenarios. Calibration tables between BFs and P-values are provided for a range of sample sizes, as well as an approximation approach for sample sizes that are not in the calibration table. Although P-values are sometimes thought more intuitive, these tables assist in removing the opaqueness of Bayesian thresholds and may also be used in the selection of a BF threshold to meet a certain type I error rate. An application of our methods is used to identify variants associated with both obesity and osteoarthritis. © 2015 The Authors. *Genetic Epidemiology published by Wiley Periodicals, Inc.

An approach based on Hierarchical Bayesian Graphical Models for measurement interpretation under uncertainty

NASA Astrophysics Data System (ADS)

Skataric, Maja; Bose, Sandip; Zeroug, Smaine; Tilke, Peter

2017-02-01

It is not uncommon in the field of non-destructive evaluation that multiple measurements encompassing a variety of modalities are available for analysis and interpretation for determining the underlying states of nature of the materials or parts being tested. Despite and sometimes due to the richness of data, significant challenges arise in the interpretation manifested as ambiguities and inconsistencies due to various uncertain factors in the physical properties (inputs), environment, measurement device properties, human errors, and the measurement data (outputs). Most of these uncertainties cannot be described by any rigorous mathematical means, and modeling of all possibilities is usually infeasible for many real time applications. In this work, we will discuss an approach based on Hierarchical Bayesian Graphical Models (HBGM) for the improved interpretation of complex (multi-dimensional) problems with parametric uncertainties that lack usable physical models. In this setting, the input space of the physical properties is specified through prior distributions based on domain knowledge and expertise, which are represented as Gaussian mixtures to model the various possible scenarios of interest for non-destructive testing applications. Forward models are then used offline to generate the expected distribution of the proposed measurements which are used to train a hierarchical Bayesian network. In Bayesian analysis, all model parameters are treated as random variables, and inference of the parameters is made on the basis of posterior distribution given the observed data. Learned parameters of the posterior distribution obtained after the training can therefore be used to build an efficient classifier for differentiating new observed data in real time on the basis of pre-trained models. We will illustrate the implementation of the HBGM approach to ultrasonic measurements used for cement evaluation of cased wells in the oil industry.

Bayesian Modeling of NMR Data: Quantifying Longitudinal Relaxation in Vivo, and in Vitro with a Tissue-Water-Relaxation Mimic (Crosslinked Bovine Serum Albumin).

PubMed

Meinerz, Kelsey; Beeman, Scott C; Duan, Chong; Bretthorst, G Larry; Garbow, Joel R; Ackerman, Joseph J H

2018-01-01

Recently, a number of MRI protocols have been reported that seek to exploit the effect of dissolved oxygen (O 2 , paramagnetic) on the longitudinal 1 H relaxation of tissue water, thus providing image contrast related to tissue oxygen content. However, tissue water relaxation is dependent on a number of mechanisms, and this raises the issue of how best to model the relaxation data. This problem, the model selection problem, occurs in many branches of science and is optimally addressed by Bayesian probability theory. High signal-to-noise, densely sampled, longitudinal 1 H relaxation data were acquired from rat brain in vivo and from a cross-linked bovine serum albumin (xBSA) phantom, a sample that recapitulates the relaxation characteristics of tissue water in vivo . Bayesian-based model selection was applied to a cohort of five competing relaxation models: (i) monoexponential, (ii) stretched-exponential, (iii) biexponential, (iv) Gaussian (normal) R 1 -distribution, and (v) gamma R 1 -distribution. Bayesian joint analysis of multiple replicate datasets revealed that water relaxation of both the xBSA phantom and in vivo rat brain was best described by a biexponential model, while xBSA relaxation datasets truncated to remove evidence of the fast relaxation component were best modeled as a stretched exponential. In all cases, estimated model parameters were compared to the commonly used monoexponential model. Reducing the sampling density of the relaxation data and adding Gaussian-distributed noise served to simulate cases in which the data are acquisition-time or signal-to-noise restricted, respectively. As expected, reducing either the number of data points or the signal-to-noise increases the uncertainty in estimated parameters and, ultimately, reduces support for more complex relaxation models.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gagné, Jonathan; Lafrenière, David; Doyon, René

We present Bayesian Analysis for Nearby Young AssociatioNs II (BANYAN II), a modified Bayesian analysis for assessing the membership of later-than-M5 objects to any of several Nearby Young Associations (NYAs). In addition to using kinematic information (from sky position and proper motion), this analysis exploits 2MASS-WISE color-magnitude diagrams in which old and young objects follow distinct sequences. As an improvement over our earlier work, the spatial and kinematic distributions for each association are now modeled as ellipsoids whose axes need not be aligned with the Galactic coordinate axes, and we use prior probabilities matching the expected populations of the NYAsmore » considered versus field stars. We present an extensive contamination analysis to characterize the performance of our new method. We find that Bayesian probabilities are generally representative of contamination rates, except when a parallax measurement is considered. In this case contamination rates become significantly smaller and hence Bayesian probabilities for NYA memberships are pessimistic. We apply this new algorithm to a sample of 158 objects from the literature that are either known to display spectroscopic signs of youth or have unusually red near-infrared colors for their spectral type. Based on our analysis, we identify 25 objects as new highly probable candidates to NYAs, including a new M7.5 bona fide member to Tucana-Horologium, making it the latest-type member. In addition, we reveal that a known L2γ dwarf is co-moving with a bright M5 dwarf, and we show for the first time that two of the currently known ultra red L dwarfs are strong candidates to the AB Doradus moving group. Several objects identified here as highly probable members to NYAs could be free-floating planetary-mass objects if their membership is confirmed.« less

Variation in life expectancy and mortality by cause among neighbourhoods in King County, WA, USA, 1990-2014: a census tract-level analysis for the Global Burden of Disease Study 2015.

PubMed

Dwyer-Lindgren, Laura; Stubbs, Rebecca W; Bertozzi-Villa, Amelia; Morozoff, Chloe; Callender, Charlton; Finegold, Samuel B; Shirude, Shreya; Flaxman, Abraham D; Laurent, Amy; Kern, Eli; Duchin, Jeffrey S; Fleming, David; Mokdad, Ali H; Murray, Christopher J L

2017-09-01

Health outcomes are known to vary at both the country and local levels, but trends in mortality across a detailed and comprehensive set of causes have not been previously described at a very local level. Life expectancy in King County, WA, USA, is in the 95th percentile among all counties in the USA. However, little is known about how life expectancy and mortality from different causes of death vary at a local, neighbourhood level within this county. In this analysis, we estimated life expectancy and cause-specific mortality within King County to describe spatial trends, quantify disparities in mortality, and assess the contribution of each cause of death to overall disparities in all-cause mortality. We applied established so-called garbage code redistribution algorithms and small area estimation methods to death registration data for King County to estimate life expectancy, cause-specific mortality rates, and years of life lost (YLL) rates from 152 causes of death for 397 census tracts from Jan 1, 1990, to Dec 31, 2014. We used the cause list developed for the Global Burden of Disease 2015 study for this analysis. Deaths were tabulated by age group, sex, census tract, and cause of death. We used Bayesian mixed-effects regression models to estimate mortality overall and from each cause. Between 1990 and 2014, life expectancy in King County increased by 5·4 years (95% uncertainty interval [UI] 5·0-5·7) among men (from 74·0 years [73·7-74·3] to 79·3 years [79·1-79·6]) and by 3·4 years (3·0-3·7) among women (from 80·0 years [79·7-80·2] to 83·3 years [83·1-83·5]). In 2014, life expectancy ranged from 68·4 years (95% UI 66·9-70·1) to 86·7 years (85·0-88·2) for men and from 73·6 years (71·6-75·5) to 88·4 years (86·9-89·9) for women among census tracts within King County. Rates of YLL by cause also varied substantially among census tracts for each cause of death. Geographical areas with relatively high and relatively low YLL rates differed by cause. In general, causes of death responsible for more YLLs overall also contributed more significantly to geographical inequality within King County. However, certain causes contributed more to inequality than to overall YLLs. This census tract-level analysis of life expectancy and cause-specific YLL rates highlights important differences in health among neighbourhoods in King County that are masked by county-level estimates. Efforts to improve population health in King County should focus on reducing geographical inequality, by targeting those health conditions that contribute the most to overall YLLs and to inequality. This analysis should be replicated in other locations to more fully describe fine-grained local-level variation in population health and contribute to efforts to improve health while reducing inequalities. John W Stanton and Theresa E Gillespie. Copyright © 2017 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 license. Published by Elsevier Ltd.. All rights reserved.

Individual diet variation in a marine fish assemblage: Optimal Foraging Theory, Niche Variation Hypothesis and functional identity

NASA Astrophysics Data System (ADS)

Cachera, M.; Ernande, B.; Villanueva, M. C.; Lefebvre, S.

2017-02-01

Individual diet variation (i.e. diet variation among individuals) impacts intra- and inter-specific interactions. Investigating its sources and relationship with species trophic niche organization is important for understanding community structure and dynamics. Individual diet variation may increase with intra-specific phenotypic (or "individual state") variation and habitat variability, according to Optimal Foraging Theory (OFT), and with species trophic niche width, according to the Niche Variation Hypothesis (NVH). OFT proposes "proximate sources" of individual diet variation such as variations in habitat or size whereas NVH relies on "ultimate sources" related to the competitive balance between intra- and inter-specific competitions. The latter implies as a corollary that species trophic niche overlap, taken as inter-specific competition measure, decreases as species niche width and individual niche variation increase. We tested the complementary predictions of OFT and NVH in a marine fish assemblage using stomach content data and associated trophic niche metrics. The NVH predictions were tested between species of the assemblage and decomposed into a between- and a within-functional group component to assess the potential influence of species' ecological function. For most species, individual diet variation and niche overlap were consistently larger than expected. Individual diet variation increased with intra-specific variability in individual state and habitat, as expected from OFT. It also increased with species niche width but in compliance with the null expectation, thus not supporting the NVH. In contrast, species niche overlap increased significantly less than null expectation with both species niche width and individual diet variation, supporting NVH corollary. The between- and within-functional group components of the NVH relationships were consistent with those between species at the assemblage level. Changing the number of prey categories used to describe diet (from 16 to 41) did not change the results qualitatively. These results suggest that, besides proximate sources, intra-specific competition favors higher individual diet variation than expected while inter-specific competition limits the increase of individual diet variation and of species niche overlap with species niche expansion. This reveals partial trophic resource partitioning between species. Various niche metrics used in combination allow inferring competition effects on trophic niches' organization within communities.

Population size, center-periphery, and seed dispersers' effects on the genetic diversity and population structure of the Mediterranean relict shrub Cneorum tricoccon.

PubMed

Lázaro-Nogal, Ana; Matesanz, Silvia; García-Fernández, Alfredo; Traveset, Anna; Valladares, Fernando

2017-09-01

The effect of population size on population genetic diversity and structure has rarely been studied jointly with other factors such as the position of a population within the species' distribution range or the presence of mutualistic partners influencing dispersal. Understanding these determining factors for genetic variation is critical for conservation of relict plants that are generally suffering from genetic deterioration. Working with 16 populations of the vulnerable relict shrub Cneorum tricoccon throughout the majority of its western Mediterranean distribution range, and using nine polymorphic microsatellite markers, we examined the effects of periphery (peripheral vs. central), population size (large vs. small), and seed disperser (introduced carnivores vs. endemic lizards) on the genetic diversity and population structure of the species. Contrasting genetic variation ( H E : 0.04-0.476) was found across populations. Peripheral populations showed lower genetic diversity, but this was dependent on population size. Large peripheral populations showed high levels of genetic diversity, whereas small central populations were less diverse. Significant isolation by distance was detected, indicating that the effect of long-distance gene flow is limited relative to that of genetic drift, probably due to high selfing rates ( F IS  = 0.155-0.887), restricted pollen flow, and ineffective seed dispersal. Bayesian clustering also supported the strong population differentiation and highly fragmented structure. Contrary to expectations, the type of disperser showed no significant effect on either population genetic diversity or structure. Our results challenge the idea of an effect of periphery per se that can be mainly explained by population size, drawing attention to the need of integrative approaches considering different determinants of genetic variation. Furthermore, the very low genetic diversity observed in several small populations and the strong among-population differentiation highlight the conservation value of large populations throughout the species' range, particularly in light of climate change and direct human threats.

Scale-dependent variation in forest structures in naturally dynamic boreal forest landscapes

NASA Astrophysics Data System (ADS)

Kulha, Niko; Pasanen, Leena; De Grandpré, Louis; Kuuluvainen, Timo; Aakala, Tuomas

2017-04-01

Natural forest structures vary at multiple spatial scales. This variation reflects the occurrence of driving factors, such as disturbances and variation in soil or topography. To explore and understand the linkages of forest structural characteristics and factors driving their variation, we need to recognize how the structural characteristics vary in relation to spatial scale. This can be achieved by identifying scale-dependent features in forest structure within unmanaged forest landscapes. By identifying these features and examining their relationship with potential driving factors, we can better understand the dynamics of forest structural development. Here, we examine the spatial variation in forest structures at multiple spatial scales, utilizing data from old-growth boreal forests in two regions with contrasting disturbance regimes: northern Finland and north-eastern Québec, Canada ( 67° 45'N, 29° 36'E, 49° 39'N, 67° 55'W, respectively). The three landscapes (4 km2 each) in Finland are dominated by Pinus sylvestris and Picea abies, whereas the two landscapes in Québec are dominated by Abies balsamea and Picea mariana. Québec's forests are a subject to cyclic outbreaks of the eastern spruce budworm, causing extensive mortality especially in A. balsamea-dominated stands. In the Finnish landscapes, gap- to patch-scale disturbances due to tree senescence, fungi and wind, as well as infrequent surface fires in areas dominated by P. sylvestris, prevail. Owing to the differences in the species compositions and the disturbance regimes, we expect differing scales of variation between the landscapes. To quantify patterns of variation, we visually interpret stereopairs of recent aerial photographs. From the photographs, we collect information on forest canopy coverage, species composition and dead wood. For the interpretation, each 4 km2 plot is divided into 0.1ha square cells (4096 per plot). Interpretations are validated against field observations and compiled to raster maps. We analyze the raster maps with Bayesian scale space approach (iBSiZer), which aims in capturing credible variations at different spatial scales. As a result, we can detect structural entities (e.g. patches with higher canopy cover), which deviate credibly from their surroundings. The detected entities can further be linked to specific drivers. Our results show that the role of a particular driving factor varies in relation to spatial scale. For example, in the Finnish landscapes, topoedaphic factors exerted a stronger control on broad-scale forest structural characteristics, whereas recent disturbances (quantified as the amount of dead wood) appeared to play an important role in explaining the smaller scale variation of forest structures. Here, we showcase the methodology used in the detection of scale-dependent forest structural entities and present the results of our analysis of the spatial scales of variation in the natural boreal forest structures.

Genetic diversity and divergence at the Arbutus unedo L. (Ericaceae) westernmost distribution limit.

PubMed

Ribeiro, Maria Margarida; Piotti, Andrea; Ricardo, Alexandra; Gaspar, Daniel; Costa, Rita; Parducci, Laura; Vendramin, Giovanni Giuseppe

2017-01-01

Mediterranean forests are fragile ecosystems vulnerable to recent global warming and reduction of precipitation, and a long-term negative effect is expected on vegetation with increasing drought and in areas burnt by fires. We investigated the spatial distribution of genetic variation of Arbutus unedo in the western Iberia Peninsula, using plastid markers with conservation and provenance regions design purposes. This species is currently undergoing an intense domestication process in the region, and, like other species, is increasingly under the threat from climate change, habitat fragmentation and wildfires. We sampled 451 trees from 15 natural populations from different ecological conditions spanning the whole species' distribution range in the region. We applied Bayesian analysis and identified four clusters (north, centre, south, and a single-population cluster). Hierarchical AMOVA showed higher differentiation among clusters than among populations within clusters. The relatively low within-clusters differentiation can be explained by a common postglacial history of nearby populations. The genetic structure found, supported by the few available palaeobotanical records, cannot exclude the hypothesis of two independent A. unedo refugia in western Iberia Peninsula during the Last Glacial Maximum. Based on the results we recommend a conservation strategy by selecting populations for conservation based on their allelic richness and diversity and careful seed transfer consistent with current species' genetic structure.

Genetic diversity and divergence at the Arbutus unedo L. (Ericaceae) westernmost distribution limit

PubMed Central

Ribeiro, Maria Margarida; Piotti, Andrea; Ricardo, Alexandra; Gaspar, Daniel; Costa, Rita; Parducci, Laura; Vendramin, Giovanni Giuseppe

2017-01-01

Mediterranean forests are fragile ecosystems vulnerable to recent global warming and reduction of precipitation, and a long-term negative effect is expected on vegetation with increasing drought and in areas burnt by fires. We investigated the spatial distribution of genetic variation of Arbutus unedo in the western Iberia Peninsula, using plastid markers with conservation and provenance regions design purposes. This species is currently undergoing an intense domestication process in the region, and, like other species, is increasingly under the threat from climate change, habitat fragmentation and wildfires. We sampled 451 trees from 15 natural populations from different ecological conditions spanning the whole species’ distribution range in the region. We applied Bayesian analysis and identified four clusters (north, centre, south, and a single-population cluster). Hierarchical AMOVA showed higher differentiation among clusters than among populations within clusters. The relatively low within-clusters differentiation can be explained by a common postglacial history of nearby populations. The genetic structure found, supported by the few available palaeobotanical records, cannot exclude the hypothesis of two independent A. unedo refugia in western Iberia Peninsula during the Last Glacial Maximum. Based on the results we recommend a conservation strategy by selecting populations for conservation based on their allelic richness and diversity and careful seed transfer consistent with current species’ genetic structure. PMID:28384294

Constraining mass anomalies in the interior of spherical bodies using Trans-dimensional Bayesian Hierarchical inference.

NASA Astrophysics Data System (ADS)

Izquierdo, K.; Lekic, V.; Montesi, L.

2017-12-01

Gravity inversions are especially important for planetary applications since measurements of the variations in gravitational acceleration are often the only constraint available to map out lateral density variations in the interiors of planets and other Solar system objects. Currently, global gravity data is available for the terrestrial planets and the Moon. Although several methods for inverting these data have been developed and applied, the non-uniqueness of global density models that fit the data has not yet been fully characterized. We make use of Bayesian inference and a Reversible Jump Markov Chain Monte Carlo (RJMCMC) approach to develop a Trans-dimensional Hierarchical Bayesian (THB) inversion algorithm that yields a large sample of models that fit a gravity field. From this group of models, we can determine the most likely value of parameters of a global density model and a measure of the non-uniqueness of each parameter when the number of anomalies describing the gravity field is not fixed a priori. We explore the use of a parallel tempering algorithm and fast multipole method to reduce the number of iterations and computing time needed. We applied this method to a synthetic gravity field of the Moon and a long wavelength synthetic model of density anomalies in the Earth's lower mantle. We obtained a good match between the given gravity field and the gravity field produced by the most likely model in each inversion. The number of anomalies of the models showed parsimony of the algorithm, the value of the noise variance of the input data was retrieved, and the non-uniqueness of the models was quantified. Our results show that the ability to constrain the latitude and longitude of density anomalies, which is excellent at shallow locations (<200 km), decreases with increasing depth. With higher computational resources, this THB method for gravity inversion could give new information about the overall density distribution of celestial bodies even when there is no other geophysical data available.

Accounting for between-study variation in incremental net benefit in value of information methodology.

PubMed

Willan, Andrew R; Eckermann, Simon

2012-10-01

Previous applications of value of information methods for determining optimal sample size in randomized clinical trials have assumed no between-study variation in mean incremental net benefit. By adopting a hierarchical model, we provide a solution for determining optimal sample size with this assumption relaxed. The solution is illustrated with two examples from the literature. Expected net gain increases with increasing between-study variation, reflecting the increased uncertainty in incremental net benefit and reduced extent to which data are borrowed from previous evidence. Hence, a trial can become optimal where current evidence is sufficient assuming no between-study variation. However, despite the expected net gain increasing, the optimal sample size in the illustrated examples is relatively insensitive to the amount of between-study variation. Further percentage losses in expected net gain were small even when choosing sample sizes that reflected widely different between-study variation. Copyright © 2011 John Wiley & Sons, Ltd.

Including non-additive genetic effects in Bayesian methods for the prediction of genetic values based on genome-wide markers

PubMed Central

2011-01-01

Background Molecular marker information is a common source to draw inferences about the relationship between genetic and phenotypic variation. Genetic effects are often modelled as additively acting marker allele effects. The true mode of biological action can, of course, be different from this plain assumption. One possibility to better understand the genetic architecture of complex traits is to include intra-locus (dominance) and inter-locus (epistasis) interaction of alleles as well as the additive genetic effects when fitting a model to a trait. Several Bayesian MCMC approaches exist for the genome-wide estimation of genetic effects with high accuracy of genetic value prediction. Including pairwise interaction for thousands of loci would probably go beyond the scope of such a sampling algorithm because then millions of effects are to be estimated simultaneously leading to months of computation time. Alternative solving strategies are required when epistasis is studied. Methods We extended a fast Bayesian method (fBayesB), which was previously proposed for a purely additive model, to include non-additive effects. The fBayesB approach was used to estimate genetic effects on the basis of simulated datasets. Different scenarios were simulated to study the loss of accuracy of prediction, if epistatic effects were not simulated but modelled and vice versa. Results If 23 QTL were simulated to cause additive and dominance effects, both fBayesB and a conventional MCMC sampler BayesB yielded similar results in terms of accuracy of genetic value prediction and bias of variance component estimation based on a model including additive and dominance effects. Applying fBayesB to data with epistasis, accuracy could be improved by 5% when all pairwise interactions were modelled as well. The accuracy decreased more than 20% if genetic variation was spread over 230 QTL. In this scenario, accuracy based on modelling only additive and dominance effects was generally superior to that of the complex model including epistatic effects. Conclusions This simulation study showed that the fBayesB approach is convenient for genetic value prediction. Jointly estimating additive and non-additive effects (especially dominance) has reasonable impact on the accuracy of prediction and the proportion of genetic variation assigned to the additive genetic source. PMID:21867519

Bayesian methods to determine performance differences and to quantify variability among centers in multi-center trials: the IHAST trial.

PubMed

Bayman, Emine O; Chaloner, Kathryn M; Hindman, Bradley J; Todd, Michael M

2013-01-16

To quantify the variability among centers and to identify centers whose performance are potentially outside of normal variability in the primary outcome and to propose a guideline that they are outliers. Novel statistical methodology using a Bayesian hierarchical model is used. Bayesian methods for estimation and outlier detection are applied assuming an additive random center effect on the log odds of response: centers are similar but different (exchangeable). The Intraoperative Hypothermia for Aneurysm Surgery Trial (IHAST) is used as an example. Analyses were adjusted for treatment, age, gender, aneurysm location, World Federation of Neurological Surgeons scale, Fisher score and baseline NIH stroke scale scores. Adjustments for differences in center characteristics were also examined. Graphical and numerical summaries of the between-center standard deviation (sd) and variability, as well as the identification of potential outliers are implemented. In the IHAST, the center-to-center variation in the log odds of favorable outcome at each center is consistent with a normal distribution with posterior sd of 0.538 (95% credible interval: 0.397 to 0.726) after adjusting for the effects of important covariates. Outcome differences among centers show no outlying centers. Four potential outlying centers were identified but did not meet the proposed guideline for declaring them as outlying. Center characteristics (number of subjects enrolled from the center, geographical location, learning over time, nitrous oxide, and temporary clipping use) did not predict outcome, but subject and disease characteristics did. Bayesian hierarchical methods allow for determination of whether outcomes from a specific center differ from others and whether specific clinical practices predict outcome, even when some centers/subgroups have relatively small sample sizes. In the IHAST no outlying centers were found. The estimated variability between centers was moderately large.

Bayesian relaxed clock estimation of divergence times in foraminifera.

PubMed

Groussin, Mathieu; Pawlowski, Jan; Yang, Ziheng

2011-10-01

Accurate and precise estimation of divergence times during the Neo-Proterozoic is necessary to understand the speciation dynamic of early Eukaryotes. However such deep divergences are difficult to date, as the molecular clock is seriously violated. Recent improvements in Bayesian molecular dating techniques allow the relaxation of the molecular clock hypothesis as well as incorporation of multiple and flexible fossil calibrations. Divergence times can then be estimated even when the evolutionary rate varies among lineages and even when the fossil calibrations involve substantial uncertainties. In this paper, we used a Bayesian method to estimate divergence times in Foraminifera, a group of unicellular eukaryotes, known for their excellent fossil record but also for the high evolutionary rates of their genomes. Based on multigene data we reconstructed the phylogeny of Foraminifera and dated their origin and the major radiation events. Our estimates suggest that Foraminifera emerged during the Cryogenian (650-920 Ma, Neo-Proterozoic), with a mean time around 770 Ma, about 220 Myr before the first appearance of reliable foraminiferal fossils in sediments (545 Ma). Most dates are in agreement with the fossil record, but in general our results suggest earlier origins of foraminiferal orders. We found that the posterior time estimates were robust to specifications of the prior. Our results highlight inter-species variations of evolutionary rates in Foraminifera. Their effect was partially overcome by using the partitioned Bayesian analysis to accommodate rate heterogeneity among data partitions and using the relaxed molecular clock to account for changing evolutionary rates. However, more coding genes appear necessary to obtain more precise estimates of divergence times and to resolve the conflicts between fossil and molecular date estimates. Copyright © 2011 Elsevier Inc. All rights reserved.

Wavelet extractor: A Bayesian well-tie and wavelet extraction program

NASA Astrophysics Data System (ADS)

Gunning, James; Glinsky, Michael E.

2006-06-01

We introduce a new open-source toolkit for the well-tie or wavelet extraction problem of estimating seismic wavelets from seismic data, time-to-depth information, and well-log suites. The wavelet extraction model is formulated as a Bayesian inverse problem, and the software will simultaneously estimate wavelet coefficients, other parameters associated with uncertainty in the time-to-depth mapping, positioning errors in the seismic imaging, and useful amplitude-variation-with-offset (AVO) related parameters in multi-stack extractions. It is capable of multi-well, multi-stack extractions, and uses continuous seismic data-cube interpolation to cope with the problem of arbitrary well paths. Velocity constraints in the form of checkshot data, interpreted markers, and sonic logs are integrated in a natural way. The Bayesian formulation allows computation of full posterior uncertainties of the model parameters, and the important problem of the uncertain wavelet span is addressed uses a multi-model posterior developed from Bayesian model selection theory. The wavelet extraction tool is distributed as part of the Delivery seismic inversion toolkit. A simple log and seismic viewing tool is included in the distribution. The code is written in Java, and thus platform independent, but the Seismic Unix (SU) data model makes the inversion particularly suited to Unix/Linux environments. It is a natural companion piece of software to Delivery, having the capacity to produce maximum likelihood wavelet and noise estimates, but will also be of significant utility to practitioners wanting to produce wavelet estimates for other inversion codes or purposes. The generation of full parameter uncertainties is a crucial function for workers wishing to investigate questions of wavelet stability before proceeding to more advanced inversion studies.

Bayesian QTL mapping using genome-wide SSR markers and segregating population derived from a cross of two commercial F1 hybrids of tomato.

PubMed

Ohyama, Akio; Shirasawa, Kenta; Matsunaga, Hiroshi; Negoro, Satomi; Miyatake, Koji; Yamaguchi, Hirotaka; Nunome, Tsukasa; Iwata, Hiroyoshi; Fukuoka, Hiroyuki; Hayashi, Takeshi

2017-08-01

Using newly developed euchromatin-derived genomic SSR markers and a flexible Bayesian mapping method, 13 significant agricultural QTLs were identified in a segregating population derived from a four-way cross of tomato. So far, many QTL mapping studies in tomato have been performed for progeny obtained from crosses between two genetically distant parents, e.g., domesticated tomatoes and wild relatives. However, QTL information of quantitative traits related to yield (e.g., flower or fruit number, and total or average weight of fruits) in such intercross populations would be of limited use for breeding commercial tomato cultivars because individuals in the populations have specific genetic backgrounds underlying extremely different phenotypes between the parents such as large fruit in domesticated tomatoes and small fruit in wild relatives, which may not be reflective of the genetic variation in tomato breeding populations. In this study, we constructed F 2 population derived from a cross between two commercial F 1 cultivars in tomato to extract QTL information practical for tomato breeding. This cross corresponded to a four-way cross, because the four parental lines of the two F 1 cultivars were considered to be the founders. We developed 2510 new expressed sequence tag (EST)-based (euchromatin-derived) genomic SSR markers and selected 262 markers from these new SSR markers and publicly available SSR markers to construct a linkage map. QTL analysis for ten agricultural traits of tomato was performed based on the phenotypes and marker genotypes of F 2 plants using a flexible Bayesian method. As results, 13 QTL regions were detected for six traits by the Bayesian method developed in this study.

Parameter estimation for an immortal model of colonic stem cell division using approximate Bayesian computation.

PubMed

Walters, Kevin

2012-08-07

In this paper we use approximate Bayesian computation to estimate the parameters in an immortal model of colonic stem cell division. We base the inferences on the observed DNA methylation patterns of cells sampled from the human colon. Utilising DNA methylation patterns as a form of molecular clock is an emerging area of research and has been used in several studies investigating colonic stem cell turnover. There is much debate concerning the two competing models of stem cell turnover: the symmetric (immortal) and asymmetric models. Early simulation studies concluded that the observed methylation data were not consistent with the immortal model. A later modified version of the immortal model that included preferential strand segregation was subsequently shown to be consistent with the same methylation data. Most of this earlier work assumes site independent methylation models that do not take account of the known processivity of methyltransferases whilst other work does not take into account the methylation errors that occur in differentiated cells. This paper addresses both of these issues for the immortal model and demonstrates that approximate Bayesian computation provides accurate estimates of the parameters in this neighbour-dependent model of methylation error rates. The results indicate that if colonic stem cells divide asymmetrically then colon stem cell niches are maintained by more than 8 stem cells. Results also indicate the possibility of preferential strand segregation and provide clear evidence against a site-independent model for methylation errors. In addition, algebraic expressions for some of the summary statistics used in the approximate Bayesian computation (that allow for the additional variation arising from cell division in differentiated cells) are derived and their utility discussed. Copyright © 2012 Elsevier Ltd. All rights reserved.

Parallelized Bayesian inversion for three-dimensional dental X-ray imaging.

PubMed

Kolehmainen, Ville; Vanne, Antti; Siltanen, Samuli; Järvenpää, Seppo; Kaipio, Jari P; Lassas, Matti; Kalke, Martti

2006-02-01

Diagnostic and operational tasks based on dental radiology often require three-dimensional (3-D) information that is not available in a single X-ray projection image. Comprehensive 3-D information about tissues can be obtained by computerized tomography (CT) imaging. However, in dental imaging a conventional CT scan may not be available or practical because of high radiation dose, low-resolution or the cost of the CT scanner equipment. In this paper, we consider a novel type of 3-D imaging modality for dental radiology. We consider situations in which projection images of the teeth are taken from a few sparsely distributed projection directions using the dentist's regular (digital) X-ray equipment and the 3-D X-ray attenuation function is reconstructed. A complication in these experiments is that the reconstruction of the 3-D structure based on a few projection images becomes an ill-posed inverse problem. Bayesian inversion is a well suited framework for reconstruction from such incomplete data. In Bayesian inversion, the ill-posed reconstruction problem is formulated in a well-posed probabilistic form in which a priori information is used to compensate for the incomplete information of the projection data. In this paper we propose a Bayesian method for 3-D reconstruction in dental radiology. The method is partially based on Kolehmainen et al. 2003. The prior model for dental structures consist of a weighted l1 and total variation (TV)-prior together with the positivity prior. The inverse problem is stated as finding the maximum a posteriori (MAP) estimate. To make the 3-D reconstruction computationally feasible, a parallelized version of an optimization algorithm is implemented for a Beowulf cluster computer. The method is tested with projection data from dental specimens and patient data. Tomosynthetic reconstructions are given as reference for the proposed method.

A critique of statistical hypothesis testing in clinical research

PubMed Central

Raha, Somik

2011-01-01

Many have documented the difficulty of using the current paradigm of Randomized Controlled Trials (RCTs) to test and validate the effectiveness of alternative medical systems such as Ayurveda. This paper critiques the applicability of RCTs for all clinical knowledge-seeking endeavors, of which Ayurveda research is a part. This is done by examining statistical hypothesis testing, the underlying foundation of RCTs, from a practical and philosophical perspective. In the philosophical critique, the two main worldviews of probability are that of the Bayesian and the frequentist. The frequentist worldview is a special case of the Bayesian worldview requiring the unrealistic assumptions of knowing nothing about the universe and believing that all observations are unrelated to each other. Many have claimed that the first belief is necessary for science, and this claim is debunked by comparing variations in learning with different prior beliefs. Moving beyond the Bayesian and frequentist worldviews, the notion of hypothesis testing itself is challenged on the grounds that a hypothesis is an unclear distinction, and assigning a probability on an unclear distinction is an exercise that does not lead to clarity of action. This critique is of the theory itself and not any particular application of statistical hypothesis testing. A decision-making frame is proposed as a way of both addressing this critique and transcending ideological debates on probability. An example of a Bayesian decision-making approach is shown as an alternative to statistical hypothesis testing, utilizing data from a past clinical trial that studied the effect of Aspirin on heart attacks in a sample population of doctors. As a big reason for the prevalence of RCTs in academia is legislation requiring it, the ethics of legislating the use of statistical methods for clinical research is also examined. PMID:22022152

Forecasting neutrino masses from combining KATRIN and the CMB observations: Frequentist and Bayesian analyses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Host, Ole; Lahav, Ofer; Abdalla, Filipe B.

We present a showcase for deriving bounds on the neutrino masses from laboratory experiments and cosmological observations. We compare the frequentist and Bayesian bounds on the effective electron neutrino mass m{sub {beta}} which the KATRIN neutrino mass experiment is expected to obtain, using both an analytical likelihood function and Monte Carlo simulations of KATRIN. Assuming a uniform prior in m{sub {beta}}, we find that a null result yields an upper bound of about 0.17 eV at 90% confidence in the Bayesian analysis, to be compared with the frequentist KATRIN reference value of 0.20 eV. This is a significant difference whenmore » judged relative to the systematic and statistical uncertainties of the experiment. On the other hand, an input m{sub {beta}}=0.35 eV, which is the KATRIN 5{sigma} detection threshold, would be detected at virtually the same level. Finally, we combine the simulated KATRIN results with cosmological data in the form of present (post-WMAP) and future (simulated Planck) observations. If an input of m{sub {beta}}=0.2 eV is assumed in our simulations, KATRIN alone excludes a zero neutrino mass at 2.2{sigma}. Adding Planck data increases the probability of detection to a median 2.7{sigma}. The analysis highlights the importance of combining cosmological and laboratory data on an equal footing.« less

Cholinergic stimulation enhances Bayesian belief updating in the deployment of spatial attention.

PubMed

Vossel, Simone; Bauer, Markus; Mathys, Christoph; Adams, Rick A; Dolan, Raymond J; Stephan, Klaas E; Friston, Karl J

2014-11-19

The exact mechanisms whereby the cholinergic neurotransmitter system contributes to attentional processing remain poorly understood. Here, we applied computational modeling to psychophysical data (obtained from a spatial attention task) under a psychopharmacological challenge with the cholinesterase inhibitor galantamine (Reminyl). This allowed us to characterize the cholinergic modulation of selective attention formally, in terms of hierarchical Bayesian inference. In a placebo-controlled, within-subject, crossover design, 16 healthy human subjects performed a modified version of Posner's location-cueing task in which the proportion of validly and invalidly cued targets (percentage of cue validity, % CV) changed over time. Saccadic response speeds were used to estimate the parameters of a hierarchical Bayesian model to test whether cholinergic stimulation affected the trial-wise updating of probabilistic beliefs that underlie the allocation of attention or whether galantamine changed the mapping from those beliefs to subsequent eye movements. Behaviorally, galantamine led to a greater influence of probabilistic context (% CV) on response speed than placebo. Crucially, computational modeling suggested this effect was due to an increase in the rate of belief updating about cue validity (as opposed to the increased sensitivity of behavioral responses to those beliefs). We discuss these findings with respect to cholinergic effects on hierarchical cortical processing and in relation to the encoding of expected uncertainty or precision. Copyright © 2014 the authors 0270-6474/14/3415735-08$15.00/0.

Lip-reading aids word recognition most in moderate noise: a Bayesian explanation using high-dimensional feature space.

PubMed

Ma, Wei Ji; Zhou, Xiang; Ross, Lars A; Foxe, John J; Parra, Lucas C

2009-01-01

Watching a speaker's facial movements can dramatically enhance our ability to comprehend words, especially in noisy environments. From a general doctrine of combining information from different sensory modalities (the principle of inverse effectiveness), one would expect that the visual signals would be most effective at the highest levels of auditory noise. In contrast, we find, in accord with a recent paper, that visual information improves performance more at intermediate levels of auditory noise than at the highest levels, and we show that a novel visual stimulus containing only temporal information does the same. We present a Bayesian model of optimal cue integration that can explain these conflicts. In this model, words are regarded as points in a multidimensional space and word recognition is a probabilistic inference process. When the dimensionality of the feature space is low, the Bayesian model predicts inverse effectiveness; when the dimensionality is high, the enhancement is maximal at intermediate auditory noise levels. When the auditory and visual stimuli differ slightly in high noise, the model makes a counterintuitive prediction: as sound quality increases, the proportion of reported words corresponding to the visual stimulus should first increase and then decrease. We confirm this prediction in a behavioral experiment. We conclude that auditory-visual speech perception obeys the same notion of optimality previously observed only for simple multisensory stimuli.

Bayesian probabilistic population projections for all countries.

PubMed

Raftery, Adrian E; Li, Nan; Ševčíková, Hana; Gerland, Patrick; Heilig, Gerhard K

2012-08-28

Projections of countries' future populations, broken down by age and sex, are widely used for planning and research. They are mostly done deterministically, but there is a widespread need for probabilistic projections. We propose a bayesian method for probabilistic population projections for all countries. The total fertility rate and female and male life expectancies at birth are projected probabilistically using bayesian hierarchical models estimated via Markov chain Monte Carlo using United Nations population data for all countries. These are then converted to age-specific rates and combined with a cohort component projection model. This yields probabilistic projections of any population quantity of interest. The method is illustrated for five countries of different demographic stages, continents and sizes. The method is validated by an out of sample experiment in which data from 1950-1990 are used for estimation, and applied to predict 1990-2010. The method appears reasonably accurate and well calibrated for this period. The results suggest that the current United Nations high and low variants greatly underestimate uncertainty about the number of oldest old from about 2050 and that they underestimate uncertainty for high fertility countries and overstate uncertainty for countries that have completed the demographic transition and whose fertility has started to recover towards replacement level, mostly in Europe. The results also indicate that the potential support ratio (persons aged 20-64 per person aged 65+) will almost certainly decline dramatically in most countries over the coming decades.

Efficiency of nuclear and mitochondrial markers recovering and supporting known amniote groups.

PubMed

Lambret-Frotté, Julia; Perini, Fernando Araújo; de Moraes Russo, Claudia Augusta

2012-01-01

We have analysed the efficiency of all mitochondrial protein coding genes and six nuclear markers (Adora3, Adrb2, Bdnf, Irbp, Rag2 and Vwf) in reconstructing and statistically supporting known amniote groups (murines, rodents, primates, eutherians, metatherians, therians). The efficiencies of maximum likelihood, Bayesian inference, maximum parsimony, neighbor-joining and UPGMA were also evaluated, by assessing the number of correct and incorrect recovered groupings. In addition, we have compared support values using the conservative bootstrap test and the Bayesian posterior probabilities. First, no correlation was observed between gene size and marker efficiency in recovering or supporting correct nodes. As expected, tree-building methods performed similarly, even UPGMA that, in some cases, outperformed other most extensively used methods. Bayesian posterior probabilities tend to show much higher support values than the conservative bootstrap test, for correct and incorrect nodes. Our results also suggest that nuclear markers do not necessarily show a better performance than mitochondrial genes. The so-called dependency among mitochondrial markers was not observed comparing genome performances. Finally, the amniote groups with lowest recovery rates were therians and rodents, despite the morphological support for their monophyletic status. We suggest that, regardless of the tree-building method, a few carefully selected genes are able to unfold a detailed and robust scenario of phylogenetic hypotheses, particularly if taxon sampling is increased.

An evaluation of behavior inferences from Bayesian state-space models: A case study with the Pacific walrus

USGS Publications Warehouse

Beatty, William; Jay, Chadwick V.; Fischbach, Anthony S.

2016-01-01

State-space models offer researchers an objective approach to modeling complex animal location data sets, and state-space model behavior classifications are often assumed to have a link to animal behavior. In this study, we evaluated the behavioral classification accuracy of a Bayesian state-space model in Pacific walruses using Argos satellite tags with sensors to detect animal behavior in real time. We fit a two-state discrete-time continuous-space Bayesian state-space model to data from 306 Pacific walruses tagged in the Chukchi Sea. We matched predicted locations and behaviors from the state-space model (resident, transient behavior) to true animal behavior (foraging, swimming, hauled out) and evaluated classification accuracy with kappa statistics (κ) and root mean square error (RMSE). In addition, we compared biased random bridge utilization distributions generated with resident behavior locations to true foraging behavior locations to evaluate differences in space use patterns. Results indicated that the two-state model fairly classified true animal behavior (0.06 ≤ κ ≤ 0.26, 0.49 ≤ RMSE ≤ 0.59). Kernel overlap metrics indicated utilization distributions generated with resident behavior locations were generally smaller than utilization distributions generated with true foraging behavior locations. Consequently, we encourage researchers to carefully examine parameters and priors associated with behaviors in state-space models, and reconcile these parameters with the study species and its expected behaviors.

The dynamics of fidelity over the time course of long-term memory.

PubMed

Persaud, Kimele; Hemmer, Pernille

2016-08-01

Bayesian models of cognition assume that prior knowledge about the world influences judgments. Recent approaches have suggested that the loss of fidelity from working to long-term (LT) memory is simply due to an increased rate of guessing (e.g. Brady, Konkle, Gill, Oliva, & Alvarez, 2013). That is, recall is the result of either remembering (with some noise) or guessing. This stands in contrast to Bayesian models of cognition while assume that prior knowledge about the world influences judgments, and that recall is a combination of expectations learned from the environment and noisy memory representations. Here, we evaluate the time course of fidelity in LT episodic memory, and the relative contribution of prior category knowledge and guessing, using a continuous recall paradigm. At an aggregate level, performance reflects a high rate of guessing. However, when aggregate data is partitioned by lag (i.e., the number of presentations from study to test), or is un-aggregated, performance appears to be more complex than just remembering with some noise and guessing. We implemented three models: the standard remember-guess model, a three-component remember-guess model, and a Bayesian mixture model and evaluated these models against the data. The results emphasize the importance of taking into account the influence of prior category knowledge on memory. Copyright © 2016 Elsevier Inc. All rights reserved.

Selecting Strategies to Reduce High-Risk Unsafe Work Behaviors Using the Safety Behavior Sampling Technique and Bayesian Network Analysis.

PubMed

Ghasemi, Fakhradin; Kalatpour, Omid; Moghimbeigi, Abbas; Mohammadfam, Iraj

2017-03-04

High-risk unsafe behaviors (HRUBs) have been known as the main cause of occupational accidents. Considering the financial and societal costs of accidents and the limitations of available resources, there is an urgent need for managing unsafe behaviors at workplaces. The aim of the present study was to find strategies for decreasing the rate of HRUBs using an integrated approach of safety behavior sampling technique and Bayesian networks analysis. A cross-sectional study. The Bayesian network was constructed using a focus group approach. The required data was collected using the safety behavior sampling, and the parameters of the network were estimated using Expectation-Maximization algorithm. Using sensitivity analysis and belief updating, it was determined that which factors had the highest influences on unsafe behavior. Based on BN analyses, safety training was the most important factor influencing employees' behavior at the workplace. High quality safety training courses can reduce the rate of HRUBs about 10%. Moreover, the rate of HRUBs increased by decreasing the age of employees. The rate of HRUBs was higher in the afternoon and last days of a week. Among the investigated variables, training was the most important factor affecting safety behavior of employees. By holding high quality safety training courses, companies would be able to reduce the rate of HRUBs significantly.

A unifying Bayesian account of contextual effects in value-based choice

PubMed Central

Friston, Karl J.; Dolan, Raymond J.

2017-01-01

Empirical evidence suggests the incentive value of an option is affected by other options available during choice and by options presented in the past. These contextual effects are hard to reconcile with classical theories and have inspired accounts where contextual influences play a crucial role. However, each account only addresses one or the other of the empirical findings and a unifying perspective has been elusive. Here, we offer a unifying theory of context effects on incentive value attribution and choice based on normative Bayesian principles. This formulation assumes that incentive value corresponds to a precision-weighted prediction error, where predictions are based upon expectations about reward. We show that this scheme explains a wide range of contextual effects, such as those elicited by other options available during choice (or within-choice context effects). These include both conditions in which choice requires an integration of multiple attributes and conditions where a multi-attribute integration is not necessary. Moreover, the same scheme explains context effects elicited by options presented in the past or between-choice context effects. Our formulation encompasses a wide range of contextual influences (comprising both within- and between-choice effects) by calling on Bayesian principles, without invoking ad-hoc assumptions. This helps clarify the contextual nature of incentive value and choice behaviour and may offer insights into psychopathologies characterized by dysfunctional decision-making, such as addiction and pathological gambling. PMID:28981514

Logistic Mixed Models to Investigate Implicit and Explicit Belief Tracking.

PubMed

Lages, Martin; Scheel, Anne

2016-01-01

We investigated the proposition of a two-systems Theory of Mind in adults' belief tracking. A sample of N = 45 participants predicted the choice of one of two opponent players after observing several rounds in an animated card game. Three matches of this card game were played and initial gaze direction on target and subsequent choice predictions were recorded for each belief task and participant. We conducted logistic regressions with mixed effects on the binary data and developed Bayesian logistic mixed models to infer implicit and explicit mentalizing in true belief and false belief tasks. Although logistic regressions with mixed effects predicted the data well a Bayesian logistic mixed model with latent task- and subject-specific parameters gave a better account of the data. As expected explicit choice predictions suggested a clear understanding of true and false beliefs (TB/FB). Surprisingly, however, model parameters for initial gaze direction also indicated belief tracking. We discuss why task-specific parameters for initial gaze directions are different from choice predictions yet reflect second-order perspective taking.

Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.

PubMed

Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji

2016-09-01

It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.

Bayesian Revision of Residual Detection Power

NASA Technical Reports Server (NTRS)

DeLoach, Richard

2013-01-01

This paper addresses some issues with quality assessment and quality assurance in response surface modeling experiments executed in wind tunnels. The role of data volume on quality assurance for response surface models is reviewed. Specific wind tunnel response surface modeling experiments are considered for which apparent discrepancies exist between fit quality expectations based on implemented quality assurance tactics, and the actual fit quality achieved in those experiments. These discrepancies are resolved by using Bayesian inference to account for certain imperfections in the assessment methodology. Estimates of the fraction of out-of-tolerance model predictions based on traditional frequentist methods are revised to account for uncertainty in the residual assessment process. The number of sites in the design space for which residuals are out of tolerance is seen to exceed the number of sites where the model actually fails to fit the data. A method is presented to estimate how much of the design space in inadequately modeled by low-order polynomial approximations to the true but unknown underlying response function.

Evaluating Bayesian spatial methods for modelling species distributions with clumped and restricted occurrence data.

PubMed

Redding, David W; Lucas, Tim C D; Blackburn, Tim M; Jones, Kate E

2017-01-01

Statistical approaches for inferring the spatial distribution of taxa (Species Distribution Models, SDMs) commonly rely on available occurrence data, which is often clumped and geographically restricted. Although available SDM methods address some of these factors, they could be more directly and accurately modelled using a spatially-explicit approach. Software to fit models with spatial autocorrelation parameters in SDMs are now widely available, but whether such approaches for inferring SDMs aid predictions compared to other methodologies is unknown. Here, within a simulated environment using 1000 generated species' ranges, we compared the performance of two commonly used non-spatial SDM methods (Maximum Entropy Modelling, MAXENT and boosted regression trees, BRT), to a spatial Bayesian SDM method (fitted using R-INLA), when the underlying data exhibit varying combinations of clumping and geographic restriction. Finally, we tested how any recommended methodological settings designed to account for spatially non-random patterns in the data impact inference. Spatial Bayesian SDM method was the most consistently accurate method, being in the top 2 most accurate methods in 7 out of 8 data sampling scenarios. Within high-coverage sample datasets, all methods performed fairly similarly. When sampling points were randomly spread, BRT had a 1-3% greater accuracy over the other methods and when samples were clumped, the spatial Bayesian SDM method had a 4%-8% better AUC score. Alternatively, when sampling points were restricted to a small section of the true range all methods were on average 10-12% less accurate, with greater variation among the methods. Model inference under the recommended settings to account for autocorrelation was not impacted by clumping or restriction of data, except for the complexity of the spatial regression term in the spatial Bayesian model. Methods, such as those made available by R-INLA, can be successfully used to account for spatial autocorrelation in an SDM context and, by taking account of random effects, produce outputs that can better elucidate the role of covariates in predicting species occurrence. Given that it is often unclear what the drivers are behind data clumping in an empirical occurrence dataset, or indeed how geographically restricted these data are, spatially-explicit Bayesian SDMs may be the better choice when modelling the spatial distribution of target species.

Sequence diversity patterns suggesting balancing selection in partially sex-linked genes of the plant Silene latifolia are not generated by demographic history or gene flow.

PubMed

Guirao-Rico, Sara; Sánchez-Gracia, Alejandro; Charlesworth, Deborah

2017-03-01

DNA sequence diversity in genes in the partially sex-linked pseudoautosomal region (PAR) of the sex chromosomes of the plant Silene latifolia is higher than expected from within-species diversity of other genes. This could be the footprint of sexually antagonistic (SA) alleles that are maintained by balancing selection in a PAR gene (or genes) and affect polymorphism in linked genome regions. SA selection is predicted to occur during sex chromosome evolution, but it is important to test whether the unexpectedly high sequence polymorphism could be explained without it, purely by the combined effects of partial linkage with the sex-determining region and the population's demographic history, including possible introgression from Silene dioica. To test this, we applied approximate Bayesian computation-based model choice to autosomal sequence diversity data, to find the most plausible scenario for the recent history of S. latifolia and then to estimate the posterior density of the most relevant parameters. We then used these densities to simulate variation to be expected at PAR genes. We conclude that an excess of variants at high frequencies at PAR genes should arise in S. latifolia populations only for genes with strong associations with fully sex-linked genes, which requires closer linkage with the fully sex-linked region than that estimated for the PAR genes where apparent deviations from neutrality were observed. These results support the need to invoke selection to explain the S. latifolia PAR gene diversity, and encourage further work to test the possibility of balancing selection due to sexual antagonism. © 2016 John Wiley & Sons Ltd.

Unsupervised Gaussian Mixture-Model With Expectation Maximization for Detecting Glaucomatous Progression in Standard Automated Perimetry Visual Fields.

PubMed

Yousefi, Siamak; Balasubramanian, Madhusudhanan; Goldbaum, Michael H; Medeiros, Felipe A; Zangwill, Linda M; Weinreb, Robert N; Liebmann, Jeffrey M; Girkin, Christopher A; Bowd, Christopher

2016-05-01

To validate Gaussian mixture-model with expectation maximization (GEM) and variational Bayesian independent component analysis mixture-models (VIM) for detecting glaucomatous progression along visual field (VF) defect patterns (GEM-progression of patterns (POP) and VIM-POP). To compare GEM-POP and VIM-POP with other methods. GEM and VIM models separated cross-sectional abnormal VFs from 859 eyes and normal VFs from 1117 eyes into abnormal and normal clusters. Clusters were decomposed into independent axes. The confidence limit (CL) of stability was established for each axis with a set of 84 stable eyes. Sensitivity for detecting progression was assessed in a sample of 83 eyes with known progressive glaucomatous optic neuropathy (PGON). Eyes were classified as progressed if any defect pattern progressed beyond the CL of stability. Performance of GEM-POP and VIM-POP was compared to point-wise linear regression (PLR), permutation analysis of PLR (PoPLR), and linear regression (LR) of mean deviation (MD), and visual field index (VFI). Sensitivity and specificity for detecting glaucomatous VFs were 89.9% and 93.8%, respectively, for GEM and 93.0% and 97.0%, respectively, for VIM. Receiver operating characteristic (ROC) curve areas for classifying progressed eyes were 0.82 for VIM-POP, 0.86 for GEM-POP, 0.81 for PoPLR, 0.69 for LR of MD, and 0.76 for LR of VFI. GEM-POP was significantly more sensitive to PGON than PoPLR and linear regression of MD and VFI in our sample, while providing localized progression information. Detection of glaucomatous progression can be improved by assessing longitudinal changes in localized patterns of glaucomatous defect identified by unsupervised machine learning.

Bayesian Analysis of Hmi Images and Comparison to Tsi Variations and MWO Image Observables

NASA Astrophysics Data System (ADS)

Parker, D. G.; Ulrich, R. K.; Beck, J.; Tran, T. V.

2015-12-01

We have previously applied the Bayesian automatic classification system AutoClass to solar magnetogram and intensity images from the 150 Foot Solar Tower at Mount Wilson to identify classes of solar surface features associated with variations in total solar irradiance (TSI) and, using those identifications, modeled TSI time series with improved accuracy (r > 0.96). (Ulrich, et al, 2010) AutoClass identifies classes by a two-step process in which it: (1) finds, without human supervision, a set of class definitions based on specified attributes of a sample of the image data pixels, such as magnetic field and intensity in the case of MWO images, and (2) applies the class definitions thus found to new data sets to identify automatically in them the classes found in the sample set. HMI high resolution images capture four observables-magnetic field, continuum intensity, line depth and line width-in contrast to MWO's two observables-magnetic field and intensity. In this study, we apply AutoClass to the HMI observables for images from June, 2010 to December, 2014 to identify solar surface feature classes. We use contemporaneous TSI measurements to determine whether and how variations in the HMI classes are related to TSI variations and compare the characteristic statistics of the HMI classes to those found from MWO images. We also attempt to derive scale factors between the HMI and MWO magnetic and intensity observables.The ability to categorize automatically surface features in the HMI images holds out the promise of consistent, relatively quick and manageable analysis of the large quantity of data available in these images. Given that the classes found in MWO images using AutoClass have been found to improve modeling of TSI, application of AutoClass to the more complex HMI images should enhance understanding of the physical processes at work in solar surface features and their implications for the solar-terrestrial environment.Ulrich, R.K., Parker, D, Bertello, L. and Boyden, J. 2010, Solar Phys. , 261 , 11.

Bayesian estimation of the dynamics of pandemic (H1N1) 2009 influenza transmission in Queensland: A space-time SIR-based model.

PubMed

Huang, Xiaodong; Clements, Archie C A; Williams, Gail; Mengersen, Kerrie; Tong, Shilu; Hu, Wenbiao

2016-04-01

A pandemic strain of influenza A spread rapidly around the world in 2009, now referred to as pandemic (H1N1) 2009. This study aimed to examine the spatiotemporal variation in the transmission rate of pandemic (H1N1) 2009 associated with changes in local socio-environmental conditions from May 7-December 31, 2009, at a postal area level in Queensland, Australia. We used the data on laboratory-confirmed H1N1 cases to examine the spatiotemporal dynamics of transmission using a flexible Bayesian, space-time, Susceptible-Infected-Recovered (SIR) modelling approach. The model incorporated parameters describing spatiotemporal variation in H1N1 infection and local socio-environmental factors. The weekly transmission rate of pandemic (H1N1) 2009 was negatively associated with the weekly area-mean maximum temperature at a lag of 1 week (LMXT) (posterior mean: -0.341; 95% credible interval (CI): -0.370--0.311) and the socio-economic index for area (SEIFA) (posterior mean: -0.003; 95% CI: -0.004--0.001), and was positively associated with the product of LMXT and the weekly area-mean vapour pressure at a lag of 1 week (LVAP) (posterior mean: 0.008; 95% CI: 0.007-0.009). There was substantial spatiotemporal variation in transmission rate of pandemic (H1N1) 2009 across Queensland over the epidemic period. High random effects of estimated transmission rates were apparent in remote areas and some postal areas with higher proportion of indigenous populations and smaller overall populations. Local SEIFA and local atmospheric conditions were associated with the transmission rate of pandemic (H1N1) 2009. The more populated regions displayed consistent and synchronized epidemics with low average transmission rates. The less populated regions had high average transmission rates with more variations during the H1N1 epidemic period. Copyright © 2016 Elsevier Inc. All rights reserved.

Brain activity underlying auditory perceptual learning during short period training: simultaneous fMRI and EEG recording

PubMed Central

2013-01-01

Background There is an accumulating body of evidence indicating that neuronal functional specificity to basic sensory stimulation is mutable and subject to experience. Although fMRI experiments have investigated changes in brain activity after relative to before perceptual learning, brain activity during perceptual learning has not been explored. This work investigated brain activity related to auditory frequency discrimination learning using a variational Bayesian approach for source localization, during simultaneous EEG and fMRI recording. We investigated whether the practice effects are determined solely by activity in stimulus-driven mechanisms or whether high-level attentional mechanisms, which are linked to the perceptual task, control the learning process. Results The results of fMRI analyses revealed significant attention and learning related activity in left and right superior temporal gyrus STG as well as the left inferior frontal gyrus IFG. Current source localization of simultaneously recorded EEG data was estimated using a variational Bayesian method. Analysis of current localized to the left inferior frontal gyrus and the right superior temporal gyrus revealed gamma band activity correlated with behavioral performance. Conclusions Rapid improvement in task performance is accompanied by plastic changes in the sensory cortex as well as superior areas gated by selective attention. Together the fMRI and EEG results suggest that gamma band activity in the right STG and left IFG plays an important role during perceptual learning. PMID:23316957

Local differentiation amidst extensive allele sharing in Oryza nivara and O. rufipogon

PubMed Central

Banaticla-Hilario, Maria Celeste N; van den Berg, Ronald G; Hamilton, Nigel Ruaraidh Sackville; McNally, Kenneth L

2013-01-01

Genetic variation patterns within and between species may change along geographic gradients and at different spatial scales. This was revealed by microsatellite data at 29 loci obtained from 119 accessions of three Oryza series Sativae species in Asia Pacific: Oryza nivara Sharma and Shastry, O. rufipogon Griff., and O. meridionalis Ng. Genetic similarities between O. nivara and O. rufipogon across their distribution are evident in the clustering and ordination results and in the large proportion of shared alleles between these taxa. However, local-level species separation is recognized by Bayesian clustering and neighbor-joining analyses. At the regional scale, the two species seem more differentiated in South Asia than in Southeast Asia as revealed by FST analysis. The presence of strong gene flow barriers in smaller spatial units is also suggested in the analysis of molecular variance (AMOVA) results where 64% of the genetic variation is contained among populations (as compared to 26% within populations and 10% among species). Oryza nivara (HE = 0.67) exhibits slightly lower diversity and greater population differentiation than O. rufipogon (HE = 0.70). Bayesian inference identified four, and at a finer structural level eight, genetically distinct population groups that correspond to geographic populations within the three taxa. Oryza meridionalis and the Nepalese O. nivara seemed diverged from all the population groups of the series, whereas the Australasian O. rufipogon appeared distinct from the rest of the species. PMID:24101993

Geographic Variation of Overweight and Obesity among Women in Nigeria: A Case for Nutritional Transition in Sub-Saharan Africa

PubMed Central

Kandala, Ngianga-Bakwin; Stranges, Saverio

2014-01-01

Background Nutritional research in sub-Saharan Africa has primarily focused on under-nutrition. However, there is evidence of an ongoing nutritional transition in these settings. This study aimed to examine the geographic variation of overweight and obesity prevalence at the state-level among women in Nigeria, while accounting for individual-level risk factors. Methods The analysis was based on the 2008 Nigerian Demographic and Health Survey (NDHS), including 27,967 women aged 15–49 years. Individual data were collected on socio-demographics, but were aggregated to the country's states. We used a Bayesian geo-additive mixed model to map the geographic distribution of overweight and obesity at the state-level, accounting for individual-level risk factors. Results The overall prevalence of combined overweight and obesity (body mass index ≥25) was 20.9%. In multivariate Bayesian geo-additive models, higher education [odds ratio (OR) & 95% Credible Region (CR): 1.68 (1.38, 2.00)], higher wealth index [3.45 (2.98, 4.05)], living in urban settings [1.24 (1.14, 1.36)] and increasing age were all significantly associated with a higher prevalence of overweight/obesity. There was also a striking variation in overweight/obesity prevalence across ethnic groups and state of residence, the highest being in Cross River State, in south-eastern Nigeria [2.32 (1.62, 3.40)], the lowest in Osun State in south-western Nigeria [0.48 (0.36, 0.61)]. Conclusions This study suggests distinct geographic patterns in the combined prevalence of overweight and obesity among Nigerian women, as well as the role of demographic, socio-economic and environmental factors in the ongoing nutritional transition in these settings. PMID:24979753

Model-Based Individualized Treatment of Chemotherapeutics: Bayesian Population Modeling and Dose Optimization

PubMed Central

Jayachandran, Devaraj; Laínez-Aguirre, José; Rundell, Ann; Vik, Terry; Hannemann, Robert; Reklaitis, Gintaras; Ramkrishna, Doraiswami

2015-01-01

6-Mercaptopurine (6-MP) is one of the key drugs in the treatment of many pediatric cancers, auto immune diseases and inflammatory bowel disease. 6-MP is a prodrug, converted to an active metabolite 6-thioguanine nucleotide (6-TGN) through enzymatic reaction involving thiopurine methyltransferase (TPMT). Pharmacogenomic variation observed in the TPMT enzyme produces a significant variation in drug response among the patient population. Despite 6-MP’s widespread use and observed variation in treatment response, efforts at quantitative optimization of dose regimens for individual patients are limited. In addition, research efforts devoted on pharmacogenomics to predict clinical responses are proving far from ideal. In this work, we present a Bayesian population modeling approach to develop a pharmacological model for 6-MP metabolism in humans. In the face of scarcity of data in clinical settings, a global sensitivity analysis based model reduction approach is used to minimize the parameter space. For accurate estimation of sensitive parameters, robust optimal experimental design based on D-optimality criteria was exploited. With the patient-specific model, a model predictive control algorithm is used to optimize the dose scheduling with the objective of maintaining the 6-TGN concentration within its therapeutic window. More importantly, for the first time, we show how the incorporation of information from different levels of biological chain-of response (i.e. gene expression-enzyme phenotype-drug phenotype) plays a critical role in determining the uncertainty in predicting therapeutic target. The model and the control approach can be utilized in the clinical setting to individualize 6-MP dosing based on the patient’s ability to metabolize the drug instead of the traditional standard-dose-for-all approach. PMID:26226448

Incorporating real-time traffic and weather data to explore road accident likelihood and severity in urban arterials.

PubMed

Theofilatos, Athanasios

2017-06-01

The effective treatment of road accidents and thus the enhancement of road safety is a major concern to societies due to the losses in human lives and the economic and social costs. The investigation of road accident likelihood and severity by utilizing real-time traffic and weather data has recently received significant attention by researchers. However, collected data mainly stem from freeways and expressways. Consequently, the aim of the present paper is to add to the current knowledge by investigating accident likelihood and severity by exploiting real-time traffic and weather data collected from urban arterials in Athens, Greece. Random Forests (RF) are firstly applied for preliminary analysis purposes. More specifically, it is aimed to rank candidate variables according to their relevant importance and provide a first insight on the potential significant variables. Then, Bayesian logistic regression as well finite mixture and mixed effects logit models are applied to further explore factors associated with accident likelihood and severity respectively. Regarding accident likelihood, the Bayesian logistic regression showed that variations in traffic significantly influence accident occurrence. On the other hand, accident severity analysis revealed a generally mixed influence of traffic variations on accident severity, although international literature states that traffic variations increase severity. Lastly, weather parameters did not find to have a direct influence on accident likelihood or severity. The study added to the current knowledge by incorporating real-time traffic and weather data from urban arterials to investigate accident occurrence and accident severity mechanisms. The identification of risk factors can lead to the development of effective traffic management strategies to reduce accident occurrence and severity of injuries in urban arterials. Copyright © 2017 Elsevier Ltd and National Safety Council. All rights reserved.

Bayesian Quantification of Contrast-Enhanced Ultrasound Images With Adaptive Inclusion of an Irreversible Component.

PubMed

Rizzo, Gaia; Tonietto, Matteo; Castellaro, Marco; Raffeiner, Bernd; Coran, Alessandro; Fiocco, Ugo; Stramare, Roberto; Grisan, Enrico

2017-04-01

Contrast Enhanced Ultrasound (CEUS) is a sensitive imaging technique to assess tissue vascularity and it can be particularly useful in early detection and grading of arthritis. In a recent study we have shown that a Gamma-variate can accurately quantify synovial perfusion and it is flexible enough to describe many heterogeneous patterns. However, in some cases the heterogeneity of the kinetics can be such that even the Gamma model does not properly describe the curve, with a high number of outliers. In this work we apply to CEUS data the single compartment recirculation model (SCR) which takes explicitly into account the trapping of the microbubbles contrast agent by adding to the single Gamma-variate model its integral. The SCR model, originally proposed for dynamic-susceptibility magnetic resonance imaging, is solved here at pixel level within a Bayesian framework using Variational Bayes (VB). We also include the automatic relevant determination (ARD) algorithm to automatically infer the model complexity (SCR vs. Gamma model) from the data. We demonstrate that the inclusion of trapping best describes the CEUS patterns in 50% of the pixels, with the other 50% best fitted by a single Gamma. Such results highlight the necessity of the use ARD, to automatically exclude the irreversible component where not supported by the data. VB with ARD returns precise estimates in the majority of the kinetics (88% of total percentage of pixels) in a limited computational time (on average, 3.6 min per subject). Moreover, the impact of the additional trapping component has been evaluated for the differentiation of rheumatoid and non-rheumatoid patients, by means of a support vector machine classifier with backward feature selection. The results show that the trapping parameter is always present in the selected feature set, and improves the classification.

Riding across the selection landscape: fitness consequences of annual variation in reproductive characteristics

PubMed Central

Tremblay, Raymond L.; Ackerman, James D.; Pérez, Maria-Eglée

2010-01-01

Evolutionary models estimating phenotypic selection in character size usually assume that the character is invariant across reproductive bouts. We show that variation in the size of reproductive traits may be large over multiple events and can influence fitness in organisms where these traits are produced anew each season. With data from populations of two orchid species, Caladenia valida and Tolumnia variegata, we used Bayesian statistics to investigate the effect on the distribution in fitness of individuals when the fitness landscape is not flat and when characters vary across reproductive bouts. Inconsistency in character size across reproductive periods within an individual increases the uncertainty of mean fitness and, consequently, the uncertainty in individual fitness. The trajectory of selection is likely to be muddled as a consequence of variation in morphology of individuals across reproductive bouts. The frequency and amplitude of such changes will certainly affect the dynamics between selection and genetic drift. PMID:20047875

Trends in Life Expectancy and Lifespan Variation by Educational Attainment: United States, 1990-2010.

PubMed

Sasson, Isaac

2016-04-01

The educational gradient in life expectancy is well documented in the United States and in other low-mortality countries. Highly educated Americans, on average, live longer than their low-educated counterparts, who have recently seen declines in adult life expectancy. However, limiting the discussion on lifespan inequality to mean differences alone overlooks other dimensions of inequality and particularly disparities in lifespan variation. The latter represents a unique form of inequality, with higher variation translating into greater uncertainty in the time of death from an individual standpoint, and higher group heterogeneity from a population perspective. Using data from the National Vital Statistics System from 1990 to 2010, this is the first study to document trends in both life expectancy and S25--the standard deviation of age at death above 25--by educational attainment. Among low-educated whites, adult life expectancy declined by 3.1 years for women and by 0.6 years for men. At the same time, S25 increased by about 1.5 years among high school-educated whites of both genders, becoming an increasingly important component of total lifespan inequality. By contrast, college-educated whites benefited from rising life expectancy and record low variation in age at death, consistent with the shifting mortality scenario. Among blacks, adult life expectancy increased, and S25 plateaued or declined in nearly all educational attainment groups, although blacks generally lagged behind whites of the same gender on both measures. Documenting trends in lifespan variation can therefore improve our understanding of lifespan inequality and point to diverging trajectories in adult mortality across socioeconomic strata.

Improving satellite-based PM2.5 estimates in China using Gaussian processes modeling in a Bayesian hierarchical setting.

PubMed

Yu, Wenxi; Liu, Yang; Ma, Zongwei; Bi, Jun

2017-08-01

Using satellite-based aerosol optical depth (AOD) measurements and statistical models to estimate ground-level PM 2.5 is a promising way to fill the areas that are not covered by ground PM 2.5 monitors. The statistical models used in previous studies are primarily Linear Mixed Effects (LME) and Geographically Weighted Regression (GWR) models. In this study, we developed a new regression model between PM 2.5 and AOD using Gaussian processes in a Bayesian hierarchical setting. Gaussian processes model the stochastic nature of the spatial random effects, where the mean surface and the covariance function is specified. The spatial stochastic process is incorporated under the Bayesian hierarchical framework to explain the variation of PM 2.5 concentrations together with other factors, such as AOD, spatial and non-spatial random effects. We evaluate the results of our model and compare them with those of other, conventional statistical models (GWR and LME) by within-sample model fitting and out-of-sample validation (cross validation, CV). The results show that our model possesses a CV result (R 2  = 0.81) that reflects higher accuracy than that of GWR and LME (0.74 and 0.48, respectively). Our results indicate that Gaussian process models have the potential to improve the accuracy of satellite-based PM 2.5 estimates.

Hierarchical Bayesian analysis of outcome- and process-based social preferences and beliefs in Dictator Games and sequential Prisoner's Dilemmas.

PubMed

Aksoy, Ozan; Weesie, Jeroen

2014-05-01

In this paper, using a within-subjects design, we estimate the utility weights that subjects attach to the outcome of their interaction partners in four decision situations: (1) binary Dictator Games (DG), second player's role in the sequential Prisoner's Dilemma (PD) after the first player (2) cooperated and (3) defected, and (4) first player's role in the sequential Prisoner's Dilemma game. We find that the average weights in these four decision situations have the following order: (1)>(2)>(4)>(3). Moreover, the average weight is positive in (1) but negative in (2), (3), and (4). Our findings indicate the existence of strong negative and small positive reciprocity for the average subject, but there is also high interpersonal variation in the weights in these four nodes. We conclude that the PD frame makes subjects more competitive than the DG frame. Using hierarchical Bayesian modeling, we simultaneously analyze beliefs of subjects about others' utility weights in the same four decision situations. We compare several alternative theoretical models on beliefs, e.g., rational beliefs (Bayesian-Nash equilibrium) and a consensus model. Our results on beliefs strongly support the consensus effect and refute rational beliefs: there is a strong relationship between own preferences and beliefs and this relationship is relatively stable across the four decision situations. Copyright © 2014 Elsevier Inc. All rights reserved.

Multi-level Bayesian safety analysis with unprocessed Automatic Vehicle Identification data for an urban expressway.

PubMed

Shi, Qi; Abdel-Aty, Mohamed; Yu, Rongjie

2016-03-01

In traffic safety studies, crash frequency modeling of total crashes is the cornerstone before proceeding to more detailed safety evaluation. The relationship between crash occurrence and factors such as traffic flow and roadway geometric characteristics has been extensively explored for a better understanding of crash mechanisms. In this study, a multi-level Bayesian framework has been developed in an effort to identify the crash contributing factors on an urban expressway in the Central Florida area. Two types of traffic data from the Automatic Vehicle Identification system, which are the processed data capped at speed limit and the unprocessed data retaining the original speed were incorporated in the analysis along with road geometric information. The model framework was proposed to account for the hierarchical data structure and the heterogeneity among the traffic and roadway geometric data. Multi-level and random parameters models were constructed and compared with the Negative Binomial model under the Bayesian inference framework. Results showed that the unprocessed traffic data was superior. Both multi-level models and random parameters models outperformed the Negative Binomial model and the models with random parameters achieved the best model fitting. The contributing factors identified imply that on the urban expressway lower speed and higher speed variation could significantly increase the crash likelihood. Other geometric factors were significant including auxiliary lanes and horizontal curvature. Copyright © 2015 Elsevier Ltd. All rights reserved.

A phylogenetic study of Laeliinae (Orchidaceae) based on combined nuclear and plastid DNA sequences

PubMed Central

van den Berg, Cássio; Higgins, Wesley E.; Dressler, Robert L.; Whitten, W. Mark; Soto-Arenas, Miguel A.; Chase, Mark W.

2009-01-01

Background and Aims Laeliinae are a neotropical orchid subtribe with approx. 1500 species in 50 genera. In this study, an attempt is made to assess generic alliances based on molecular phylogenetic analysis of DNA sequence data. Methods Six DNA datasets were gathered: plastid trnL intron, trnL-F spacer, matK gene and trnK introns upstream and dowstream from matK and nuclear ITS rDNA. Data were analysed with maximum parsimony (MP) and Bayesian analysis with mixed models (BA). Key Results Although relationships between Laeliinae and outgroups are well supported, within the subtribe sequence variation is low considering the broad taxonomic range covered. Localized incongruence between the ITS and plastid trees was found. A combined tree followed the ITS trees more closely, but the levels of support obtained with MP were low. The Bayesian analysis recovered more well-supported nodes. The trees from combined MP and BA allowed eight generic alliances to be recognized within Laeliinae, all of which show trends in morphological characters but lack unambiguous synapomorphies. Conclusions By using combined plastid and nuclear DNA data in conjunction with mixed-models Bayesian inference, it is possible to delimit smaller groups within Laeliinae and discuss general patterns of pollination and hybridization compatibility. Furthermore, these small groups can now be used for further detailed studies to explain morphological evolution and diversification patterns within the subtribe. PMID:19423551

Socio-ecological factors and hand, foot and mouth disease in dry climate regions: a Bayesian spatial approach in Gansu, China

NASA Astrophysics Data System (ADS)

Gou, Faxiang; Liu, Xinfeng; Ren, Xiaowei; Liu, Dongpeng; Liu, Haixia; Wei, Kongfu; Yang, Xiaoting; Cheng, Yao; Zheng, Yunhe; Jiang, Xiaojuan; Li, Juansheng; Meng, Lei; Hu, Wenbiao

2017-01-01

The influence of socio-ecological factors on hand, foot and mouth disease (HFMD) were explored in this study using Bayesian spatial modeling and spatial patterns identified in dry regions of Gansu, China. Notified HFMD cases and socio-ecological data were obtained from the China Information System for Disease Control and Prevention, Gansu Yearbook and Gansu Meteorological Bureau. A Bayesian spatial conditional autoregressive model was used to quantify the effects of socio-ecological factors on the HFMD and explore spatial patterns, with the consideration of its socio-ecological effects. Our non-spatial model suggests temperature (relative risk (RR) 1.15, 95 % CI 1.01-1.31), GDP per capita (RR 1.19, 95 % CI 1.01-1.39) and population density (RR 1.98, 95 % CI 1.19-3.17) to have a significant effect on HFMD transmission. However, after controlling for spatial random effects, only temperature (RR 1.25, 95 % CI 1.04-1.53) showed significant association with HFMD. The spatial model demonstrates temperature to play a major role in the transmission of HFMD in dry regions. Estimated residual variation after taking into account the socio-ecological variables indicated that high incidences of HFMD were mainly clustered in the northwest of Gansu. And, spatial structure showed a unique distribution after taking account of socio-ecological effects.

The use of genomic information increases the accuracy of breeding value predictions for sea louse (Caligus rogercresseyi) resistance in Atlantic salmon (Salmo salar).

PubMed

Correa, Katharina; Bangera, Rama; Figueroa, René; Lhorente, Jean P; Yáñez, José M

2017-01-31

Sea lice infestations caused by Caligus rogercresseyi are a main concern to the salmon farming industry due to associated economic losses. Resistance to this parasite was shown to have low to moderate genetic variation and its genetic architecture was suggested to be polygenic. The aim of this study was to compare accuracies of breeding value predictions obtained with pedigree-based best linear unbiased prediction (P-BLUP) methodology against different genomic prediction approaches: genomic BLUP (G-BLUP), Bayesian Lasso, and Bayes C. To achieve this, 2404 individuals from 118 families were measured for C. rogercresseyi count after a challenge and genotyped using 37 K single nucleotide polymorphisms. Accuracies were assessed using fivefold cross-validation and SNP densities of 0.5, 1, 5, 10, 25 and 37 K. Accuracy of genomic predictions increased with increasing SNP density and was higher than pedigree-based BLUP predictions by up to 22%. Both Bayesian and G-BLUP methods can predict breeding values with higher accuracies than pedigree-based BLUP, however, G-BLUP may be the preferred method because of reduced computation time and ease of implementation. A relatively low marker density (i.e. 10 K) is sufficient for maximal increase in accuracy when using G-BLUP or Bayesian methods for genomic prediction of C. rogercresseyi resistance in Atlantic salmon.

Bayesian Nonparametric Ordination for the Analysis of Microbial Communities.

PubMed

Ren, Boyu; Bacallado, Sergio; Favaro, Stefano; Holmes, Susan; Trippa, Lorenzo

2017-01-01

Human microbiome studies use sequencing technologies to measure the abundance of bacterial species or Operational Taxonomic Units (OTUs) in samples of biological material. Typically the data are organized in contingency tables with OTU counts across heterogeneous biological samples. In the microbial ecology community, ordination methods are frequently used to investigate latent factors or clusters that capture and describe variations of OTU counts across biological samples. It remains important to evaluate how uncertainty in estimates of each biological sample's microbial distribution propagates to ordination analyses, including visualization of clusters and projections of biological samples on low dimensional spaces. We propose a Bayesian analysis for dependent distributions to endow frequently used ordinations with estimates of uncertainty. A Bayesian nonparametric prior for dependent normalized random measures is constructed, which is marginally equivalent to the normalized generalized Gamma process, a well-known prior for nonparametric analyses. In our prior, the dependence and similarity between microbial distributions is represented by latent factors that concentrate in a low dimensional space. We use a shrinkage prior to tune the dimensionality of the latent factors. The resulting posterior samples of model parameters can be used to evaluate uncertainty in analyses routinely applied in microbiome studies. Specifically, by combining them with multivariate data analysis techniques we can visualize credible regions in ecological ordination plots. The characteristics of the proposed model are illustrated through a simulation study and applications in two microbiome datasets.

Assessing compositional variability through graphical analysis and Bayesian statistical approaches: case studies on transgenic crops.

PubMed

Harrigan, George G; Harrison, Jay M

2012-01-01

New transgenic (GM) crops are subjected to extensive safety assessments that include compositional comparisons with conventional counterparts as a cornerstone of the process. The influence of germplasm, location, environment, and agronomic treatments on compositional variability is, however, often obscured in these pair-wise comparisons. Furthermore, classical statistical significance testing can often provide an incomplete and over-simplified summary of highly responsive variables such as crop composition. In order to more clearly describe the influence of the numerous sources of compositional variation we present an introduction to two alternative but complementary approaches to data analysis and interpretation. These include i) exploratory data analysis (EDA) with its emphasis on visualization and graphics-based approaches and ii) Bayesian statistical methodology that provides easily interpretable and meaningful evaluations of data in terms of probability distributions. The EDA case-studies include analyses of herbicide-tolerant GM soybean and insect-protected GM maize and soybean. Bayesian approaches are presented in an analysis of herbicide-tolerant GM soybean. Advantages of these approaches over classical frequentist significance testing include the more direct interpretation of results in terms of probabilities pertaining to quantities of interest and no confusion over the application of corrections for multiple comparisons. It is concluded that a standardized framework for these methodologies could provide specific advantages through enhanced clarity of presentation and interpretation in comparative assessments of crop composition.

Statistical analysis of textural features for improved classification of oral histopathological images.

PubMed

Muthu Rama Krishnan, M; Shah, Pratik; Chakraborty, Chandan; Ray, Ajoy K

2012-04-01

The objective of this paper is to provide an improved technique, which can assist oncopathologists in correct screening of oral precancerous conditions specially oral submucous fibrosis (OSF) with significant accuracy on the basis of collagen fibres in the sub-epithelial connective tissue. The proposed scheme is composed of collagen fibres segmentation, its textural feature extraction and selection, screening perfomance enhancement under Gaussian transformation and finally classification. In this study, collagen fibres are segmented on R,G,B color channels using back-probagation neural network from 60 normal and 59 OSF histological images followed by histogram specification for reducing the stain intensity variation. Henceforth, textural features of collgen area are extracted using fractal approaches viz., differential box counting and brownian motion curve . Feature selection is done using Kullback-Leibler (KL) divergence criterion and the screening performance is evaluated based on various statistical tests to conform Gaussian nature. Here, the screening performance is enhanced under Gaussian transformation of the non-Gaussian features using hybrid distribution. Moreover, the routine screening is designed based on two statistical classifiers viz., Bayesian classification and support vector machines (SVM) to classify normal and OSF. It is observed that SVM with linear kernel function provides better classification accuracy (91.64%) as compared to Bayesian classifier. The addition of fractal features of collagen under Gaussian transformation improves Bayesian classifier's performance from 80.69% to 90.75%. Results are here studied and discussed.

Geographic isolation drives divergence of uncorrelated genetic and song variation in the Ruddy-capped Nightingale-Thrush (Catharus frantzii; Aves: Turdidae).

PubMed

Ortiz-Ramírez, Marco F; Andersen, Michael J; Zaldívar-Riverón, Alejandro; Ornelas, Juan Francisco; Navarro-Sigüenza, Adolfo G

2016-01-01

Montane barriers influence the evolutionary history of lineages by promoting isolation of populations. The effects of these historical processes are evident in patterns of differentiation among extant populations, which are often expressed as genetic and behavioral variation between populations. We investigated the effects of geographic barriers on the evolutionary history of a Mesoamerican bird by studying patterns of genetic and vocal variation in the Ruddy-capped Nightingale-Thrush (Turdidae: Catharus frantzii), a non-migratory oscine bird that inhabits montane forests from central Mexico to Panama. We reconstructed the phylogeographic history and estimated divergence times between populations using Bayesian and maximum likelihood methods. We found strong support for the existence of four mitochondrial lineages of C. frantzii corresponding to isolated mountain ranges: Sierra Madre Oriental; Sierra Madre del Sur; the highlands of Chiapas, Guatemala, and El Salvador; and the Talamanca Cordillera. Vocal features in C. frantzii were highly variable among the four observed clades, but vocal variation and genetic variation were uncorrelated. Song variation in C. frantzii suggests that sexual selection and cultural drift could be important factors driving song differentiation in C. frantzii. Copyright © 2015 Elsevier Inc. All rights reserved.

The phylogenetic relationships of known mosquito (Diptera: Culicidae) mitogenomes.

PubMed

Chu, Hongliang; Li, Chunxiao; Guo, Xiaoxia; Zhang, Hengduan; Luo, Peng; Wu, Zhonghua; Wang, Gang; Zhao, Tongyan

2018-01-01

The known mosquito mitogenomes, containing a total of 34 species, which belong to five genera, were collected from GenBank, and the practicality and effectiveness of the variation in the complete mitochondrial DNA genome and portions of mitochondrial COI gene were assessed to reconstruct the phylogeny of mosquitoes. Phylogenetic trees were reconstructed on the basis of parsimony, maximum likelihood, and Bayesian (BI) methods. It is concluded that: (1) Both mitogenomes and COI gene support the monophly of following taxa: Subgenus Nyssorhynchus, Subgenus Cellia, Anopheles albitarsis complex, Anopheles gambiae complex, and Anopheles punctulatus group; (2) Genus Aedes is not monophyletic relative to Ochlerotatus vigilax; (3) The mitogenome results indicate a close relationship between Anopheles epiroticus and Anopheles gambiae complex, Anopheles dirus complex and Anopheles punctulatus group, respectively; (4) The Bayesian posterior probability (BPP) within phylogenetic tree reconstructed by mitogenomes is higher than COI tree. The results show that phylogenetic relationships reconstructed using the mitogenomes were more similar to those based on morphological data.

Diving into the consumer nutrition environment: A Bayesian spatial factor analysis of neighborhood restaurant environment.

PubMed

Luan, Hui; Law, Jane; Lysy, Martin

2018-02-01

Neighborhood restaurant environment (NRE) plays a vital role in shaping residents' eating behaviors. While NRE 'healthfulness' is a multi-facet concept, most studies evaluate it based only on restaurant type, thus largely ignoring variations of in-restaurant features. In the few studies that do account for such features, healthfulness scores are simply averaged over accessible restaurants, thereby concealing any uncertainty that attributed to neighborhoods' size or spatial correlation. To address these limitations, this paper presents a Bayesian Spatial Factor Analysis for assessing NRE healthfulness in the city of Kitchener, Canada. Several in-restaurant characteristics are included. By treating NRE healthfulness as a spatially correlated latent variable, the adopted modeling approach can: (i) identify specific indicators most relevant to NRE healthfulness, (ii) provide healthfulness estimates for neighborhoods without accessible restaurants, and (iii) readily quantify uncertainties in the healthfulness index. Implications of the analysis for intervention program development and community food planning are discussed. Copyright © 2017 Elsevier Ltd. All rights reserved.

New subspace methods for ATR

NASA Astrophysics Data System (ADS)

Zhang, Peng; Peng, Jing; Sims, S. Richard F.

2005-05-01

In ATR applications, each feature is a convolution of an image with a filter. It is important to use most discriminant features to produce compact representations. We propose two novel subspace methods for dimension reduction to address limitations associated with Fukunaga-Koontz Transform (FKT). The first method, Scatter-FKT, assumes that target is more homogeneous, while clutter can be anything other than target and anywhere. Thus, instead of estimating a clutter covariance matrix, Scatter-FKT computes a clutter scatter matrix that measures the spread of clutter from the target mean. We choose dimensions along which the difference in variation between target and clutter is most pronounced. When the target follows a Gaussian distribution, Scatter-FKT can be viewed as a generalization of FKT. The second method, Optimal Bayesian Subspace, is derived from the optimal Bayesian classifier. It selects dimensions such that the minimum Bayes error rate can be achieved. When both target and clutter follow Gaussian distributions, OBS computes optimal subspace representations. We compare our methods against FKT using character image as well as IR data.

COSMOABC: Likelihood-free inference via Population Monte Carlo Approximate Bayesian Computation

NASA Astrophysics Data System (ADS)

Ishida, E. E. O.; Vitenti, S. D. P.; Penna-Lima, M.; Cisewski, J.; de Souza, R. S.; Trindade, A. M. M.; Cameron, E.; Busti, V. C.; COIN Collaboration

2015-11-01

Approximate Bayesian Computation (ABC) enables parameter inference for complex physical systems in cases where the true likelihood function is unknown, unavailable, or computationally too expensive. It relies on the forward simulation of mock data and comparison between observed and synthetic catalogues. Here we present COSMOABC, a Python ABC sampler featuring a Population Monte Carlo variation of the original ABC algorithm, which uses an adaptive importance sampling scheme. The code is very flexible and can be easily coupled to an external simulator, while allowing to incorporate arbitrary distance and prior functions. As an example of practical application, we coupled COSMOABC with the NUMCOSMO library and demonstrate how it can be used to estimate posterior probability distributions over cosmological parameters based on measurements of galaxy clusters number counts without computing the likelihood function. COSMOABC is published under the GPLv3 license on PyPI and GitHub and documentation is available at http://goo.gl/SmB8EX.

Circularly-symmetric complex normal ratio distribution for scalar transmissibility functions. Part III: Application to statistical modal analysis

NASA Astrophysics Data System (ADS)

Yan, Wang-Ji; Ren, Wei-Xin

2018-01-01

This study applies the theoretical findings of circularly-symmetric complex normal ratio distribution Yan and Ren (2016) [1,2] to transmissibility-based modal analysis from a statistical viewpoint. A probabilistic model of transmissibility function in the vicinity of the resonant frequency is formulated in modal domain, while some insightful comments are offered. It theoretically reveals that the statistics of transmissibility function around the resonant frequency is solely dependent on 'noise-to-signal' ratio and mode shapes. As a sequel to the development of the probabilistic model of transmissibility function in modal domain, this study poses the process of modal identification in the context of Bayesian framework by borrowing a novel paradigm. Implementation issues unique to the proposed approach are resolved by Lagrange multiplier approach. Also, this study explores the possibility of applying Bayesian analysis in distinguishing harmonic components and structural ones. The approaches are verified through simulated data and experimentally testing data. The uncertainty behavior due to variation of different factors is also discussed in detail.

Sequential inference as a mode of cognition and its correlates in fronto-parietal and hippocampal brain regions

PubMed Central

Friston, Karl J.; Dolan, Raymond J.

2017-01-01

Normative models of human cognition often appeal to Bayesian filtering, which provides optimal online estimates of unknown or hidden states of the world, based on previous observations. However, in many cases it is necessary to optimise beliefs about sequences of states rather than just the current state. Importantly, Bayesian filtering and sequential inference strategies make different predictions about beliefs and subsequent choices, rendering them behaviourally dissociable. Taking data from a probabilistic reversal task we show that subjects’ choices provide strong evidence that they are representing short sequences of states. Between-subject measures of this implicit sequential inference strategy had a neurobiological underpinning and correlated with grey matter density in prefrontal and parietal cortex, as well as the hippocampus. Our findings provide, to our knowledge, the first evidence for sequential inference in human cognition, and by exploiting between-subject variation in this measure we provide pointers to its neuronal substrates. PMID:28486504

Problems in the fingerprints based polycyclic aromatic hydrocarbons source apportionment analysis and a practical solution.

PubMed

Zou, Yonghong; Wang, Lixia; Christensen, Erik R

2015-10-01

This work intended to explain the challenges of the fingerprints based source apportionment method for polycyclic aromatic hydrocarbons (PAH) in the aquatic environment, and to illustrate a practical and robust solution. The PAH data detected in the sediment cores from the Illinois River provide the basis of this study. Principal component analysis (PCA) separates PAH compounds into two groups reflecting their possible airborne transport patterns; but it is not able to suggest specific sources. Not all positive matrix factorization (PMF) determined sources are distinguishable due to the variability of source fingerprints. However, they constitute useful suggestions for inputs for a Bayesian chemical mass balance (CMB) analysis. The Bayesian CMB analysis takes into account the measurement errors as well as the variations of source fingerprints, and provides a credible source apportionment. Major PAH sources for Illinois River sediments are traffic (35%), coke oven (24%), coal combustion (18%), and wood combustion (14%). Copyright © 2015. Published by Elsevier Ltd.

Active inference and epistemic value.

PubMed

Friston, Karl; Rigoli, Francesco; Ognibene, Dimitri; Mathys, Christoph; Fitzgerald, Thomas; Pezzulo, Giovanni

2015-01-01

We offer a formal treatment of choice behavior based on the premise that agents minimize the expected free energy of future outcomes. Crucially, the negative free energy or quality of a policy can be decomposed into extrinsic and epistemic (or intrinsic) value. Minimizing expected free energy is therefore equivalent to maximizing extrinsic value or expected utility (defined in terms of prior preferences or goals), while maximizing information gain or intrinsic value (or reducing uncertainty about the causes of valuable outcomes). The resulting scheme resolves the exploration-exploitation dilemma: Epistemic value is maximized until there is no further information gain, after which exploitation is assured through maximization of extrinsic value. This is formally consistent with the Infomax principle, generalizing formulations of active vision based upon salience (Bayesian surprise) and optimal decisions based on expected utility and risk-sensitive (Kullback-Leibler) control. Furthermore, as with previous active inference formulations of discrete (Markovian) problems, ad hoc softmax parameters become the expected (Bayes-optimal) precision of beliefs about, or confidence in, policies. This article focuses on the basic theory, illustrating the ideas with simulations. A key aspect of these simulations is the similarity between precision updates and dopaminergic discharges observed in conditioning paradigms.

Bayes factor design analysis: Planning for compelling evidence.

PubMed

Schönbrodt, Felix D; Wagenmakers, Eric-Jan

2018-02-01

A sizeable literature exists on the use of frequentist power analysis in the null-hypothesis significance testing (NHST) paradigm to facilitate the design of informative experiments. In contrast, there is almost no literature that discusses the design of experiments when Bayes factors (BFs) are used as a measure of evidence. Here we explore Bayes Factor Design Analysis (BFDA) as a useful tool to design studies for maximum efficiency and informativeness. We elaborate on three possible BF designs, (a) a fixed-n design, (b) an open-ended Sequential Bayes Factor (SBF) design, where researchers can test after each participant and can stop data collection whenever there is strong evidence for either [Formula: see text] or [Formula: see text], and (c) a modified SBF design that defines a maximal sample size where data collection is stopped regardless of the current state of evidence. We demonstrate how the properties of each design (i.e., expected strength of evidence, expected sample size, expected probability of misleading evidence, expected probability of weak evidence) can be evaluated using Monte Carlo simulations and equip researchers with the necessary information to compute their own Bayesian design analyses.

Associative learning versus fear habituation as predictors of long-term extinction retention.

PubMed

Brown, Lily A; LeBeau, Richard T; Chat, Ka Yi; Craske, Michelle G

2017-06-01

Violation of unconditioned stimulus (US) expectancy during extinction training may enhance associative learning and result in improved long-term extinction retention compared to within-session habituation. This experiment examines variation in US expectancy (i.e., expectancy violation) as a predictor of long-term extinction retention. It also examines within-session habituation of fear-potentiated startle (electromyography, EMG) and fear of conditioned stimuli (CS) throughout extinction training as predictors of extinction retention. Participants (n = 63) underwent fear conditioning, extinction and retention and provided continuous ratings of US expectancy and EMG, as well as CS fear ratings before and after each phase. Variation in US expectancy throughout extinction and habituation of EMG and fear was entered into a regression as predictors of retention and reinstatement of levels of expectancy and fear. Greater variation in US expectancy throughout extinction training was significantly predictive of enhanced extinction performance measured at retention test, although not after reinstatement test. Slope of EMG and CS fear during extinction did not predict retention of extinction. Within-session habituation of EMG and self-reported fear is not sufficient for long-term retention of extinction learning, and models emphasizing expectation violation may result in enhanced outcomes.

A Bayesian account of ‘hysteria’

PubMed Central

Adams, Rick A.; Brown, Harriet; Pareés, Isabel; Friston, Karl J.

2012-01-01

This article provides a neurobiological account of symptoms that have been called ‘hysterical’, ‘psychogenic’ or ‘medically unexplained’, which we will call functional motor and sensory symptoms. We use a neurobiologically informed model of hierarchical Bayesian inference in the brain to explain functional motor and sensory symptoms in terms of perception and action arising from inference based on prior beliefs and sensory information. This explanation exploits the key balance between prior beliefs and sensory evidence that is mediated by (body focused) attention, symptom expectations, physical and emotional experiences and beliefs about illness. Crucially, this furnishes an explanation at three different levels: (i) underlying neuromodulatory (synaptic) mechanisms; (ii) cognitive and experiential processes (attention and attribution of agency); and (iii) formal computations that underlie perceptual inference (representation of uncertainty or precision). Our explanation involves primary and secondary failures of inference; the primary failure is the (autonomous) emergence of a percept or belief that is held with undue certainty (precision) following top-down attentional modulation of synaptic gain. This belief can constitute a sensory percept (or its absence) or induce movement (or its absence). The secondary failure of inference is when the ensuing percept (and any somatosensory consequences) is falsely inferred to be a symptom to explain why its content was not predicted by the source of attentional modulation. This account accommodates several fundamental observations about functional motor and sensory symptoms, including: (i) their induction and maintenance by attention; (ii) their modification by expectation, prior experience and cultural beliefs and (iii) their involuntary and symptomatic nature. PMID:22641838

In situ genetic differentiation in a Hispaniolan lizard (Ameiva chrysolaema): a multilocus perspective.

PubMed

Gifford, Matthew E; Larson, Allan

2008-10-01

A previous phylogeographic study of mitochondrial haplotypes for the Hispaniolan lizard Ameiva chrysolaema revealed deep genetic structure associated with seawater inundation during the late Pliocene/early Pleistocene and evidence of subsequent population expansion into formerly inundated areas. We revisit hypotheses generated by our previous study using increased geographic sampling of populations and analysis of three nuclear markers (alpha-enolase intron 8, alpha-cardiac-actin intron 4, and beta-actin intron 3) in addition to mitochondrial haplotypes (ND2). Large genetic discontinuities correspond spatially and temporally with historical barriers to gene flow (sea inundations). NCPA cross-validation analysis and Bayesian multilocus analyses of divergence times (IMa and MCMCcoal) reveal two separate episodes of fragmentation associated with Pliocene and Pleistocene sea inundations, separating the species into historically separate Northern, East-Central, West-Central, and Southern population lineages. Multilocus Bayesian analysis using IMa indicates asymmetrical migration from the East-Central to the West-Central populations following secondary contact, consistent with expectations from the more pervasive sea inundation in the western region. The West-Central lineage has a genetic signature of population growth consistent with the expectation of geographic expansion into formerly inundated areas. Within each lineage, significant spatial genetic structure indicates isolation by distance at comparable temporal scales. This study adds to the growing body of evidence that vicariant speciation may be the prevailing source of lineage accumulation on oceanic islands. Thus, prior theories of island biogeography generally underestimate the role and temporal scale of intra-island vicariant processes.

An offline approach for output-only Bayesian identification of stochastic nonlinear systems using unscented Kalman filtering

NASA Astrophysics Data System (ADS)

Erazo, Kalil; Nagarajaiah, Satish

2017-06-01

In this paper an offline approach for output-only Bayesian identification of stochastic nonlinear systems is presented. The approach is based on a re-parameterization of the joint posterior distribution of the parameters that define a postulated state-space stochastic model class. In the re-parameterization the state predictive distribution is included, marginalized, and estimated recursively in a state estimation step using an unscented Kalman filter, bypassing state augmentation as required by existing online methods. In applications expectations of functions of the parameters are of interest, which requires the evaluation of potentially high-dimensional integrals; Markov chain Monte Carlo is adopted to sample the posterior distribution and estimate the expectations. The proposed approach is suitable for nonlinear systems subjected to non-stationary inputs whose realization is unknown, and that are modeled as stochastic processes. Numerical verification and experimental validation examples illustrate the effectiveness and advantages of the approach, including: (i) an increased numerical stability with respect to augmented-state unscented Kalman filtering, avoiding divergence of the estimates when the forcing input is unmeasured; (ii) the ability to handle arbitrary prior and posterior distributions. The experimental validation of the approach is conducted using data from a large-scale structure tested on a shake table. It is shown that the approach is robust to inherent modeling errors in the description of the system and forcing input, providing accurate prediction of the dynamic response when the excitation history is unknown.

Introduction in IND and recursive partitioning

NASA Technical Reports Server (NTRS)

Buntine, Wray; Caruana, Rich

1991-01-01

This manual describes the IND package for learning tree classifiers from data. The package is an integrated C and C shell re-implementation of tree learning routines such as CART, C4, and various MDL and Bayesian variations. The package includes routines for experiment control, interactive operation, and analysis of tree building. The manual introduces the system and its many options, gives a basic review of tree learning, contains a guide to the literature and a glossary, and lists the manual pages for the routines and instructions on installation.

Valuing Trial Designs from a Pharmaceutical Perspective Using Value-Based Pricing.

PubMed

Breeze, Penny; Brennan, Alan

2015-11-01

Our aim was to adapt the traditional framework for expected net benefit of sampling (ENBS) to be more compatible with drug development trials from the pharmaceutical perspective. We modify the traditional framework for conducting ENBS and assume that the price of the drug is conditional on the trial outcomes. We use a value-based pricing (VBP) criterion to determine price conditional on trial data using Bayesian updating of cost-effectiveness (CE) model parameters. We assume that there is a threshold price below which the company would not market the new intervention. We present a case study in which a phase III trial sample size and trial duration are varied. For each trial design, we sampled 10,000 trial outcomes and estimated VBP using a CE model. The expected commercial net benefit is calculated as the expected profits minus the trial costs. A clinical trial with shorter follow-up, and larger sample size, generated the greatest expected commercial net benefit. Increasing the duration of follow-up had a modest impact on profit forecasts. Expected net benefit of sampling can be adapted to value clinical trials in the pharmaceutical industry to optimise the expected commercial net benefit. However, the analyses can be very time consuming for complex CE models. © 2014 The Authors. Health Economics published by John Wiley & Sons Ltd.

Bayesian data analysis for newcomers.

PubMed

Kruschke, John K; Liddell, Torrin M

2018-02-01

This article explains the foundational concepts of Bayesian data analysis using virtually no mathematical notation. Bayesian ideas already match your intuitions from everyday reasoning and from traditional data analysis. Simple examples of Bayesian data analysis are presented that illustrate how the information delivered by a Bayesian analysis can be directly interpreted. Bayesian approaches to null-value assessment are discussed. The article clarifies misconceptions about Bayesian methods that newcomers might have acquired elsewhere. We discuss prior distributions and explain how they are not a liability but an important asset. We discuss the relation of Bayesian data analysis to Bayesian models of mind, and we briefly discuss what methodological problems Bayesian data analysis is not meant to solve. After you have read this article, you should have a clear sense of how Bayesian data analysis works and the sort of information it delivers, and why that information is so intuitive and useful for drawing conclusions from data.

Uncertainty and the Social Cost of Methane Using Bayesian Constrained Climate Models

NASA Astrophysics Data System (ADS)

Errickson, F. C.; Anthoff, D.; Keller, K.

2016-12-01

Social cost estimates of greenhouse gases are important for the design of sound climate policies and are also plagued by uncertainty. One major source of uncertainty stems from the simplified representation of the climate system used in the integrated assessment models that provide these social cost estimates. We explore how uncertainty over the social cost of methane varies with the way physical processes and feedbacks in the methane cycle are modeled by (i) coupling three different methane models to a simple climate model, (ii) using MCMC to perform a Bayesian calibration of the three coupled climate models that simulates direct sampling from the joint posterior probability density function (pdf) of model parameters, and (iii) producing probabilistic climate projections that are then used to calculate the Social Cost of Methane (SCM) with the DICE and FUND integrated assessment models. We find that including a temperature feedback in the methane cycle acts as an additional constraint during the calibration process and results in a correlation between the tropospheric lifetime of methane and several climate model parameters. This correlation is not seen in the models lacking this feedback. Several of the estimated marginal pdfs of the model parameters also exhibit different distributional shapes and expected values depending on the methane model used. As a result, probabilistic projections of the climate system out to the year 2300 exhibit different levels of uncertainty and magnitudes of warming for each of the three models under an RCP8.5 scenario. We find these differences in climate projections result in differences in the distributions and expected values for our estimates of the SCM. We also examine uncertainty about the SCM by performing a Monte Carlo analysis using a distribution for the climate sensitivity while holding all other climate model parameters constant. Our SCM estimates using the Bayesian calibration are lower and exhibit less uncertainty about extremely high values in the right tail of the distribution compared to the Monte Carlo approach. This finding has important climate policy implications and suggests previous work that accounts for climate model uncertainty by only varying the climate sensitivity parameter may overestimate the SCM.

Disease Mapping for Stomach Cancer in Libya Based on Besag– York– Mollié (BYM) Model

PubMed

Alhdiri, Maryam Ahmed Salem; Samat, Nor Azah; Mohamed, Zulkifley

2017-06-25

Globally, Cancer is the ever-increasing health problem and most common cause of medical deaths. In Libya, it is an important health concern, especially in the setting of an aging population and limited healthcare facilities. Therefore, the goal of this research is to map of the county’ cancer incidence rate using the Bayesian method and identify the high-risk regions (for the first time in a decade). In the field of disease mapping, very little has been done to address the issue of analyzing sparse cancer diseases in Libya. Standardized Morbidity Ratio or SMR is known as a traditional approach to measure the relative risk of the disease, which is the ratio of observed and expected number of accounts in a region that has the greatest uncertainty if the disease is rare or small geographical region. Therefore, to solve some of SMR’s problems, we used statistical smoothing or Bayesian models to estimate the relative risk for stomach cancer incidence in Libya in 2007 based on the BYM model. This research begins with a short offer of the SMR and Bayesian model with BYM model, which we applied to stomach cancer incidence in Libya. We compared all of the results using maps and tables. We found that BYM model is potentially beneficial, because it gives better relative risk estimates compared to SMR method. As well as, it has can overcome the classical method problem when there is no observed stomach cancer in a region. Creative Commons Attribution License

Adaptive sequential Bayesian classification using Page's test

NASA Astrophysics Data System (ADS)

Lynch, Robert S., Jr.; Willett, Peter K.

2002-03-01

In this paper, the previously introduced Mean-Field Bayesian Data Reduction Algorithm is extended for adaptive sequential hypothesis testing utilizing Page's test. In general, Page's test is well understood as a method of detecting a permanent change in distribution associated with a sequence of observations. However, the relationship between detecting a change in distribution utilizing Page's test with that of classification and feature fusion is not well understood. Thus, the contribution of this work is based on developing a method of classifying an unlabeled vector of fused features (i.e., detect a change to an active statistical state) as quickly as possible given an acceptable mean time between false alerts. In this case, the developed classification test can be thought of as equivalent to performing a sequential probability ratio test repeatedly until a class is decided, with the lower log-threshold of each test being set to zero and the upper log-threshold being determined by the expected distance between false alerts. It is of interest to estimate the delay (or, related stopping time) to a classification decision (the number of time samples it takes to classify the target), and the mean time between false alerts, as a function of feature selection and fusion by the Mean-Field Bayesian Data Reduction Algorithm. Results are demonstrated by plotting the delay to declaring the target class versus the mean time between false alerts, and are shown using both different numbers of simulated training data and different numbers of relevant features for each class.

Bayesian methods for estimating GEBVs of threshold traits

PubMed Central

Wang, C-L; Ding, X-D; Wang, J-Y; Liu, J-F; Fu, W-X; Zhang, Z; Yin, Z-J; Zhang, Q

2013-01-01

Estimation of genomic breeding values is the key step in genomic selection (GS). Many methods have been proposed for continuous traits, but methods for threshold traits are still scarce. Here we introduced threshold model to the framework of GS, and specifically, we extended the three Bayesian methods BayesA, BayesB and BayesCπ on the basis of threshold model for estimating genomic breeding values of threshold traits, and the extended methods are correspondingly termed BayesTA, BayesTB and BayesTCπ. Computing procedures of the three BayesT methods using Markov Chain Monte Carlo algorithm were derived. A simulation study was performed to investigate the benefit of the presented methods in accuracy with the genomic estimated breeding values (GEBVs) for threshold traits. Factors affecting the performance of the three BayesT methods were addressed. As expected, the three BayesT methods generally performed better than the corresponding normal Bayesian methods, in particular when the number of phenotypic categories was small. In the standard scenario (number of categories=2, incidence=30%, number of quantitative trait loci=50, h2=0.3), the accuracies were improved by 30.4%, 2.4%, and 5.7% points, respectively. In most scenarios, BayesTB and BayesTCπ generated similar accuracies and both performed better than BayesTA. In conclusion, our work proved that threshold model fits well for predicting GEBVs of threshold traits, and BayesTCπ is supposed to be the method of choice for GS of threshold traits. PMID:23149458

Value of information analysis for interventional and counterfactual Bayesian networks in forensic medical sciences.

PubMed

Constantinou, Anthony Costa; Yet, Barbaros; Fenton, Norman; Neil, Martin; Marsh, William

2016-01-01

Inspired by real-world examples from the forensic medical sciences domain, we seek to determine whether a decision about an interventional action could be subject to amendments on the basis of some incomplete information within the model, and whether it would be worthwhile for the decision maker to seek further information prior to suggesting a decision. The method is based on the underlying principle of Value of Information to enhance decision analysis in interventional and counterfactual Bayesian networks. The method is applied to two real-world Bayesian network models (previously developed for decision support in forensic medical sciences) to examine the average gain in terms of both Value of Information (average relative gain ranging from 11.45% and 59.91%) and decision making (potential amendments in decision making ranging from 0% to 86.8%). We have shown how the method becomes useful for decision makers, not only when decision making is subject to amendments on the basis of some unknown risk factors, but also when it is not. Knowing that a decision outcome is independent of one or more unknown risk factors saves us from the trouble of seeking information about the particular set of risk factors. Further, we have also extended the assessment of this implication to the counterfactual case and demonstrated how answers about interventional actions are expected to change when some unknown factors become known, and how useful this becomes in forensic medical science. Copyright © 2015 Elsevier B.V. All rights reserved.

Bayesian probabilistic population projections for all countries

PubMed Central

Raftery, Adrian E.; Li, Nan; Ševčíková, Hana; Gerland, Patrick; Heilig, Gerhard K.

2012-01-01

Projections of countries’ future populations, broken down by age and sex, are widely used for planning and research. They are mostly done deterministically, but there is a widespread need for probabilistic projections. We propose a Bayesian method for probabilistic population projections for all countries. The total fertility rate and female and male life expectancies at birth are projected probabilistically using Bayesian hierarchical models estimated via Markov chain Monte Carlo using United Nations population data for all countries. These are then converted to age-specific rates and combined with a cohort component projection model. This yields probabilistic projections of any population quantity of interest. The method is illustrated for five countries of different demographic stages, continents and sizes. The method is validated by an out of sample experiment in which data from 1950–1990 are used for estimation, and applied to predict 1990–2010. The method appears reasonably accurate and well calibrated for this period. The results suggest that the current United Nations high and low variants greatly underestimate uncertainty about the number of oldest old from about 2050 and that they underestimate uncertainty for high fertility countries and overstate uncertainty for countries that have completed the demographic transition and whose fertility has started to recover towards replacement level, mostly in Europe. The results also indicate that the potential support ratio (persons aged 20–64 per person aged 65+) will almost certainly decline dramatically in most countries over the coming decades. PMID:22908249

Bayesian methods for the design and interpretation of clinical trials in very rare diseases

PubMed Central

Hampson, Lisa V; Whitehead, John; Eleftheriou, Despina; Brogan, Paul

2014-01-01

This paper considers the design and interpretation of clinical trials comparing treatments for conditions so rare that worldwide recruitment efforts are likely to yield total sample sizes of 50 or fewer, even when patients are recruited over several years. For such studies, the sample size needed to meet a conventional frequentist power requirement is clearly infeasible. Rather, the expectation of any such trial has to be limited to the generation of an improved understanding of treatment options. We propose a Bayesian approach for the conduct of rare-disease trials comparing an experimental treatment with a control where patient responses are classified as a success or failure. A systematic elicitation from clinicians of their beliefs concerning treatment efficacy is used to establish Bayesian priors for unknown model parameters. The process of determining the prior is described, including the possibility of formally considering results from related trials. As sample sizes are small, it is possible to compute all possible posterior distributions of the two success rates. A number of allocation ratios between the two treatment groups can be considered with a view to maximising the prior probability that the trial concludes recommending the new treatment when in fact it is non-inferior to control. Consideration of the extent to which opinion can be changed, even by data from the best feasible design, can help to determine whether such a trial is worthwhile. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24957522

Signals of large scale climate drivers, hatchery enhancement, and marine factors in Yukon River Chinook salmon survival revealed with a Bayesian life history model.

PubMed

Cunningham, Curry J; Westley, Peter A H; Adkison, Milo D

2018-05-18

Understanding how species might respond to climate change involves disentangling the influence of co-occurring environmental factors on population dynamics, and is especially problematic for migratory species like Pacific salmon that move between ecosystems. To date, debate surrounding the causes of recent declines in Yukon River Chinook salmon (Oncorhynchus tshawytscha) abundance has centered on whether factors in freshwater or marine environments control variation in survival, and how these populations at the northern extremity of the species range will respond to climate change. To estimate the effect of factors in marine and freshwater environments on Chinook salmon survival, we constructed a stage-structured assessment model that incorporates the best available data, estimates incidental marine bycatch mortality in trawl fisheries, and uses Bayesian model selection methods to quantify support for alternative hypotheses. Models fitted to two index populations of Yukon River Chinook salmon indicate that processes in the nearshore and marine environments are the most important determinants of survival. Specifically, survival declines when ice leaves the Yukon River later in the spring, increases with wintertime temperature in the Bering Sea, and declines with the abundance of globally enhanced salmon species consistent with competition at sea. In addition, we found support for density-dependent survival limitations in freshwater but not marine portions of the life cycle, increasing average survival with ocean age, and age-specific selectivity of bycatch mortality in the Bering Sea. This study underscores the utility of flexible estimation models capable of fitting multiple data types and evaluating mortality from both natural and anthropogenic sources in multiple habitats. Overall, these analyses suggest that mortality at sea is the primary driver of population dynamics, yet under a warming climate Chinook salmon populations at the northern extent of the species' range may be expected to fare better than southern populations, but are influenced by foreign salmon production. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.

Phylogenomic analysis of a rapid radiation of misfit fishes (Syngnathiformes) using ultraconserved elements.

PubMed

Longo, S J; Faircloth, B C; Meyer, A; Westneat, M W; Alfaro, M E; Wainwright, P C

2017-08-01

Phylogenetics is undergoing a revolution as large-scale molecular datasets reveal unexpected but repeatable rearrangements of clades that were previously thought to be disparate lineages. One of the most unusual clades of fishes that has been found using large-scale molecular datasets is an expanded Syngnathiformes including traditional long-snouted syngnathiform lineages (Aulostomidae, Centriscidae, Fistulariidae, Solenostomidae, Syngnathidae), as well as a diverse set of largely benthic-associated fishes (Callionymoidei, Dactylopteridae, Mullidae, Pegasidae) that were previously dispersed across three orders. The monophyly of this surprising clade of fishes has been upheld by recent studies utilizing both nuclear and mitogenomic data, but the relationships among major lineages within Syngnathiformes remain ambiguous; previous analyses have inconsistent topologies and are plagued by low support at deep divergences between the major lineages. In this study, we use a dataset of ultraconserved elements (UCEs) to conduct the first phylogenomic study of Syngnathiformes. UCEs have been effective markers for resolving deep phylogenetic relationships in fishes and, combined with increased taxon sampling, we expected UCEs to resolve problematic syngnathiform relationships. Overall, UCEs were effective at resolving relationships within Syngnathiformes at a range of evolutionary timescales. We find consistent support for the monophyly of traditional long-snouted syngnathiform lineages (Aulostomidae, Centriscidae, Fistulariidae, Solenostomidae, Syngnathidae), which better agrees with morphological hypotheses than previously published topologies from molecular data. This result was supported by all Bayesian and maximum likelihood analyses, was robust to differences in matrix completeness and potential sources of bias, and was highly supported in coalescent-based analyses in ASTRAL when matrices were filtered to contain the most phylogenetically informative loci. While Bayesian and maximum likelihood analyses found support for a benthic-associated clade (Callionymidae, Dactylopteridae, Mullidae, and Pegasidae) as sister to the long-snouted clade, this result was not replicated in the ASTRAL analyses. The base of our phylogeny is characterized by short internodes separating major syngnathiform lineages and is consistent with the hypothesis of an ancient rapid radiation at the base of Syngnathiformes. Syngnathiformes therefore present an exciting opportunity to study patterns of morphological variation and functional innovation arising from rapid but ancient radiation. Copyright © 2017 Elsevier Inc. All rights reserved.

Geographical variation in life expectancy at birth in England and Wales is largely explained by deprivation.

PubMed

Woods, Laura M; Rachet, Bernard; Riga, Michael; Stone, Noell; Shah, Anjali; Coleman, Michel P

2005-02-01

To describe the population mortality profile of England and Wales by deprivation and in each government office region (GOR) during 1998, and to quantify the influence of geography and deprivation in determining life expectancy. Construction of life tables describing age specific mortality rates and life expectancy at birth from death registrations and estimated population counts. Life tables were created for (a) quintiles of income deprivation based on the income domain score of the index of multiple deprivation 2000, (b) each GOR and Wales, and (c) every combination of deprivation and geography. England and Wales.PATIENTS/ PARTICIPANTS: Residents of England and Wales, 1998. Life expectancy at birth varies with deprivation quintile and is highest in the most affluent groups. The differences are mainly attributable to differences in mortality rates under 75 years of age. Regional life expectancies display a clear north-south gradient. Linear regression analysis shows that deprivation explains most of the geographical variation in life expectancy. Geographical patterns of life expectancy identified within these data for England and Wales in 1998 are mainly attributable to variations in deprivation status as defined by the IMD 2000 income domain score.

Phenomenological constraints on the bulk viscosity of QCD

NASA Astrophysics Data System (ADS)

Paquet, Jean-François; Shen, Chun; Denicol, Gabriel; Jeon, Sangyong; Gale, Charles

2017-11-01

While small at very high temperature, the bulk viscosity of Quantum Chromodynamics is expected to grow in the confinement region. Although its precise magnitude and temperature-dependence in the cross-over region is not fully understood, recent theoretical and phenomenological studies provided evidence that the bulk viscosity can be sufficiently large to have measurable consequences on the evolution of the quark-gluon plasma. In this work, a Bayesian statistical analysis is used to establish probabilistic constraints on the temperature-dependence of bulk viscosity using hadronic measurements from RHIC and LHC.

OPTHYLIC: An Optimised Tool for Hybrid Limits Computation

NASA Astrophysics Data System (ADS)

Busato, Emmanuel; Calvet, David; Theveneaux-Pelzer, Timothée

2018-05-01

A software tool, computing observed and expected upper limits on Poissonian process rates using a hybrid frequentist-Bayesian CLs method, is presented. This tool can be used for simple counting experiments where only signal, background and observed yields are provided or for multi-bin experiments where binned distributions of discriminating variables are provided. It allows the combination of several channels and takes into account statistical and systematic uncertainties, as well as correlations of systematic uncertainties between channels. It has been validated against other software tools and analytical calculations, for several realistic cases.

Spatial Distribution of the Coefficient of Variation for the Paleo-Earthquakes in Japan

NASA Astrophysics Data System (ADS)

Nomura, S.; Ogata, Y.

2015-12-01

Renewal processes, point prccesses in which intervals between consecutive events are independently and identically distributed, are frequently used to describe this repeating earthquake mechanism and forecast the next earthquakes. However, one of the difficulties in applying recurrent earthquake models is the scarcity of the historical data. Most studied fault segments have few, or only one observed earthquake that often have poorly constrained historic and/or radiocarbon ages. The maximum likelihood estimate from such a small data set can have a large bias and error, which tends to yield high probability for the next event in a very short time span when the recurrence intervals have similar lengths. On the other hand, recurrence intervals at a fault depend on the long-term slip rate caused by the tectonic motion in average. In addition, recurrence times are also fluctuated by nearby earthquakes or fault activities which encourage or discourage surrounding seismicity. These factors have spatial trends due to the heterogeneity of tectonic motion and seismicity. Thus, this paper introduces a spatial structure on the key parameters of renewal processes for recurrent earthquakes and estimates it by using spatial statistics. Spatial variation of mean and variance parameters of recurrence times are estimated in Bayesian framework and the next earthquakes are forecasted by Bayesian predictive distributions. The proposal model is applied for recurrent earthquake catalog in Japan and its result is compared with the current forecast adopted by the Earthquake Research Committee of Japan.

Identification of somatic mutations in cancer through Bayesian-based analysis of sequenced genome pairs

PubMed Central

2013-01-01

Background The field of cancer genomics has rapidly adopted next-generation sequencing (NGS) in order to study and characterize malignant tumors with unprecedented resolution. In particular for cancer, one is often trying to identify somatic mutations – changes specific to a tumor and not within an individual’s germline. However, false positive and false negative detections often result from lack of sufficient variant evidence, contamination of the biopsy by stromal tissue, sequencing errors, and the erroneous classification of germline variation as tumor-specific. Results We have developed a generalized Bayesian analysis framework for matched tumor/normal samples with the purpose of identifying tumor-specific alterations such as single nucleotide mutations, small insertions/deletions, and structural variation. We describe our methodology, and discuss its application to other types of paired-tissue analysis such as the detection of loss of heterozygosity as well as allelic imbalance. We also demonstrate the high level of sensitivity and specificity in discovering simulated somatic mutations, for various combinations of a) genomic coverage and b) emulated heterogeneity. Conclusion We present a Java-based implementation of our methods named Seurat, which is made available for free academic use. We have demonstrated and reported on the discovery of different types of somatic change by applying Seurat to an experimentally-derived cancer dataset using our methods; and have discussed considerations and practices regarding the accurate detection of somatic events in cancer genomes. Seurat is available at https://sites.google.com/site/seuratsomatic. PMID:23642077

Identification of somatic mutations in cancer through Bayesian-based analysis of sequenced genome pairs.

PubMed

Christoforides, Alexis; Carpten, John D; Weiss, Glen J; Demeure, Michael J; Von Hoff, Daniel D; Craig, David W

2013-05-04

The field of cancer genomics has rapidly adopted next-generation sequencing (NGS) in order to study and characterize malignant tumors with unprecedented resolution. In particular for cancer, one is often trying to identify somatic mutations--changes specific to a tumor and not within an individual's germline. However, false positive and false negative detections often result from lack of sufficient variant evidence, contamination of the biopsy by stromal tissue, sequencing errors, and the erroneous classification of germline variation as tumor-specific. We have developed a generalized Bayesian analysis framework for matched tumor/normal samples with the purpose of identifying tumor-specific alterations such as single nucleotide mutations, small insertions/deletions, and structural variation. We describe our methodology, and discuss its application to other types of paired-tissue analysis such as the detection of loss of heterozygosity as well as allelic imbalance. We also demonstrate the high level of sensitivity and specificity in discovering simulated somatic mutations, for various combinations of a) genomic coverage and b) emulated heterogeneity. We present a Java-based implementation of our methods named Seurat, which is made available for free academic use. We have demonstrated and reported on the discovery of different types of somatic change by applying Seurat to an experimentally-derived cancer dataset using our methods; and have discussed considerations and practices regarding the accurate detection of somatic events in cancer genomes. Seurat is available at https://sites.google.com/site/seuratsomatic.

Using a Bayesian network to predict barrier island geomorphologic characteristics

USGS Publications Warehouse

Gutierrez, Ben; Plant, Nathaniel G.; Thieler, E. Robert; Turecek, Aaron

2015-01-01

Quantifying geomorphic variability of coastal environments is important for understanding and describing the vulnerability of coastal topography, infrastructure, and ecosystems to future storms and sea level rise. Here we use a Bayesian network (BN) to test the importance of multiple interactions between barrier island geomorphic variables. This approach models complex interactions and handles uncertainty, which is intrinsic to future sea level rise, storminess, or anthropogenic processes (e.g., beach nourishment and other forms of coastal management). The BN was developed and tested at Assateague Island, Maryland/Virginia, USA, a barrier island with sufficient geomorphic and temporal variability to evaluate our approach. We tested the ability to predict dune height, beach width, and beach height variables using inputs that included longer-term, larger-scale, or external variables (historical shoreline change rates, distances to inlets, barrier width, mean barrier elevation, and anthropogenic modification). Data sets from three different years spanning nearly a decade sampled substantial temporal variability and serve as a proxy for analysis of future conditions. We show that distinct geomorphic conditions are associated with different long-term shoreline change rates and that the most skillful predictions of dune height, beach width, and beach height depend on including multiple input variables simultaneously. The predictive relationships are robust to variations in the amount of input data and to variations in model complexity. The resulting model can be used to evaluate scenarios related to coastal management plans and/or future scenarios where shoreline change rates may differ from those observed historically.

OGLE-2008-BLG-355Lb: A massive planet around a late-type star

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koshimoto, N.; Sumi, T.; Fukagawa, M.

2014-06-20

We report the discovery of a massive planet, OGLE-2008-BLG-355Lb. The light curve analysis indicates a planet:host mass ratio of q = 0.0118 ± 0.0006 at a separation of 0.877 ± 0.010 Einstein radii. We do not measure a significant microlensing parallax signal and do not have high angular resolution images that could detect the planetary host star. Therefore, we do not have a direct measurement of the host star mass. A Bayesian analysis, assuming that all host stars have equal probability to host a planet with the measured mass ratio, implies a host star mass of M{sub h}=0.37{sub −0.17}{sup +0.30}more » M{sub ⊙} and a companion of mass M{sub P}=4.6{sub −2.2}{sup +3.7}M{sub J}, at a projected separation of r{sub ⊥}=1.70{sub −0.30}{sup +0.29} AU. The implied distance to the planetary system is D {sub L} = 6.8 ± 1.1 kpc. A planetary system with the properties preferred by the Bayesian analysis may be a challenge to the core accretion model of planet formation, as the core accretion model predicts that massive planets are far more likely to form around more massive host stars. This core accretion model prediction is not consistent with our Bayesian prior of an equal probability of host stars of all masses to host a planet with the measured mass ratio. Thus, if the core accretion model prediction is right, we should expect that follow-up high angular resolution observations will detect a host star with a mass in the upper part of the range allowed by the Bayesian analysis. That is, the host would probably be a K or G dwarf.« less

Comparison of different strategies for using fossil calibrations to generate the time prior in Bayesian molecular clock dating.

PubMed

Barba-Montoya, Jose; Dos Reis, Mario; Yang, Ziheng

2017-09-01

Fossil calibrations are the utmost source of information for resolving the distances between molecular sequences into estimates of absolute times and absolute rates in molecular clock dating analysis. The quality of calibrations is thus expected to have a major impact on divergence time estimates even if a huge amount of molecular data is available. In Bayesian molecular clock dating, fossil calibration information is incorporated in the analysis through the prior on divergence times (the time prior). Here, we evaluate three strategies for converting fossil calibrations (in the form of minimum- and maximum-age bounds) into the prior on times, which differ according to whether they borrow information from the maximum age of ancestral nodes and minimum age of descendent nodes to form constraints for any given node on the phylogeny. We study a simple example that is analytically tractable, and analyze two real datasets (one of 10 primate species and another of 48 seed plant species) using three Bayesian dating programs: MCMCTree, MrBayes and BEAST2. We examine how different calibration strategies, the birth-death process, and automatic truncation (to enforce the constraint that ancestral nodes are older than descendent nodes) interact to determine the time prior. In general, truncation has a great impact on calibrations so that the effective priors on the calibration node ages after the truncation can be very different from the user-specified calibration densities. The different strategies for generating the effective prior also had considerable impact, leading to very different marginal effective priors. Arbitrary parameters used to implement minimum-bound calibrations were found to have a strong impact upon the prior and posterior of the divergence times. Our results highlight the importance of inspecting the joint time prior used by the dating program before any Bayesian dating analysis. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

A Bayesian Method for Evaluating and Discovering Disease Loci Associations

PubMed Central

Jiang, Xia; Barmada, M. Michael; Cooper, Gregory F.; Becich, Michael J.

2011-01-01

Background A genome-wide association study (GWAS) typically involves examining representative SNPs in individuals from some population. A GWAS data set can concern a million SNPs and may soon concern billions. Researchers investigate the association of each SNP individually with a disease, and it is becoming increasingly commonplace to also analyze multi-SNP associations. Techniques for handling so many hypotheses include the Bonferroni correction and recently developed Bayesian methods. These methods can encounter problems. Most importantly, they are not applicable to a complex multi-locus hypothesis which has several competing hypotheses rather than only a null hypothesis. A method that computes the posterior probability of complex hypotheses is a pressing need. Methodology/Findings We introduce the Bayesian network posterior probability (BNPP) method which addresses the difficulties. The method represents the relationship between a disease and SNPs using a directed acyclic graph (DAG) model, and computes the likelihood of such models using a Bayesian network scoring criterion. The posterior probability of a hypothesis is computed based on the likelihoods of all competing hypotheses. The BNPP can not only be used to evaluate a hypothesis that has previously been discovered or suspected, but also to discover new disease loci associations. The results of experiments using simulated and real data sets are presented. Our results concerning simulated data sets indicate that the BNPP exhibits both better evaluation and discovery performance than does a p-value based method. For the real data sets, previous findings in the literature are confirmed and additional findings are found. Conclusions/Significance We conclude that the BNPP resolves a pressing problem by providing a way to compute the posterior probability of complex multi-locus hypotheses. A researcher can use the BNPP to determine the expected utility of investigating a hypothesis further. Furthermore, we conclude that the BNPP is a promising method for discovering disease loci associations. PMID:21853025

The Development of Bayesian Theory and Its Applications in Business and Bioinformatics

NASA Astrophysics Data System (ADS)

Zhang, Yifei

2018-03-01

Bayesian Theory originated from an Essay of a British mathematician named Thomas Bayes in 1763, and after its development in 20th century, Bayesian Statistics has been taking a significant part in statistical study of all fields. Due to the recent breakthrough of high-dimensional integral, Bayesian Statistics has been improved and perfected, and now it can be used to solve problems that Classical Statistics failed to solve. This paper summarizes Bayesian Statistics’ history, concepts and applications, which are illustrated in five parts: the history of Bayesian Statistics, the weakness of Classical Statistics, Bayesian Theory and its development and applications. The first two parts make a comparison between Bayesian Statistics and Classical Statistics in a macroscopic aspect. And the last three parts focus on Bayesian Theory in specific -- from introducing some particular Bayesian Statistics’ concepts to listing their development and finally their applications.

Bayesian demography 250 years after Bayes

PubMed Central

Bijak, Jakub; Bryant, John

2016-01-01

Bayesian statistics offers an alternative to classical (frequentist) statistics. It is distinguished by its use of probability distributions to describe uncertain quantities, which leads to elegant solutions to many difficult statistical problems. Although Bayesian demography, like Bayesian statistics more generally, is around 250 years old, only recently has it begun to flourish. The aim of this paper is to review the achievements of Bayesian demography, address some misconceptions, and make the case for wider use of Bayesian methods in population studies. We focus on three applications: demographic forecasts, limited data, and highly structured or complex models. The key advantages of Bayesian methods are the ability to integrate information from multiple sources and to describe uncertainty coherently. Bayesian methods also allow for including additional (prior) information next to the data sample. As such, Bayesian approaches are complementary to many traditional methods, which can be productively re-expressed in Bayesian terms. PMID:26902889

Variation of bar-press duration: where do new responses come from?

PubMed

Roberts, Seth; Gharib, Afshin

2006-06-01

Instrumental learning involves both variation and selection: variation of what the animal does, and selection by reward from among the variation. Four experiments with rats suggested a rule about how variation is controlled by recent events. Experiment 1 used the peak procedure. Measurements of bar-press durations showed a sharp increase in mean duration after the time that food was sometimes given. The increase was triggered by the omission of expected food. Our first explanation of the increase was that it was a frustration effect. Experiment 2 tested this explanation with a procedure in which the first response of a trial usually produced food, ending the trial. In Experiment 2, unlike Experiment 1, omission of expected food did not produce a large increase in bar-press duration, which cast doubt on the frustration explanation. Experiments 3 and 4 tested an alternative explanation: a decrease in expectation of reward increases variation. Both used two signals associated with different probabilities of reward. Bar presses were more variable in duration during the signal with the lower probability of reward, supporting this alternative. These experiments show how variation can be studied with ordinary equipment and responses.

Speech Enhancement Using Gaussian Scale Mixture Models

PubMed Central

Hao, Jiucang; Lee, Te-Won; Sejnowski, Terrence J.

2011-01-01

This paper presents a novel probabilistic approach to speech enhancement. Instead of a deterministic logarithmic relationship, we assume a probabilistic relationship between the frequency coefficients and the log-spectra. The speech model in the log-spectral domain is a Gaussian mixture model (GMM). The frequency coefficients obey a zero-mean Gaussian whose covariance equals to the exponential of the log-spectra. This results in a Gaussian scale mixture model (GSMM) for the speech signal in the frequency domain, since the log-spectra can be regarded as scaling factors. The probabilistic relation between frequency coefficients and log-spectra allows these to be treated as two random variables, both to be estimated from the noisy signals. Expectation-maximization (EM) was used to train the GSMM and Bayesian inference was used to compute the posterior signal distribution. Because exact inference of this full probabilistic model is computationally intractable, we developed two approaches to enhance the efficiency: the Laplace method and a variational approximation. The proposed methods were applied to enhance speech corrupted by Gaussian noise and speech-shaped noise (SSN). For both approximations, signals reconstructed from the estimated frequency coefficients provided higher signal-to-noise ratio (SNR) and those reconstructed from the estimated log-spectra produced lower word recognition error rate because the log-spectra fit the inputs to the recognizer better. Our algorithms effectively reduced the SSN, which algorithms based on spectral analysis were not able to suppress. PMID:21359139

A Framework for Quantifying Measurement Uncertainties and Uncertainty Propagation in HCCI/LTGC Engine Experiments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Petitpas, Guillaume; McNenly, Matthew J.; Whitesides, Russell A.

In this study, a framework for estimating experimental measurement uncertainties for a Homogenous Charge Compression Ignition (HCCI)/Low-Temperature Gasoline Combustion (LTGC) engine testing facility is presented. Detailed uncertainty quantification is first carried out for the measurement of the in-cylinder pressure, whose variations during the cycle provide most of the information for performance evaluation. Standard uncertainties of other measured quantities, such as the engine geometry and speed, the air and fuel flow rate and the intake/exhaust dry molar fractions are also estimated. Propagating those uncertainties using a Monte Carlo simulation and Bayesian inference methods then allows for estimation of uncertainties of themore » mass-average temperature and composition at IVC and throughout the cycle; and also of the engine performances such as gross Integrated Mean Effective Pressure, Heat Release and Ringing Intensity. Throughout the analysis, nominal values for uncertainty inputs were taken from a well-characterized engine test facility. However, the analysis did not take into account the calibration practice of experiments run in that facility and the resulting uncertainty values are therefore not indicative of the expected accuracy of those experimental results. A future study will employ the methodology developed here to explore the effects of different calibration methods on the different uncertainty values in order to evaluate best practices for accurate engine measurements.« less

A Framework for Quantifying Measurement Uncertainties and Uncertainty Propagation in HCCI/LTGC Engine Experiments

DOE PAGES

Petitpas, Guillaume; McNenly, Matthew J.; Whitesides, Russell A.

2017-03-28

In this study, a framework for estimating experimental measurement uncertainties for a Homogenous Charge Compression Ignition (HCCI)/Low-Temperature Gasoline Combustion (LTGC) engine testing facility is presented. Detailed uncertainty quantification is first carried out for the measurement of the in-cylinder pressure, whose variations during the cycle provide most of the information for performance evaluation. Standard uncertainties of other measured quantities, such as the engine geometry and speed, the air and fuel flow rate and the intake/exhaust dry molar fractions are also estimated. Propagating those uncertainties using a Monte Carlo simulation and Bayesian inference methods then allows for estimation of uncertainties of themore » mass-average temperature and composition at IVC and throughout the cycle; and also of the engine performances such as gross Integrated Mean Effective Pressure, Heat Release and Ringing Intensity. Throughout the analysis, nominal values for uncertainty inputs were taken from a well-characterized engine test facility. However, the analysis did not take into account the calibration practice of experiments run in that facility and the resulting uncertainty values are therefore not indicative of the expected accuracy of those experimental results. A future study will employ the methodology developed here to explore the effects of different calibration methods on the different uncertainty values in order to evaluate best practices for accurate engine measurements.« less

The impact of rare variation on gene expression across tissues.

PubMed

Li, Xin; Kim, Yungil; Tsang, Emily K; Davis, Joe R; Damani, Farhan N; Chiang, Colby; Hess, Gaelen T; Zappala, Zachary; Strober, Benjamin J; Scott, Alexandra J; Li, Amy; Ganna, Andrea; Bassik, Michael C; Merker, Jason D; Hall, Ira M; Battle, Alexis; Montgomery, Stephen B

2017-10-11

Rare genetic variants are abundant in humans and are expected to contribute to individual disease risk. While genetic association studies have successfully identified common genetic variants associated with susceptibility, these studies are not practical for identifying rare variants. Efforts to distinguish pathogenic variants from benign rare variants have leveraged the genetic code to identify deleterious protein-coding alleles, but no analogous code exists for non-coding variants. Therefore, ascertaining which rare variants have phenotypic effects remains a major challenge. Rare non-coding variants have been associated with extreme gene expression in studies using single tissues, but their effects across tissues are unknown. Here we identify gene expression outliers, or individuals showing extreme expression levels for a particular gene, across 44 human tissues by using combined analyses of whole genomes and multi-tissue RNA-sequencing data from the Genotype-Tissue Expression (GTEx) project v6p release. We find that 58% of underexpression and 28% of overexpression outliers have nearby conserved rare variants compared to 8% of non-outliers. Additionally, we developed RIVER (RNA-informed variant effect on regulation), a Bayesian statistical model that incorporates expression data to predict a regulatory effect for rare variants with higher accuracy than models using genomic annotations alone. Overall, we demonstrate that rare variants contribute to large gene expression changes across tissues and provide an integrative method for interpretation of rare variants in individual genomes.

Emulation of reionization simulations for Bayesian inference of astrophysics parameters using neural networks

NASA Astrophysics Data System (ADS)

Schmit, C. J.; Pritchard, J. R.

2018-03-01

Next generation radio experiments such as LOFAR, HERA, and SKA are expected to probe the Epoch of Reionization (EoR) and claim a first direct detection of the cosmic 21cm signal within the next decade. Data volumes will be enormous and can thus potentially revolutionize our understanding of the early Universe and galaxy formation. However, numerical modelling of the EoR can be prohibitively expensive for Bayesian parameter inference and how to optimally extract information from incoming data is currently unclear. Emulation techniques for fast model evaluations have recently been proposed as a way to bypass costly simulations. We consider the use of artificial neural networks as a blind emulation technique. We study the impact of training duration and training set size on the quality of the network prediction and the resulting best-fitting values of a parameter search. A direct comparison is drawn between our emulation technique and an equivalent analysis using 21CMMC. We find good predictive capabilities of our network using training sets of as low as 100 model evaluations, which is within the capabilities of fully numerical radiative transfer codes.

A decision aid for intensity-modulated radiation-therapy plan selection in prostate cancer based on a prognostic Bayesian network and a Markov model.

PubMed

Smith, Wade P; Doctor, Jason; Meyer, Jürgen; Kalet, Ira J; Phillips, Mark H

2009-06-01

The prognosis of cancer patients treated with intensity-modulated radiation-therapy (IMRT) is inherently uncertain, depends on many decision variables, and requires that a physician balance competing objectives: maximum tumor control with minimal treatment complications. In order to better deal with the complex and multiple objective nature of the problem we have combined a prognostic probabilistic model with multi-attribute decision theory which incorporates patient preferences for outcomes. The response to IMRT for prostate cancer was modeled. A Bayesian network was used for prognosis for each treatment plan. Prognoses included predicting local tumor control, regional spread, distant metastases, and normal tissue complications resulting from treatment. A Markov model was constructed and used to calculate a quality-adjusted life-expectancy which aids in the multi-attribute decision process. Our method makes explicit the tradeoffs patients face between quality and quantity of life. This approach has advantages over current approaches because with our approach risks of health outcomes and patient preferences determine treatment decisions.

Explicitly integrating parameter, input, and structure uncertainties into Bayesian Neural Networks for probabilistic hydrologic forecasting

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Xuesong; Liang, Faming; Yu, Beibei

2011-11-09

Estimating uncertainty of hydrologic forecasting is valuable to water resources and other relevant decision making processes. Recently, Bayesian Neural Networks (BNNs) have been proved powerful tools for quantifying uncertainty of streamflow forecasting. In this study, we propose a Markov Chain Monte Carlo (MCMC) framework to incorporate the uncertainties associated with input, model structure, and parameter into BNNs. This framework allows the structure of the neural networks to change by removing or adding connections between neurons and enables scaling of input data by using rainfall multipliers. The results show that the new BNNs outperform the BNNs that only consider uncertainties associatedmore » with parameter and model structure. Critical evaluation of posterior distribution of neural network weights, number of effective connections, rainfall multipliers, and hyper-parameters show that the assumptions held in our BNNs are not well supported. Further understanding of characteristics of different uncertainty sources and including output error into the MCMC framework are expected to enhance the application of neural networks for uncertainty analysis of hydrologic forecasting.« less

Bayesian decision analysis as a tool for defining monitoring needs in the field of effects of CSOs on receiving waters.

PubMed

Korving, H; Clemens, F

2002-01-01

In recent years, decision analysis has become an important technique in many disciplines. It provides a methodology for rational decision-making allowing for uncertainties in the outcome of several possible actions to be undertaken. An example in urban drainage is the situation in which an engineer has to decide upon a major reconstruction of a system in order to prevent pollution of receiving waters due to CSOs. This paper describes the possibilities of Bayesian decision-making in urban drainage. In particular, the utility of monitoring prior to deciding on the reconstruction of a sewer system to reduce CSO emissions is studied. Our concern is with deciding whether a price should be paid for new information and which source of information is the best choice given the expected uncertainties in the outcome. The influence of specific uncertainties (sewer system data and model parameters) on the probability of CSO volumes is shown to be significant. Using Bayes' rule, to combine prior impressions with new observations, reduces the risks linked with the planning of sewer system reconstructions.

The Biasing Influence of Worldview on Climate Change Attitudes

NASA Astrophysics Data System (ADS)

Cook, J.

2012-12-01

It is well established that political ideology has a strong influence on public opinion about climate change. According to one survey (Leiserowitz et al 2011), the percentage of Democrats accepting that climate change is happening is over double the percentage of Tea Partiers. There is also evidence of ideologically driven belief polarization, where two people receiving the same evidence update their beliefs in opposite direction. Presenting scientific evidence can result in a backfire effect where conservatives become more sceptical of climate change. It is possible to model (and hence better understand) the backfire effect using Bayesian Networks which simulate belief updating using Bayes Law. In this model, trust in science is the driving force behind polarization and worldview is the knob that controls trust. One consequence of this model is that attempts to increase trust in science are expected to be largely ineffective for conservatives. It suggests that a potentially constructive approach is to reduce the biasing influence of worldview by affirming conservative values while presenting climate messages. Experimental data comparing the effectiveness of various interventions are presented and discussed in the context of the Bayesian Network model.

Collinear Latent Variables in Multilevel Confirmatory Factor Analysis

PubMed Central

van de Schoot, Rens; Hox, Joop

2014-01-01

Because variables may be correlated in the social and behavioral sciences, multicollinearity might be problematic. This study investigates the effect of collinearity manipulated in within and between levels of a two-level confirmatory factor analysis by Monte Carlo simulation. Furthermore, the influence of the size of the intraclass correlation coefficient (ICC) and estimation method; maximum likelihood estimation with robust chi-squares and standard errors and Bayesian estimation, on the convergence rate are investigated. The other variables of interest were rate of inadmissible solutions and the relative parameter and standard error bias on the between level. The results showed that inadmissible solutions were obtained when there was between level collinearity and the estimation method was maximum likelihood. In the within level multicollinearity condition, all of the solutions were admissible but the bias values were higher compared with the between level collinearity condition. Bayesian estimation appeared to be robust in obtaining admissible parameters but the relative bias was higher than for maximum likelihood estimation. Finally, as expected, high ICC produced less biased results compared to medium ICC conditions. PMID:29795827

Logistic Mixed Models to Investigate Implicit and Explicit Belief Tracking

PubMed Central

Lages, Martin; Scheel, Anne

2016-01-01

We investigated the proposition of a two-systems Theory of Mind in adults’ belief tracking. A sample of N = 45 participants predicted the choice of one of two opponent players after observing several rounds in an animated card game. Three matches of this card game were played and initial gaze direction on target and subsequent choice predictions were recorded for each belief task and participant. We conducted logistic regressions with mixed effects on the binary data and developed Bayesian logistic mixed models to infer implicit and explicit mentalizing in true belief and false belief tasks. Although logistic regressions with mixed effects predicted the data well a Bayesian logistic mixed model with latent task- and subject-specific parameters gave a better account of the data. As expected explicit choice predictions suggested a clear understanding of true and false beliefs (TB/FB). Surprisingly, however, model parameters for initial gaze direction also indicated belief tracking. We discuss why task-specific parameters for initial gaze directions are different from choice predictions yet reflect second-order perspective taking. PMID:27853440

Expectant management of veterans with early-stage prostate cancer.

PubMed

Filson, Christopher P; Shelton, Jeremy B; Tan, Hung-Jui; Kwan, Lorna; Skolarus, Ted A; Saigal, Christopher S; Litwin, Mark S

2016-02-15

For certain men with low-risk prostate cancer, aggressive treatment results in marginal survival benefits while exposing them to urinary and sexual side effects. Nevertheless, expectant management has been underused. In the current study, the authors evaluated the association between various factors and expectant management use among veterans diagnosed with prostate cancer. The authors identified men diagnosed with prostate cancer in 2008. The outcome of interest was use of expectant management, based on documentation captured through an in-depth chart review. Multivariable regression models were fit to examine associations between use of expectant management and patient demographics, cancer severity, and facility characteristics. The authors assessed variation across 21 tertiary care regions and 52 facilities by generating predicted probabilities for receipt of expectant management. Expectant management was more common among patients aged ≥75 years (40% vs 27% for those aged < 55 years; odds ratio, 2.57) and those with low-risk tumors (49% vs 20% for patients with high-risk tumors; odds ratio, 5.35). There was no association noted between patient comorbidity and receipt of expectant management (P = .90). There were also no associations found between facility factors and use of expectant management (all P>.05). Among ideal candidates for expectant management, receipt of expectant management varied considerably across individual facilities (0%-85%; P<.001). Patient age and tumor risk were found to be more strongly associated with use of expectant management than patient comorbidity. Although use of expectant management appears broadly appropriate, there was variation in expectant management noted between hospitals that was apparently not attributable to facility factors. Research determining the basis of this variation, with a focus on providers, will be critical to help optimize prostate cancer treatment for veterans. © 2015 American Cancer Society.