Testing adaptive toolbox models: a Bayesian hierarchical approach.

PubMed

Scheibehenne, Benjamin; Rieskamp, Jörg; Wagenmakers, Eric-Jan

2013-01-01

Many theories of human cognition postulate that people are equipped with a repertoire of strategies to solve the tasks they face. This theoretical framework of a cognitive toolbox provides a plausible account of intra- and interindividual differences in human behavior. Unfortunately, it is often unclear how to rigorously test the toolbox framework. How can a toolbox model be quantitatively specified? How can the number of toolbox strategies be limited to prevent uncontrolled strategy sprawl? How can a toolbox model be formally tested against alternative theories? The authors show how these challenges can be met by using Bayesian inference techniques. By means of parameter recovery simulations and the analysis of empirical data across a variety of domains (i.e., judgment and decision making, children's cognitive development, function learning, and perceptual categorization), the authors illustrate how Bayesian inference techniques allow toolbox models to be quantitatively specified, strategy sprawl to be contained, and toolbox models to be rigorously tested against competing theories. The authors demonstrate that their approach applies at the individual level but can also be generalized to the group level with hierarchical Bayesian procedures. The suggested Bayesian inference techniques represent a theoretical and methodological advancement for toolbox theories of cognition and behavior.

Hierarchical Bayesian Modeling of Fluid-Induced Seismicity

NASA Astrophysics Data System (ADS)

Broccardo, M.; Mignan, A.; Wiemer, S.; Stojadinovic, B.; Giardini, D.

2017-11-01

In this study, we present a Bayesian hierarchical framework to model fluid-induced seismicity. The framework is based on a nonhomogeneous Poisson process with a fluid-induced seismicity rate proportional to the rate of injected fluid. The fluid-induced seismicity rate model depends upon a set of physically meaningful parameters and has been validated for six fluid-induced case studies. In line with the vision of hierarchical Bayesian modeling, the rate parameters are considered as random variables. We develop both the Bayesian inference and updating rules, which are used to develop a probabilistic forecasting model. We tested the Basel 2006 fluid-induced seismic case study to prove that the hierarchical Bayesian model offers a suitable framework to coherently encode both epistemic uncertainty and aleatory variability. Moreover, it provides a robust and consistent short-term seismic forecasting model suitable for online risk quantification and mitigation.

A Bayesian Hierarchical Modeling Approach to Predicting Flow in Ungauged Basins

EPA Science Inventory

Recent innovative approaches to identifying and applying regression-based relationships between land use patterns (such as increasing impervious surface area and decreasing vegetative cover) and rainfall-runoff model parameters represent novel and promising improvements to predic...

A spectral-spatial-dynamic hierarchical Bayesian (SSD-HB) model for estimating soybean yield

NASA Astrophysics Data System (ADS)

Kazama, Yoriko; Kujirai, Toshihiro

2014-10-01

A method called a "spectral-spatial-dynamic hierarchical-Bayesian (SSD-HB) model," which can deal with many parameters (such as spectral and weather information all together) by reducing the occurrence of multicollinearity, is proposed. Experiments conducted on soybean yields in Brazil fields with a RapidEye satellite image indicate that the proposed SSD-HB model can predict soybean yield with a higher degree of accuracy than other estimation methods commonly used in remote-sensing applications. In the case of the SSD-HB model, the mean absolute error between estimated yield of the target area and actual yield is 0.28 t/ha, compared to 0.34 t/ha when conventional PLS regression was applied, showing the potential effectiveness of the proposed model.

When mechanism matters: Bayesian forecasting using models of ecological diffusion

USGS Publications Warehouse

Hefley, Trevor J.; Hooten, Mevin B.; Russell, Robin E.; Walsh, Daniel P.; Powell, James A.

2017-01-01

Ecological diffusion is a theory that can be used to understand and forecast spatio-temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white-tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression-based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.

Hierarchical Bayesian sparse image reconstruction with application to MRFM.

PubMed

Dobigeon, Nicolas; Hero, Alfred O; Tourneret, Jean-Yves

2009-09-01

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument.

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.

Relating Memory To Functional Performance In Normal Aging to Dementia Using Hierarchical Bayesian Cognitive Processing Models

PubMed Central

Shankle, William R.; Pooley, James P.; Steyvers, Mark; Hara, Junko; Mangrola, Tushar; Reisberg, Barry; Lee, Michael D.

2012-01-01

Determining how cognition affects functional abilities is important in Alzheimer’s disease and related disorders (ADRD). 280 patients (normal or ADRD) received a total of 1,514 assessments using the Functional Assessment Staging Test (FAST) procedure and the MCI Screen (MCIS). A hierarchical Bayesian cognitive processing (HBCP) model was created by embedding a signal detection theory (SDT) model of the MCIS delayed recognition memory task into a hierarchical Bayesian framework. The SDT model used latent parameters of discriminability (memory process) and response bias (executive function) to predict, simultaneously, recognition memory performance for each patient and each FAST severity group. The observed recognition memory data did not distinguish the six FAST severity stages, but the latent parameters completely separated them. The latent parameters were also used successfully to transform the ordinal FAST measure into a continuous measure reflecting the underlying continuum of functional severity. HBCP models applied to recognition memory data from clinical practice settings accurately translated a latent measure of cognition to a continuous measure of functional severity for both individuals and FAST groups. Such a translation links two levels of brain information processing, and may enable more accurate correlations with other levels, such as those characterized by biomarkers. PMID:22407225

Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring.

PubMed

Carroll, Carlos; Johnson, Devin S; Dunk, Jeffrey R; Zielinski, William J

2010-12-01

Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data's spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and invertebrate taxa of conservation concern (Church's sideband snails [Monadenia churchi], red tree voles [Arborimus longicaudus], and Pacific fishers [Martes pennanti pacifica]) that provide examples of a range of distributional extents and dispersal abilities. We used presence-absence data derived from regional monitoring programs to develop models with both landscape and site-level environmental covariates. We used Markov chain Monte Carlo algorithms and a conditional autoregressive or intrinsic conditional autoregressive model framework to fit spatial models. The fit of Bayesian spatial models was between 35 and 55% better than the fit of nonspatial analogue models. Bayesian spatial models outperformed analogous models developed with maximum entropy (Maxent) methods. Although the best spatial and nonspatial models included similar environmental variables, spatial models provided estimates of residual spatial effects that suggested how ecological processes might structure distribution patterns. Spatial models built from presence-absence data improved fit most for localized endemic species with ranges constrained by poorly known biogeographic factors and for widely distributed species suspected to be strongly affected by unmeasured environmental variables or population processes. By treating spatial effects as a variable of interest rather than a nuisance, hierarchical Bayesian spatial models, especially when they are based on a common broad-scale spatial lattice (here the national Forest Inventory and Analysis grid of 24 km(2) hexagons), can increase the relevance of habitat models to multispecies conservation planning. Journal compilation © 2010 Society for Conservation Biology. No claim to original US government works.

Probabilistic Inference: Task Dependency and Individual Differences of Probability Weighting Revealed by Hierarchical Bayesian Modeling

PubMed Central

Boos, Moritz; Seer, Caroline; Lange, Florian; Kopp, Bruno

2016-01-01

Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modeling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities) by two (likelihoods) design. Five computational models of cognitive processes were compared with the observed behavior. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted) S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model's success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modeling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modeling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision. PMID:27303323

Multi-subject hierarchical inverse covariance modelling improves estimation of functional brain networks.

PubMed

Colclough, Giles L; Woolrich, Mark W; Harrison, Samuel J; Rojas López, Pedro A; Valdes-Sosa, Pedro A; Smith, Stephen M

2018-05-07

A Bayesian model for sparse, hierarchical, inver-covariance estimation is presented, and applied to multi-subject functional connectivity estimation in the human brain. It enables simultaneous inference of the strength of connectivity between brain regions at both subject and population level, and is applicable to fMRI, MEG and EEG data. Two versions of the model can encourage sparse connectivity, either using continuous priors to suppress irrelevant connections, or using an explicit description of the network structure to estimate the connection probability between each pair of regions. A large evaluation of this model, and thirteen methods that represent the state of the art of inverse covariance modelling, is conducted using both simulated and resting-state functional imaging datasets. Our novel Bayesian approach has similar performance to the best extant alternative, Ng et al.'s Sparse Group Gaussian Graphical Model algorithm, which also is based on a hierarchical structure. Using data from the Human Connectome Project, we show that these hierarchical models are able to reduce the measurement error in MEG beta-band functional networks by 10%, producing concomitant increases in estimates of the genetic influence on functional connectivity. Copyright © 2018. Published by Elsevier Inc.

Environmental Factors Affecting Brook Trout Occurrence in Headwater Stream Segments

Treesearch

Yoichiro Kanno; Benjamin H. Letcher; Ana L. Rosner; Kyle P. O' Neil; Keith H. Nislow

2015-01-01

We analyzed the associations of catchment-scale and riparian-scale environmental factors with occurrence of Brook Trout Salvelinus fontinalis in Connecticut headwater stream segments with catchment areas of 15 < km2. A hierarchical Bayesian approach was applied to a statewide stream survey data set, in which Brook...

Estimating effectiveness in HIV prevention trials with a Bayesian hierarchical compound Poisson frailty model

PubMed Central

Coley, Rebecca Yates; Browna, Elizabeth R.

2016-01-01

Inconsistent results in recent HIV prevention trials of pre-exposure prophylactic interventions may be due to heterogeneity in risk among study participants. Intervention effectiveness is most commonly estimated with the Cox model, which compares event times between populations. When heterogeneity is present, this population-level measure underestimates intervention effectiveness for individuals who are at risk. We propose a likelihood-based Bayesian hierarchical model that estimates the individual-level effectiveness of candidate interventions by accounting for heterogeneity in risk with a compound Poisson-distributed frailty term. This model reflects the mechanisms of HIV risk and allows that some participants are not exposed to HIV and, therefore, have no risk of seroconversion during the study. We assess model performance via simulation and apply the model to data from an HIV prevention trial. PMID:26869051

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 Models for Astrophysical Data Using R, JAGS, Python, and Stan

NASA Astrophysics Data System (ADS)

Hilbe, Joseph M.; de Souza, Rafael S.; Ishida, Emille E. O.

2017-05-01

This comprehensive guide to Bayesian methods in astronomy enables hands-on work by supplying complete R, JAGS, Python, and Stan code, to use directly or to adapt. It begins by examining the normal model from both frequentist and Bayesian perspectives and then progresses to a full range of Bayesian generalized linear and mixed or hierarchical models, as well as additional types of models such as ABC and INLA. The book provides code that is largely unavailable elsewhere and includes details on interpreting and evaluating Bayesian models. Initial discussions offer models in synthetic form so that readers can easily adapt them to their own data; later the models are applied to real astronomical data. The consistent focus is on hands-on modeling, analysis of data, and interpretations that address scientific questions. A must-have for astronomers, its concrete approach will also be attractive to researchers in the sciences more generally.

Reuse, Recycle, Reweigh: Combating Influenza through Efficient Sequential Bayesian Computation for Massive Data.

PubMed

Tom, Jennifer A; Sinsheimer, Janet S; Suchard, Marc A

Massive datasets in the gigabyte and terabyte range combined with the availability of increasingly sophisticated statistical tools yield analyses at the boundary of what is computationally feasible. Compromising in the face of this computational burden by partitioning the dataset into more tractable sizes results in stratified analyses, removed from the context that justified the initial data collection. In a Bayesian framework, these stratified analyses generate intermediate realizations, often compared using point estimates that fail to account for the variability within and correlation between the distributions these realizations approximate. However, although the initial concession to stratify generally precludes the more sensible analysis using a single joint hierarchical model, we can circumvent this outcome and capitalize on the intermediate realizations by extending the dynamic iterative reweighting MCMC algorithm. In doing so, we reuse the available realizations by reweighting them with importance weights, recycling them into a now tractable joint hierarchical model. We apply this technique to intermediate realizations generated from stratified analyses of 687 influenza A genomes spanning 13 years allowing us to revisit hypotheses regarding the evolutionary history of influenza within a hierarchical statistical framework.

Reuse, Recycle, Reweigh: Combating Influenza through Efficient Sequential Bayesian Computation for Massive Data

PubMed Central

Tom, Jennifer A.; Sinsheimer, Janet S.; Suchard, Marc A.

2015-01-01

Massive datasets in the gigabyte and terabyte range combined with the availability of increasingly sophisticated statistical tools yield analyses at the boundary of what is computationally feasible. Compromising in the face of this computational burden by partitioning the dataset into more tractable sizes results in stratified analyses, removed from the context that justified the initial data collection. In a Bayesian framework, these stratified analyses generate intermediate realizations, often compared using point estimates that fail to account for the variability within and correlation between the distributions these realizations approximate. However, although the initial concession to stratify generally precludes the more sensible analysis using a single joint hierarchical model, we can circumvent this outcome and capitalize on the intermediate realizations by extending the dynamic iterative reweighting MCMC algorithm. In doing so, we reuse the available realizations by reweighting them with importance weights, recycling them into a now tractable joint hierarchical model. We apply this technique to intermediate realizations generated from stratified analyses of 687 influenza A genomes spanning 13 years allowing us to revisit hypotheses regarding the evolutionary history of influenza within a hierarchical statistical framework. PMID:26681992

A multilevel model of the impact of farm-level best management practices on phosphorus runoff

USDA-ARS?s Scientific Manuscript database

Multilevel or hierarchical models have been applied for a number of years in the social sciences but only relatively recently in the environmental sciences. These models can be developed in either a frequentist or Bayesian context and have similarities to other methods such as empirical Bayes analys...

CONTENDING WITH SPACE-TIME INTERACTION IN THE SPATIAL PREDICTION OF POLLUTION: VANCOUVER'S HOURLY AMBIENT PM 10 FIELD

EPA Science Inventory

In this article we describe an approach for predicting average hourly concentrations of ambient PM10 in Vancouver. We know our solution also applies to hourly ozone fields and believe it may be quite generally applicable. We use a hierarchal Bayesian approach. At the primary ...

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.

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.

Estimation and Application of Ecological Memory Functions in Time and Space

NASA Astrophysics Data System (ADS)

Itter, M.; Finley, A. O.; Dawson, A.

2017-12-01

A common goal in quantitative ecology is the estimation or prediction of ecological processes as a function of explanatory variables (or covariates). Frequently, the ecological process of interest and associated covariates vary in time, space, or both. Theory indicates many ecological processes exhibit memory to local, past conditions. Despite such theoretical understanding, few methods exist to integrate observations from the recent past or within a local neighborhood as drivers of these processes. We build upon recent methodological advances in ecology and spatial statistics to develop a Bayesian hierarchical framework to estimate so-called ecological memory functions; that is, weight-generating functions that specify the relative importance of local, past covariate observations to ecological processes. Memory functions are estimated using a set of basis functions in time and/or space, allowing for flexible ecological memory based on a reduced set of parameters. Ecological memory functions are entirely data driven under the Bayesian hierarchical framework—no a priori assumptions are made regarding functional forms. Memory function uncertainty follows directly from posterior distributions for model parameters allowing for tractable propagation of error to predictions of ecological processes. We apply the model framework to simulated spatio-temporal datasets generated using memory functions of varying complexity. The framework is also applied to estimate the ecological memory of annual boreal forest growth to local, past water availability. Consistent with ecological understanding of boreal forest growth dynamics, memory to past water availability peaks in the year previous to growth and slowly decays to zero in five to eight years. The Bayesian hierarchical framework has applicability to a broad range of ecosystems and processes allowing for increased understanding of ecosystem responses to local and past conditions and improved prediction of ecological processes.

Hierarchical Bayesian spatial models for alcohol availability, drug "hot spots" and violent crime.

PubMed

Zhu, Li; Gorman, Dennis M; Horel, Scott

2006-12-07

Ecologic studies have shown a relationship between alcohol outlet densities, illicit drug use and violence. The present study examined this relationship in the City of Houston, Texas, using a sample of 439 census tracts. Neighborhood sociostructural covariates, alcohol outlet density, drug crime density and violent crime data were collected for the year 2000, and analyzed using hierarchical Bayesian models. Model selection was accomplished by applying the Deviance Information Criterion. The counts of violent crime in each census tract were modelled as having a conditional Poisson distribution. Four neighbourhood explanatory variables were identified using principal component analysis. The best fitted model was selected as the one considering both unstructured and spatial dependence random effects. The results showed that drug-law violation explained a greater amount of variance in violent crime rates than alcohol outlet densities. The relative risk for drug-law violation was 2.49 and that for alcohol outlet density was 1.16. Of the neighbourhood sociostructural covariates, males of age 15 to 24 showed an effect on violence, with a 16% decrease in relative risk for each increase the size of its standard deviation. Both unstructured heterogeneity random effect and spatial dependence need to be included in the model. The analysis presented suggests that activity around illicit drug markets is more strongly associated with violent crime than is alcohol outlet density. Unique among the ecological studies in this field, the present study not only shows the direction and magnitude of impact of neighbourhood sociostructural covariates as well as alcohol and illicit drug activities in a neighbourhood, it also reveals the importance of applying hierarchical Bayesian models in this research field as both spatial dependence and heterogeneity random effects need to be considered simultaneously.

Reconciling multiple data sources to improve accuracy of large-scale prediction of forest disease incidence

USGS Publications Warehouse

Hanks, E.M.; Hooten, M.B.; Baker, F.A.

2011-01-01

Ecological spatial data often come from multiple sources, varying in extent and accuracy. We describe a general approach to reconciling such data sets through the use of the Bayesian hierarchical framework. This approach provides a way for the data sets to borrow strength from one another while allowing for inference on the underlying ecological process. We apply this approach to study the incidence of eastern spruce dwarf mistletoe (Arceuthobium pusillum) in Minnesota black spruce (Picea mariana). A Minnesota Department of Natural Resources operational inventory of black spruce stands in northern Minnesota found mistletoe in 11% of surveyed stands, while a small, specific-pest survey found mistletoe in 56% of the surveyed stands. We reconcile these two surveys within a Bayesian hierarchical framework and predict that 35-59% of black spruce stands in northern Minnesota are infested with dwarf mistletoe. ?? 2011 by the Ecological Society of America.

Hierarchical Bayesian Model (HBM) - Derived Estimates of Air Quality for 2007: Annual Report

EPA Science Inventory

This report describes EPA's Hierarchical Bayesian model generated (HBM) estimates of ozone (O₃) and fine particulate matter (PM_2.5 particles with aerodynamic diameter < 2.5 microns)concentrations throughout the continental United States during the 2007 calen...

Hierarchical modeling and inference in ecology: The analysis of data from populations, metapopulations and communities

USGS Publications Warehouse

Royle, J. Andrew; Dorazio, Robert M.

2008-01-01

A guide to data collection, modeling and inference strategies for biological survey data using Bayesian and classical statistical methods. This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical models, with a strict focus on the use of probability models and parametric inference. Hierarchical models represent a paradigm shift in the application of statistics to ecological inference problems because they combine explicit models of ecological system structure or dynamics with models of how ecological systems are observed. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community, and metacommunity systems. The book provides the first synthetic treatment of many recent methodological advances in ecological modeling and unifies disparate methods and procedures. The authors apply principles of hierarchical modeling to ecological problems, including * occurrence or occupancy models for estimating species distribution * abundance models based on many sampling protocols, including distance sampling * capture-recapture models with individual effects * spatial capture-recapture models based on camera trapping and related methods * population and metapopulation dynamic models * models of biodiversity, community structure and dynamics.

Bayesian hierarchical models for cost-effectiveness analyses that use data from cluster randomized trials.

PubMed

Grieve, Richard; Nixon, Richard; Thompson, Simon G

2010-01-01

Cost-effectiveness analyses (CEA) may be undertaken alongside cluster randomized trials (CRTs) where randomization is at the level of the cluster (for example, the hospital or primary care provider) rather than the individual. Costs (and outcomes) within clusters may be correlated so that the assumption made by standard bivariate regression models, that observations are independent, is incorrect. This study develops a flexible modeling framework to acknowledge the clustering in CEA that use CRTs. The authors extend previous Bayesian bivariate models for CEA of multicenter trials to recognize the specific form of clustering in CRTs. They develop new Bayesian hierarchical models (BHMs) that allow mean costs and outcomes, and also variances, to differ across clusters. They illustrate how each model can be applied using data from a large (1732 cases, 70 primary care providers) CRT evaluating alternative interventions for reducing postnatal depression. The analyses compare cost-effectiveness estimates from BHMs with standard bivariate regression models that ignore the data hierarchy. The BHMs show high levels of cost heterogeneity across clusters (intracluster correlation coefficient, 0.17). Compared with standard regression models, the BHMs yield substantially increased uncertainty surrounding the cost-effectiveness estimates, and altered point estimates. The authors conclude that ignoring clustering can lead to incorrect inferences. The BHMs that they present offer a flexible modeling framework that can be applied more generally to CEA that use CRTs.

Hierarchical Bayesian Models of Subtask Learning

ERIC Educational Resources Information Center

Anglim, Jeromy; Wynton, Sarah K. A.

2015-01-01

The current study used Bayesian hierarchical methods to challenge and extend previous work on subtask learning consistency. A general model of individual-level subtask learning was proposed focusing on power and exponential functions with constraints to test for inconsistency. To study subtask learning, we developed a novel computer-based booking…

Hierarchical Bayesian Model (HBM)-Derived Estimates of Air Quality for 2004 - Annual Report

EPA Science Inventory

This report describes EPA's Hierarchical Bayesian model-generated (HBM) estimates of O₃ and PM_2.5 concentrations throughout the continental United States during the 2004 calendar year. HBM estimates provide the spatial and temporal variance of O₃ ...

Hierarchical Bayesian Model (HBM) - Derived Estimates of Air Quality for 2008: Annual Report

EPA Science Inventory

This report describes EPA’s Hierarchical Bayesian model generated (HBM) estimates of ozone (O₃) and fine particulate matter (PM_2.5, particles with aerodynamic diameter < 2.5 microns) concentrations throughout the continental United States during the 2007 ca...

An introduction to Bayesian statistics in health psychology.

PubMed

Depaoli, Sarah; Rus, Holly M; Clifton, James P; van de Schoot, Rens; Tiemensma, Jitske

2017-09-01

The aim of the current article is to provide a brief introduction to Bayesian statistics within the field of health psychology. Bayesian methods are increasing in prevalence in applied fields, and they have been shown in simulation research to improve the estimation accuracy of structural equation models, latent growth curve (and mixture) models, and hierarchical linear models. Likewise, Bayesian methods can be used with small sample sizes since they do not rely on large sample theory. In this article, we discuss several important components of Bayesian statistics as they relate to health-based inquiries. We discuss the incorporation and impact of prior knowledge into the estimation process and the different components of the analysis that should be reported in an article. We present an example implementing Bayesian estimation in the context of blood pressure changes after participants experienced an acute stressor. We conclude with final thoughts on the implementation of Bayesian statistics in health psychology, including suggestions for reviewing Bayesian manuscripts and grant proposals. We have also included an extensive amount of online supplementary material to complement the content presented here, including Bayesian examples using many different software programmes and an extensive sensitivity analysis examining the impact of priors.

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.

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.

Understanding seasonal variability of uncertainty in hydrological prediction

NASA Astrophysics Data System (ADS)

Li, M.; Wang, Q. J.

2012-04-01

Understanding uncertainty in hydrological prediction can be highly valuable for improving the reliability of streamflow prediction. In this study, a monthly water balance model, WAPABA, in a Bayesian joint probability with error models are presented to investigate the seasonal dependency of prediction error structure. A seasonal invariant error model, analogous to traditional time series analysis, uses constant parameters for model error and account for no seasonal variations. In contrast, a seasonal variant error model uses a different set of parameters for bias, variance and autocorrelation for each individual calendar month. Potential connection amongst model parameters from similar months is not considered within the seasonal variant model and could result in over-fitting and over-parameterization. A hierarchical error model further applies some distributional restrictions on model parameters within a Bayesian hierarchical framework. An iterative algorithm is implemented to expedite the maximum a posterior (MAP) estimation of a hierarchical error model. Three error models are applied to forecasting streamflow at a catchment in southeast Australia in a cross-validation analysis. This study also presents a number of statistical measures and graphical tools to compare the predictive skills of different error models. From probability integral transform histograms and other diagnostic graphs, the hierarchical error model conforms better to reliability when compared to the seasonal invariant error model. The hierarchical error model also generally provides the most accurate mean prediction in terms of the Nash-Sutcliffe model efficiency coefficient and the best probabilistic prediction in terms of the continuous ranked probability score (CRPS). The model parameters of the seasonal variant error model are very sensitive to each cross validation, while the hierarchical error model produces much more robust and reliable model parameters. Furthermore, the result of the hierarchical error model shows that most of model parameters are not seasonal variant except for error bias. The seasonal variant error model is likely to use more parameters than necessary to maximize the posterior likelihood. The model flexibility and robustness indicates that the hierarchical error model has great potential for future streamflow predictions.

Competition alters tree growth responses to climate at individual and stand scales

Treesearch

Kevin R. Ford; Ian K. Breckheimer; Jerry F. Franklin; James A. Freund; Steve J. Kroiss; Andrew J. Larson; Elinore J. Theobald; Janneke HilleRisLambers

2017-01-01

Understanding how climate affects tree growth is essential for assessing climate change impacts on forests but can be confounded by effects of competition, which strongly influences tree responses to climate. We characterized the joint influences of tree size, competition, and climate on diameter growth using hierarchical Bayesian methods applied to permanent sample...

Correlation Between Hierarchical Bayesian and Aerosol Optical Depth PM2.5 Data and Respiratory-Cardiovascular Chronic Diseases

EPA Science Inventory

Tools to estimate PM2.5 mass have expanded in recent years, and now include: 1) stationary monitor readings, 2) Community Multi-Scale Air Quality (CMAQ) model estimates, 3) Hierarchical Bayesian (HB) estimates from combined stationary monitor readings and CMAQ model output; and, ...

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 hierarchical model for discrete choice data in health care.

PubMed

Antonio, Anna Liza M; Weiss, Robert E; Saigal, Christopher S; Dahan, Ely; Crespi, Catherine M

2017-01-01

In discrete choice experiments, patients are presented with sets of health states described by various attributes and asked to make choices from among them. Discrete choice experiments allow health care researchers to study the preferences of individual patients by eliciting trade-offs between different aspects of health-related quality of life. However, many discrete choice experiments yield data with incomplete ranking information and sparsity due to the limited number of choice sets presented to each patient, making it challenging to estimate patient preferences. Moreover, methods to identify outliers in discrete choice data are lacking. We develop a Bayesian hierarchical random effects rank-ordered multinomial logit model for discrete choice data. Missing ranks are accounted for by marginalizing over all possible permutations of unranked alternatives to estimate individual patient preferences, which are modeled as a function of patient covariates. We provide a Bayesian version of relative attribute importance, and adapt the use of the conditional predictive ordinate to identify outlying choice sets and outlying individuals with unusual preferences compared to the population. The model is applied to data from a study using a discrete choice experiment to estimate individual patient preferences for health states related to prostate cancer treatment.

Bayesian cross-validation for model evaluation and selection, with application to the North American Breeding Bird Survey

USGS Publications Warehouse

Link, William; Sauer, John R.

2016-01-01

The analysis of ecological data has changed in two important ways over the last 15 years. The development and easy availability of Bayesian computational methods has allowed and encouraged the fitting of complex hierarchical models. At the same time, there has been increasing emphasis on acknowledging and accounting for model uncertainty. Unfortunately, the ability to fit complex models has outstripped the development of tools for model selection and model evaluation: familiar model selection tools such as Akaike's information criterion and the deviance information criterion are widely known to be inadequate for hierarchical models. In addition, little attention has been paid to the evaluation of model adequacy in context of hierarchical modeling, i.e., to the evaluation of fit for a single model. In this paper, we describe Bayesian cross-validation, which provides tools for model selection and evaluation. We describe the Bayesian predictive information criterion and a Bayesian approximation to the BPIC known as the Watanabe-Akaike information criterion. We illustrate the use of these tools for model selection, and the use of Bayesian cross-validation as a tool for model evaluation, using three large data sets from the North American Breeding Bird Survey.

Clarifying the Hubble constant tension with a Bayesian hierarchical model of the local distance ladder

NASA Astrophysics Data System (ADS)

Feeney, Stephen M.; Mortlock, Daniel J.; Dalmasso, Niccolò

2018-05-01

Estimates of the Hubble constant, H0, from the local distance ladder and from the cosmic microwave background (CMB) are discrepant at the ˜3σ level, indicating a potential issue with the standard Λ cold dark matter (ΛCDM) cosmology. A probabilistic (i.e. Bayesian) interpretation of this tension requires a model comparison calculation, which in turn depends strongly on the tails of the H0 likelihoods. Evaluating the tails of the local H0 likelihood requires the use of non-Gaussian distributions to faithfully represent anchor likelihoods and outliers, and simultaneous fitting of the complete distance-ladder data set to ensure correct uncertainty propagation. We have hence developed a Bayesian hierarchical model of the full distance ladder that does not rely on Gaussian distributions and allows outliers to be modelled without arbitrary data cuts. Marginalizing over the full ˜3000-parameter joint posterior distribution, we find H0 = (72.72 ± 1.67) km s-1 Mpc-1 when applied to the outlier-cleaned Riess et al. data, and (73.15 ± 1.78) km s-1 Mpc-1 with supernova outliers reintroduced (the pre-cut Cepheid data set is not available). Using our precise evaluation of the tails of the H0 likelihood, we apply Bayesian model comparison to assess the evidence for deviation from ΛCDM given the distance-ladder and CMB data. The odds against ΛCDM are at worst ˜10:1 when considering the Planck 2015 XIII data, regardless of outlier treatment, considerably less dramatic than naïvely implied by the 2.8σ discrepancy. These odds become ˜60:1 when an approximation to the more-discrepant Planck Intermediate XLVI likelihood is included.

Efficient hierarchical trans-dimensional Bayesian inversion of magnetotelluric data

NASA Astrophysics Data System (ADS)

Xiang, Enming; Guo, Rongwen; Dosso, Stan E.; Liu, Jianxin; Dong, Hao; Ren, Zhengyong

2018-06-01

This paper develops an efficient hierarchical trans-dimensional (trans-D) Bayesian algorithm to invert magnetotelluric (MT) data for subsurface geoelectrical structure, with unknown geophysical model parameterization (the number of conductivity-layer interfaces) and data-error models parameterized by an auto-regressive (AR) process to account for potential error correlations. The reversible-jump Markov-chain Monte Carlo algorithm, which adds/removes interfaces and AR parameters in birth/death steps, is applied to sample the trans-D posterior probability density for model parameterization, model parameters, error variance and AR parameters, accounting for the uncertainties of model dimension and data-error statistics in the uncertainty estimates of the conductivity profile. To provide efficient sampling over the multiple subspaces of different dimensions, advanced proposal schemes are applied. Parameter perturbations are carried out in principal-component space, defined by eigen-decomposition of the unit-lag model covariance matrix, to minimize the effect of inter-parameter correlations and provide effective perturbation directions and length scales. Parameters of new layers in birth steps are proposed from the prior, instead of focused distributions centred at existing values, to improve birth acceptance rates. Parallel tempering, based on a series of parallel interacting Markov chains with successively relaxed likelihoods, is applied to improve chain mixing over model dimensions. The trans-D inversion is applied in a simulation study to examine the resolution of model structure according to the data information content. The inversion is also applied to a measured MT data set from south-central Australia.

Probabilistic modeling of bifurcations in single-cell gene expression data using a Bayesian mixture of factor analyzers.

PubMed

Campbell, Kieran R; Yau, Christopher

2017-03-15

Modeling bifurcations in single-cell transcriptomics data has become an increasingly popular field of research. Several methods have been proposed to infer bifurcation structure from such data, but all rely on heuristic non-probabilistic inference. Here we propose the first generative, fully probabilistic model for such inference based on a Bayesian hierarchical mixture of factor analyzers. Our model exhibits competitive performance on large datasets despite implementing full Markov-Chain Monte Carlo sampling, and its unique hierarchical prior structure enables automatic determination of genes driving the bifurcation process. We additionally propose an Empirical-Bayes like extension that deals with the high levels of zero-inflation in single-cell RNA-seq data and quantify when such models are useful. We apply or model to both real and simulated single-cell gene expression data and compare the results to existing pseudotime methods. Finally, we discuss both the merits and weaknesses of such a unified, probabilistic approach in the context practical bioinformatics analyses.

Application of Bayesian networks in a hierarchical structure for environmental risk assessment: a case study of the Gabric Dam, Iran.

PubMed

Malekmohammadi, Bahram; Tayebzadeh Moghadam, Negar

2018-04-13

Environmental risk assessment (ERA) is a commonly used, effective tool applied to reduce adverse effects of environmental risk factors. In this study, ERA was investigated using the Bayesian network (BN) model based on a hierarchical structure of variables in an influence diagram (ID). ID facilitated ranking of the different alternatives under uncertainty that were then used to evaluate comparisons of the different risk factors. BN was used to present a new model for ERA applicable to complicated development projects such as dam construction. The methodology was applied to the Gabric Dam, in southern Iran. The main environmental risk factors in the region, presented by the Gabric Dam, were identified based on the Delphi technique and specific features of the study area. These included the following: flood, water pollution, earthquake, changes in land use, erosion and sedimentation, effects on the population, and ecosensitivity. These risk factors were then categorized based on results from the output decision node of the BN, including expected utility values for risk factors in the decision node. ERA was performed for the Gabric Dam using the analytical hierarchy process (AHP) method to compare results of BN modeling with those of conventional methods. Results determined that a BN-based hierarchical structure to ERA present acceptable and reasonable risk assessment prioritization in proposing suitable solutions to reduce environmental risks and can be used as a powerful decision support system for evaluating environmental risks.

Bayesian hierarchical model of ceftriaxone resistance proportions among Salmonella serotype Heidelberg infections.

PubMed

Gu, Weidong; Medalla, Felicita; Hoekstra, Robert M

2018-02-01

The National Antimicrobial Resistance Monitoring System (NARMS) at the Centers for Disease Control and Prevention tracks resistance among Salmonella infections. The annual number of Salmonella isolates of a particular serotype from states may be small, making direct estimation of resistance proportions unreliable. We developed a Bayesian hierarchical model to improve estimation by borrowing strength from relevant sampling units. We illustrate the models with different specifications of spatio-temporal interaction using 2004-2013 NARMS data for ceftriaxone-resistant Salmonella serotype Heidelberg. Our results show that Bayesian estimates of resistance proportions were smoother than observed values, and the difference between predicted and observed proportions was inversely related to the number of submitted isolates. The model with interaction allowed for tracking of annual changes in resistance proportions at the state level. We demonstrated that Bayesian hierarchical models provide a useful tool to examine spatio-temporal patterns of small sample size such as those found in NARMS. Published by Elsevier Ltd.

Bayesian Mass Estimates of the Milky Way: Including Measurement Uncertainties with Hierarchical Bayes

NASA Astrophysics Data System (ADS)

Eadie, Gwendolyn M.; Springford, Aaron; Harris, William E.

2017-02-01

We present a hierarchical Bayesian method for estimating the total mass and mass profile of the Milky Way Galaxy. The new hierarchical Bayesian approach further improves the framework presented by Eadie et al. and Eadie and Harris and builds upon the preliminary reports by Eadie et al. The method uses a distribution function f({ E },L) to model the Galaxy and kinematic data from satellite objects, such as globular clusters (GCs), to trace the Galaxy’s gravitational potential. A major advantage of the method is that it not only includes complete and incomplete data simultaneously in the analysis, but also incorporates measurement uncertainties in a coherent and meaningful way. We first test the hierarchical Bayesian framework, which includes measurement uncertainties, using the same data and power-law model assumed in Eadie and Harris and find the results are similar but more strongly constrained. Next, we take advantage of the new statistical framework and incorporate all possible GC data, finding a cumulative mass profile with Bayesian credible regions. This profile implies a mass within 125 kpc of 4.8× {10}11{M}⊙ with a 95% Bayesian credible region of (4.0{--}5.8)× {10}11{M}⊙ . Our results also provide estimates of the true specific energies of all the GCs. By comparing these estimated energies to the measured energies of GCs with complete velocity measurements, we observe that (the few) remote tracers with complete measurements may play a large role in determining a total mass estimate of the Galaxy. Thus, our study stresses the need for more remote tracers with complete velocity measurements.

Bayesian hierarchical model for large-scale covariance matrix estimation.

PubMed

Zhu, Dongxiao; Hero, Alfred O

2007-12-01

Many bioinformatics problems implicitly depend on estimating large-scale covariance matrix. The traditional approaches tend to give rise to high variance and low accuracy due to "overfitting." We cast the large-scale covariance matrix estimation problem into the Bayesian hierarchical model framework, and introduce dependency between covariance parameters. We demonstrate the advantages of our approaches over the traditional approaches using simulations and OMICS data analysis.

From least squares to multilevel modeling: A graphical introduction to Bayesian inference

NASA Astrophysics Data System (ADS)

Loredo, Thomas J.

2016-01-01

This tutorial presentation will introduce some of the key ideas and techniques involved in applying Bayesian methods to problems in astrostatistics. The focus will be on the big picture: understanding the foundations (interpreting probability, Bayes's theorem, the law of total probability and marginalization), making connections to traditional methods (propagation of errors, least squares, chi-squared, maximum likelihood, Monte Carlo simulation), and highlighting problems where a Bayesian approach can be particularly powerful (Poisson processes, density estimation and curve fitting with measurement error). The "graphical" component of the title reflects an emphasis on pictorial representations of some of the math, but also on the use of graphical models (multilevel or hierarchical models) for analyzing complex data. Code for some examples from the talk will be available to participants, in Python and in the Stan probabilistic programming language.

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

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.

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.

Risk Assessment for Mobile Systems Through a Multilayered Hierarchical Bayesian Network.

PubMed

Li, Shancang; Tryfonas, Theo; Russell, Gordon; Andriotis, Panagiotis

2016-08-01

Mobile systems are facing a number of application vulnerabilities that can be combined together and utilized to penetrate systems with devastating impact. When assessing the overall security of a mobile system, it is important to assess the security risks posed by each mobile applications (apps), thus gaining a stronger understanding of any vulnerabilities present. This paper aims at developing a three-layer framework that assesses the potential risks which apps introduce within the Android mobile systems. A Bayesian risk graphical model is proposed to evaluate risk propagation in a layered risk architecture. By integrating static analysis, dynamic analysis, and behavior analysis in a hierarchical framework, the risks and their propagation through each layer are well modeled by the Bayesian risk graph, which can quantitatively analyze risks faced to both apps and mobile systems. The proposed hierarchical Bayesian risk graph model offers a novel way to investigate the security risks in mobile environment and enables users and administrators to evaluate the potential risks. This strategy allows to strengthen both app security as well as the security of the entire system.

Application of Multiple Imputation for Missing Values in Three-Way Three-Mode Multi-Environment Trial Data

PubMed Central

Tian, Ting; McLachlan, Geoffrey J.; Dieters, Mark J.; Basford, Kaye E.

2015-01-01

It is a common occurrence in plant breeding programs to observe missing values in three-way three-mode multi-environment trial (MET) data. We proposed modifications of models for estimating missing observations for these data arrays, and developed a novel approach in terms of hierarchical clustering. Multiple imputation (MI) was used in four ways, multiple agglomerative hierarchical clustering, normal distribution model, normal regression model, and predictive mean match. The later three models used both Bayesian analysis and non-Bayesian analysis, while the first approach used a clustering procedure with randomly selected attributes and assigned real values from the nearest neighbour to the one with missing observations. Different proportions of data entries in six complete datasets were randomly selected to be missing and the MI methods were compared based on the efficiency and accuracy of estimating those values. The results indicated that the models using Bayesian analysis had slightly higher accuracy of estimation performance than those using non-Bayesian analysis but they were more time-consuming. However, the novel approach of multiple agglomerative hierarchical clustering demonstrated the overall best performances. PMID:26689369

Application of Multiple Imputation for Missing Values in Three-Way Three-Mode Multi-Environment Trial Data.

PubMed

Tian, Ting; McLachlan, Geoffrey J; Dieters, Mark J; Basford, Kaye E

2015-01-01

It is a common occurrence in plant breeding programs to observe missing values in three-way three-mode multi-environment trial (MET) data. We proposed modifications of models for estimating missing observations for these data arrays, and developed a novel approach in terms of hierarchical clustering. Multiple imputation (MI) was used in four ways, multiple agglomerative hierarchical clustering, normal distribution model, normal regression model, and predictive mean match. The later three models used both Bayesian analysis and non-Bayesian analysis, while the first approach used a clustering procedure with randomly selected attributes and assigned real values from the nearest neighbour to the one with missing observations. Different proportions of data entries in six complete datasets were randomly selected to be missing and the MI methods were compared based on the efficiency and accuracy of estimating those values. The results indicated that the models using Bayesian analysis had slightly higher accuracy of estimation performance than those using non-Bayesian analysis but they were more time-consuming. However, the novel approach of multiple agglomerative hierarchical clustering demonstrated the overall best performances.

Bayesian Hierarchical Classes Analysis

ERIC Educational Resources Information Center

Leenen, Iwin; Van Mechelen, Iven; Gelman, Andrew; De Knop, Stijn

2008-01-01

Hierarchical classes models are models for "N"-way "N"-mode data that represent the association among the "N" modes and simultaneously yield, for each mode, a hierarchical classification of its elements. In this paper we present a stochastic extension of the hierarchical classes model for two-way two-mode binary data. In line with the original…

A hierarchical, ontology-driven Bayesian concept for ubiquitous medical environments--a case study for pulmonary diseases.

PubMed

Maragoudakis, Manolis; Lymberopoulos, Dimitrios; Fakotakis, Nikos; Spiropoulos, Kostas

2008-01-01

The present paper extends work on an existing computer-based Decision Support System (DSS) that aims to provide assistance to physicians as regards to pulmonary diseases. The extension deals with allowing for a hierarchical decomposition of the task, at different levels of domain granularity, using a novel approach, i.e. Hierarchical Bayesian Networks. The proposed framework uses data from various networking appliances such as mobile phones and wireless medical sensors to establish a ubiquitous environment for medical treatment of pulmonary diseases. Domain knowledge is encoded at the upper levels of the hierarchy, thus making the process of generalization easier to accomplish. The experimental results were carried out under the Pulmonary Department, University Regional Hospital Patras, Patras, Greece. They have supported our initial beliefs about the ability of Bayesian networks to provide an effective, yet semantically-oriented, means of prognosis and reasoning under conditions of uncertainty.

Modular analysis of the probabilistic genetic interaction network.

PubMed

Hou, Lin; Wang, Lin; Qian, Minping; Li, Dong; Tang, Chao; Zhu, Yunping; Deng, Minghua; Li, Fangting

2011-03-15

Epistatic Miniarray Profiles (EMAP) has enabled the mapping of large-scale genetic interaction networks; however, the quantitative information gained from EMAP cannot be fully exploited since the data are usually interpreted as a discrete network based on an arbitrary hard threshold. To address such limitations, we adopted a mixture modeling procedure to construct a probabilistic genetic interaction network and then implemented a Bayesian approach to identify densely interacting modules in the probabilistic network. Mixture modeling has been demonstrated as an effective soft-threshold technique of EMAP measures. The Bayesian approach was applied to an EMAP dataset studying the early secretory pathway in Saccharomyces cerevisiae. Twenty-seven modules were identified, and 14 of those were enriched by gold standard functional gene sets. We also conducted a detailed comparison with state-of-the-art algorithms, hierarchical cluster and Markov clustering. The experimental results show that the Bayesian approach outperforms others in efficiently recovering biologically significant modules.

Decentralized cooperative TOA/AOA target tracking for hierarchical wireless sensor networks.

PubMed

Chen, Ying-Chih; Wen, Chih-Yu

2012-11-08

This paper proposes a distributed method for cooperative target tracking in hierarchical wireless sensor networks. The concept of leader-based information processing is conducted to achieve object positioning, considering a cluster-based network topology. Random timers and local information are applied to adaptively select a sub-cluster for the localization task. The proposed energy-efficient tracking algorithm allows each sub-cluster member to locally estimate the target position with a Bayesian filtering framework and a neural networking model, and further performs estimation fusion in the leader node with the covariance intersection algorithm. This paper evaluates the merits and trade-offs of the protocol design towards developing more efficient and practical algorithms for object position estimation.

Hierarchical Bayesian models to assess between- and within-batch variability of pathogen contamination in food.

PubMed

Commeau, Natalie; Cornu, Marie; Albert, Isabelle; Denis, Jean-Baptiste; Parent, Eric

2012-03-01

Assessing within-batch and between-batch variability is of major interest for risk assessors and risk managers in the context of microbiological contamination of food. For example, the ratio between the within-batch variability and the between-batch variability has a large impact on the results of a sampling plan. Here, we designed hierarchical Bayesian models to represent such variability. Compatible priors were built mathematically to obtain sound model comparisons. A numeric criterion is proposed to assess the contamination structure comparing the ability of the models to replicate grouped data at the batch level using a posterior predictive loss approach. Models were applied to two case studies: contamination by Listeria monocytogenes of pork breast used to produce diced bacon and contamination by the same microorganism on cold smoked salmon at the end of the process. In the first case study, a contamination structure clearly exists and is located at the batch level, that is, between batches variability is relatively strong, whereas in the second a structure also exists but is less marked. © 2012 Society for Risk Analysis.

Differential Gene Expression (DEX) and Alternative Splicing Events (ASE) for Temporal Dynamic Processes Using HMMs and Hierarchical Bayesian Modeling Approaches.

PubMed

Oh, Sunghee; Song, Seongho

2017-01-01

In gene expression profile, data analysis pipeline is categorized into four levels, major downstream tasks, i.e., (1) identification of differential expression; (2) clustering co-expression patterns; (3) classification of subtypes of samples; and (4) detection of genetic regulatory networks, are performed posterior to preprocessing procedure such as normalization techniques. To be more specific, temporal dynamic gene expression data has its inherent feature, namely, two neighboring time points (previous and current state) are highly correlated with each other, compared to static expression data which samples are assumed as independent individuals. In this chapter, we demonstrate how HMMs and hierarchical Bayesian modeling methods capture the horizontal time dependency structures in time series expression profiles by focusing on the identification of differential expression. In addition, those differential expression genes and transcript variant isoforms over time detected in core prerequisite steps can be generally further applied in detection of genetic regulatory networks to comprehensively uncover dynamic repertoires in the aspects of system biology as the coupled framework.

A bayesian hierarchical model for classification with selection of functional predictors.

PubMed

Zhu, Hongxiao; Vannucci, Marina; Cox, Dennis D

2010-06-01

In functional data classification, functional observations are often contaminated by various systematic effects, such as random batch effects caused by device artifacts, or fixed effects caused by sample-related factors. These effects may lead to classification bias and thus should not be neglected. Another issue of concern is the selection of functions when predictors consist of multiple functions, some of which may be redundant. The above issues arise in a real data application where we use fluorescence spectroscopy to detect cervical precancer. In this article, we propose a Bayesian hierarchical model that takes into account random batch effects and selects effective functions among multiple functional predictors. Fixed effects or predictors in nonfunctional form are also included in the model. The dimension of the functional data is reduced through orthonormal basis expansion or functional principal components. For posterior sampling, we use a hybrid Metropolis-Hastings/Gibbs sampler, which suffers slow mixing. An evolutionary Monte Carlo algorithm is applied to improve the mixing. Simulation and real data application show that the proposed model provides accurate selection of functional predictors as well as good classification.

Driver injury severity outcome analysis in rural interstate highway crashes: a two-level Bayesian logistic regression interpretation.

PubMed

Chen, Cong; Zhang, Guohui; Liu, Xiaoyue Cathy; Ci, Yusheng; Huang, Helai; Ma, Jianming; Chen, Yanyan; Guan, Hongzhi

2016-12-01

There is a high potential of severe injury outcomes in traffic crashes on rural interstate highways due to the significant amount of high speed traffic on these corridors. Hierarchical Bayesian models are capable of incorporating between-crash variance and within-crash correlations into traffic crash data analysis and are increasingly utilized in traffic crash severity analysis. This paper applies a hierarchical Bayesian logistic model to examine the significant factors at crash and vehicle/driver levels and their heterogeneous impacts on driver injury severity in rural interstate highway crashes. Analysis results indicate that the majority of the total variance is induced by the between-crash variance, showing the appropriateness of the utilized hierarchical modeling approach. Three crash-level variables and six vehicle/driver-level variables are found significant in predicting driver injury severities: road curve, maximum vehicle damage in a crash, number of vehicles in a crash, wet road surface, vehicle type, driver age, driver gender, driver seatbelt use and driver alcohol or drug involvement. Among these variables, road curve, functional and disabled vehicle damage in crash, single-vehicle crashes, female drivers, senior drivers, motorcycles and driver alcohol or drug involvement tend to increase the odds of drivers being incapably injured or killed in rural interstate crashes, while wet road surface, male drivers and driver seatbelt use are more likely to decrease the probability of severe driver injuries. The developed methodology and estimation results provide insightful understanding of the internal mechanism of rural interstate crashes and beneficial references for developing effective countermeasures for rural interstate crash prevention. Copyright © 2016 Elsevier Ltd. All rights reserved.

DM-BLD: differential methylation detection using a hierarchical Bayesian model exploiting local dependency.

PubMed

Wang, Xiao; Gu, Jinghua; Hilakivi-Clarke, Leena; Clarke, Robert; Xuan, Jianhua

2017-01-15

The advent of high-throughput DNA methylation profiling techniques has enabled the possibility of accurate identification of differentially methylated genes for cancer research. The large number of measured loci facilitates whole genome methylation study, yet posing great challenges for differential methylation detection due to the high variability in tumor samples. We have developed a novel probabilistic approach, D: ifferential M: ethylation detection using a hierarchical B: ayesian model exploiting L: ocal D: ependency (DM-BLD), to detect differentially methylated genes based on a Bayesian framework. The DM-BLD approach features a joint model to capture both the local dependency of measured loci and the dependency of methylation change in samples. Specifically, the local dependency is modeled by Leroux conditional autoregressive structure; the dependency of methylation changes is modeled by a discrete Markov random field. A hierarchical Bayesian model is developed to fully take into account the local dependency for differential analysis, in which differential states are embedded as hidden variables. Simulation studies demonstrate that DM-BLD outperforms existing methods for differential methylation detection, particularly when the methylation change is moderate and the variability of methylation in samples is high. DM-BLD has been applied to breast cancer data to identify important methylated genes (such as polycomb target genes and genes involved in transcription factor activity) associated with breast cancer recurrence. A Matlab package of DM-BLD is available at http://www.cbil.ece.vt.edu/software.htm CONTACT: Xuan@vt.eduSupplementary information: Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Inferring on the Intentions of Others by Hierarchical Bayesian Learning

PubMed Central

Diaconescu, Andreea O.; Mathys, Christoph; Weber, Lilian A. E.; Daunizeau, Jean; Kasper, Lars; Lomakina, Ekaterina I.; Fehr, Ernst; Stephan, Klaas E.

2014-01-01

Inferring on others' (potentially time-varying) intentions is a fundamental problem during many social transactions. To investigate the underlying mechanisms, we applied computational modeling to behavioral data from an economic game in which 16 pairs of volunteers (randomly assigned to “player” or “adviser” roles) interacted. The player performed a probabilistic reinforcement learning task, receiving information about a binary lottery from a visual pie chart. The adviser, who received more predictive information, issued an additional recommendation. Critically, the game was structured such that the adviser's incentives to provide helpful or misleading information varied in time. Using a meta-Bayesian modeling framework, we found that the players' behavior was best explained by the deployment of hierarchical learning: they inferred upon the volatility of the advisers' intentions in order to optimize their predictions about the validity of their advice. Beyond learning, volatility estimates also affected the trial-by-trial variability of decisions: participants were more likely to rely on their estimates of advice accuracy for making choices when they believed that the adviser's intentions were presently stable. Finally, our model of the players' inference predicted the players' interpersonal reactivity index (IRI) scores, explicit ratings of the advisers' helpfulness and the advisers' self-reports on their chosen strategy. Overall, our results suggest that humans (i) employ hierarchical generative models to infer on the changing intentions of others, (ii) use volatility estimates to inform decision-making in social interactions, and (iii) integrate estimates of advice accuracy with non-social sources of information. The Bayesian framework presented here can quantify individual differences in these mechanisms from simple behavioral readouts and may prove useful in future clinical studies of maladaptive social cognition. PMID:25187943

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

DTIC Science & Technology

2013-09-30

proof-of-concept results comparing a BHM surface wind ensemble with the increments in the surface momentum flux control vector in a four-dimensional...Surface   Momentum  Flux  Ensembles  from  Summaries  of  BHM  Winds  (Mediterranean)   include  ocean  current  effect   Td...Bayesian Hierarchical Model to provide surface momentum flux ensembles. 3 Figure 2: Domain of interest : squares indicate spatial locations where

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

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.

Comparing hierarchical models via the marginalized deviance information criterion.

PubMed

Quintero, Adrian; Lesaffre, Emmanuel

2018-07-20

Hierarchical models are extensively used in pharmacokinetics and longitudinal studies. When the estimation is performed from a Bayesian approach, model comparison is often based on the deviance information criterion (DIC). In hierarchical models with latent variables, there are several versions of this statistic: the conditional DIC (cDIC) that incorporates the latent variables in the focus of the analysis and the marginalized DIC (mDIC) that integrates them out. Regardless of the asymptotic and coherency difficulties of cDIC, this alternative is usually used in Markov chain Monte Carlo (MCMC) methods for hierarchical models because of practical convenience. The mDIC criterion is more appropriate in most cases but requires integration of the likelihood, which is computationally demanding and not implemented in Bayesian software. Therefore, we consider a method to compute mDIC by generating replicate samples of the latent variables that need to be integrated out. This alternative can be easily conducted from the MCMC output of Bayesian packages and is widely applicable to hierarchical models in general. Additionally, we propose some approximations in order to reduce the computational complexity for large-sample situations. The method is illustrated with simulated data sets and 2 medical studies, evidencing that cDIC may be misleading whilst mDIC appears pertinent. Copyright © 2018 John Wiley & Sons, Ltd.

Bayesian hierarchical Poisson models with a hidden Markov structure for the detection of influenza epidemic outbreaks.

PubMed

Conesa, D; Martínez-Beneito, M A; Amorós, R; López-Quílez, A

2015-04-01

Considerable effort has been devoted to the development of statistical algorithms for the automated monitoring of influenza surveillance data. In this article, we introduce a framework of models for the early detection of the onset of an influenza epidemic which is applicable to different kinds of surveillance data. In particular, the process of the observed cases is modelled via a Bayesian Hierarchical Poisson model in which the intensity parameter is a function of the incidence rate. The key point is to consider this incidence rate as a normal distribution in which both parameters (mean and variance) are modelled differently, depending on whether the system is in an epidemic or non-epidemic phase. To do so, we propose a hidden Markov model in which the transition between both phases is modelled as a function of the epidemic state of the previous week. Different options for modelling the rates are described, including the option of modelling the mean at each phase as autoregressive processes of order 0, 1 or 2. Bayesian inference is carried out to provide the probability of being in an epidemic state at any given moment. The methodology is applied to various influenza data sets. The results indicate that our methods outperform previous approaches in terms of sensitivity, specificity and timeliness. © The Author(s) 2011 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.

An Evaluation of Hierarchical Bayes Estimation for the Two- Parameter Logistic Model.

ERIC Educational Resources Information Center

Kim, Seock-Ho

Hierarchical Bayes procedures for the two-parameter logistic item response model were compared for estimating item parameters. Simulated data sets were analyzed using two different Bayes estimation procedures, the two-stage hierarchical Bayes estimation (HB2) and the marginal Bayesian with known hyperparameters (MB), and marginal maximum…

Bayesian Variable Selection for Hierarchical Gene-Environment and Gene-Gene Interactions

PubMed Central

Liu, Changlu; Ma, Jianzhong; Amos, Christopher I.

2014-01-01

We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions and gene by environment interactions in the same model. Our approach incorporates the natural hierarchical structure between the main effects and interaction effects into a mixture model, such that our methods tend to remove the irrelevant interaction effects more effectively, resulting in more robust and parsimonious models. We consider both strong and weak hierarchical models. For a strong hierarchical model, both of the main effects between interacting factors must be present for the interactions to be considered in the model development, while for a weak hierarchical model, only one of the two main effects is required to be present for the interaction to be evaluated. Our simulation results show that the proposed strong and weak hierarchical mixture models work well in controlling false positive rates and provide a powerful approach for identifying the predisposing effects and interactions in gene-environment interaction studies, in comparison with the naive model that does not impose this hierarchical constraint in most of the scenarios simulated. We illustrated our approach using data for lung cancer and cutaneous melanoma. PMID:25154630

Bayesian X-ray computed tomography using a three-level hierarchical prior model

NASA Astrophysics Data System (ADS)

Wang, Li; Mohammad-Djafari, Ali; Gac, Nicolas

2017-06-01

In recent decades X-ray Computed Tomography (CT) image reconstruction has been largely developed in both medical and industrial domain. In this paper, we propose using the Bayesian inference approach with a new hierarchical prior model. In the proposed model, a generalised Student-t distribution is used to enforce the Haar transformation of images to be sparse. Comparisons with some state of the art methods are presented. It is shown that by using the proposed model, the sparsity of sparse representation of images is enforced, so that edges of images are preserved. Simulation results are also provided to demonstrate the effectiveness of the new hierarchical model for reconstruction with fewer projections.

A Bayesian hierarchical model for mortality data from cluster-sampling household surveys in humanitarian crises.

PubMed

Heudtlass, Peter; Guha-Sapir, Debarati; Speybroeck, Niko

2018-05-31

The crude death rate (CDR) is one of the defining indicators of humanitarian emergencies. When data from vital registration systems are not available, it is common practice to estimate the CDR from household surveys with cluster-sampling design. However, sample sizes are often too small to compare mortality estimates to emergency thresholds, at least in a frequentist framework. Several authors have proposed Bayesian methods for health surveys in humanitarian crises. Here, we develop an approach specifically for mortality data and cluster-sampling surveys. We describe a Bayesian hierarchical Poisson-Gamma mixture model with generic (weakly informative) priors that could be used as default in absence of any specific prior knowledge, and compare Bayesian and frequentist CDR estimates using five different mortality datasets. We provide an interpretation of the Bayesian estimates in the context of an emergency threshold and demonstrate how to interpret parameters at the cluster level and ways in which informative priors can be introduced. With the same set of weakly informative priors, Bayesian CDR estimates are equivalent to frequentist estimates, for all practical purposes. The probability that the CDR surpasses the emergency threshold can be derived directly from the posterior of the mean of the mixing distribution. All observation in the datasets contribute to the estimation of cluster-level estimates, through the hierarchical structure of the model. In a context of sparse data, Bayesian mortality assessments have advantages over frequentist ones already when using only weakly informative priors. More informative priors offer a formal and transparent way of combining new data with existing data and expert knowledge and can help to improve decision-making in humanitarian crises by complementing frequentist estimates.

The Neural Correlates of Hierarchical Predictions for Perceptual Decisions.

PubMed

Weilnhammer, Veith A; Stuke, Heiner; Sterzer, Philipp; Schmack, Katharina

2018-05-23

Sensory information is inherently noisy, sparse, and ambiguous. In contrast, visual experience is usually clear, detailed, and stable. Bayesian theories of perception resolve this discrepancy by assuming that prior knowledge about the causes underlying sensory stimulation actively shapes perceptual decisions. The CNS is believed to entertain a generative model aligned to dynamic changes in the hierarchical states of our volatile sensory environment. Here, we used model-based fMRI to study the neural correlates of the dynamic updating of hierarchically structured predictions in male and female human observers. We devised a crossmodal associative learning task with covertly interspersed ambiguous trials in which participants engaged in hierarchical learning based on changing contingencies between auditory cues and visual targets. By inverting a Bayesian model of perceptual inference, we estimated individual hierarchical predictions, which significantly biased perceptual decisions under ambiguity. Although "high-level" predictions about the cue-target contingency correlated with activity in supramodal regions such as orbitofrontal cortex and hippocampus, dynamic "low-level" predictions about the conditional target probabilities were associated with activity in retinotopic visual cortex. Our results suggest that our CNS updates distinct representations of hierarchical predictions that continuously affect perceptual decisions in a dynamically changing environment. SIGNIFICANCE STATEMENT Bayesian theories posit that our brain entertains a generative model to provide hierarchical predictions regarding the causes of sensory information. Here, we use behavioral modeling and fMRI to study the neural underpinnings of such hierarchical predictions. We show that "high-level" predictions about the strength of dynamic cue-target contingencies during crossmodal associative learning correlate with activity in orbitofrontal cortex and the hippocampus, whereas "low-level" conditional target probabilities were reflected in retinotopic visual cortex. Our findings empirically corroborate theorizations on the role of hierarchical predictions in visual perception and contribute substantially to a longstanding debate on the link between sensory predictions and orbitofrontal or hippocampal activity. Our work fundamentally advances the mechanistic understanding of perceptual inference in the human brain. Copyright © 2018 the authors 0270-6474/18/385008-14$15.00/0.

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.

A Bayesian Approach for Summarizing and Modeling Time-Series Exposure Data with Left Censoring.

PubMed

Houseman, E Andres; Virji, M Abbas

2017-08-01

Direct reading instruments are valuable tools for measuring exposure as they provide real-time measurements for rapid decision making. However, their use is limited to general survey applications in part due to issues related to their performance. Moreover, statistical analysis of real-time data is complicated by autocorrelation among successive measurements, non-stationary time series, and the presence of left-censoring due to limit-of-detection (LOD). A Bayesian framework is proposed that accounts for non-stationary autocorrelation and LOD issues in exposure time-series data in order to model workplace factors that affect exposure and estimate summary statistics for tasks or other covariates of interest. A spline-based approach is used to model non-stationary autocorrelation with relatively few assumptions about autocorrelation structure. Left-censoring is addressed by integrating over the left tail of the distribution. The model is fit using Markov-Chain Monte Carlo within a Bayesian paradigm. The method can flexibly account for hierarchical relationships, random effects and fixed effects of covariates. The method is implemented using the rjags package in R, and is illustrated by applying it to real-time exposure data. Estimates for task means and covariates from the Bayesian model are compared to those from conventional frequentist models including linear regression, mixed-effects, and time-series models with different autocorrelation structures. Simulations studies are also conducted to evaluate method performance. Simulation studies with percent of measurements below the LOD ranging from 0 to 50% showed lowest root mean squared errors for task means and the least biased standard deviations from the Bayesian model compared to the frequentist models across all levels of LOD. In the application, task means from the Bayesian model were similar to means from the frequentist models, while the standard deviations were different. Parameter estimates for covariates were significant in some frequentist models, but in the Bayesian model their credible intervals contained zero; such discrepancies were observed in multiple datasets. Variance components from the Bayesian model reflected substantial autocorrelation, consistent with the frequentist models, except for the auto-regressive moving average model. Plots of means from the Bayesian model showed good fit to the observed data. The proposed Bayesian model provides an approach for modeling non-stationary autocorrelation in a hierarchical modeling framework to estimate task means, standard deviations, quantiles, and parameter estimates for covariates that are less biased and have better performance characteristics than some of the contemporary methods. Published by Oxford University Press on behalf of the British Occupational Hygiene Society 2017.

Bayesian Inference: with ecological applications

USGS Publications Warehouse

Link, William A.; Barker, Richard J.

2010-01-01

This text provides a mathematically rigorous yet accessible and engaging introduction to Bayesian inference with relevant examples that will be of interest to biologists working in the fields of ecology, wildlife management and environmental studies as well as students in advanced undergraduate statistics.. This text opens the door to Bayesian inference, taking advantage of modern computational efficiencies and easily accessible software to evaluate complex hierarchical models.

Model selection and assessment for multi­-species occupancy models

USGS Publications Warehouse

Broms, Kristin M.; Hooten, Mevin B.; Fitzpatrick, Ryan M.

2016-01-01

While multi-species occupancy models (MSOMs) are emerging as a popular method for analyzing biodiversity data, formal checking and validation approaches for this class of models have lagged behind. Concurrent with the rise in application of MSOMs among ecologists, a quiet regime shift is occurring in Bayesian statistics where predictive model comparison approaches are experiencing a resurgence. Unlike single-species occupancy models that use integrated likelihoods, MSOMs are usually couched in a Bayesian framework and contain multiple levels. Standard model checking and selection methods are often unreliable in this setting and there is only limited guidance in the ecological literature for this class of models. We examined several different contemporary Bayesian hierarchical approaches for checking and validating MSOMs and applied these methods to a freshwater aquatic study system in Colorado, USA, to better understand the diversity and distributions of plains fishes. Our findings indicated distinct differences among model selection approaches, with cross-validation techniques performing the best in terms of prediction.

Bayesian Multiscale Modeling of Closed Curves in Point Clouds

PubMed Central

Gu, Kelvin; Pati, Debdeep; Dunson, David B.

2014-01-01

Modeling object boundaries based on image or point cloud data is frequently necessary in medical and scientific applications ranging from detecting tumor contours for targeted radiation therapy, to the classification of organisms based on their structural information. In low-contrast images or sparse and noisy point clouds, there is often insufficient data to recover local segments of the boundary in isolation. Thus, it becomes critical to model the entire boundary in the form of a closed curve. To achieve this, we develop a Bayesian hierarchical model that expresses highly diverse 2D objects in the form of closed curves. The model is based on a novel multiscale deformation process. By relating multiple objects through a hierarchical formulation, we can successfully recover missing boundaries by borrowing structural information from similar objects at the appropriate scale. Furthermore, the model’s latent parameters help interpret the population, indicating dimensions of significant structural variability and also specifying a ‘central curve’ that summarizes the collection. Theoretical properties of our prior are studied in specific cases and efficient Markov chain Monte Carlo methods are developed, evaluated through simulation examples and applied to panorex teeth images for modeling teeth contours and also to a brain tumor contour detection problem. PMID:25544786

AzTEC Survey of the Central Molecular Zone: Modeling Dust SEDs and N-PDF with Hierarchical Bayesian Analysis

NASA Astrophysics Data System (ADS)

Tang, Yuping; Wang, Daniel; Wilson, Grant; Gutermuth, Robert; Heyer, Mark

2018-01-01

We present the AzTEC/LMT survey of dust continuum at 1.1mm on the central ˜ 200pc (CMZ) of our Galaxy. A joint SED analysis of all existing dust continuum surveys on the CMZ is performed, from 160µm to 1.1mm. Our analysis follows a MCMC sampling strategy incorporating the knowledge of PSFs in different maps, which provides unprecedented spacial resolution on distributions of dust temperature, column density and emissivity index. The dense clumps in the CMZ typically show low dust temperature ( 20K), with no significant sign of buried star formation, and a weak evolution of higher emissivity index toward dense peak. A new model is proposed, allowing for varying dust temperature inside a cloud and self-shielding of dust emission, which leads to similar conclusions on dust temperature and grain properties. We further apply a hierarchical Bayesian analysis to infer the column density probability distribution function (N-PDF), while simultaneously removing the Galactic foreground and background emission. The N-PDF shows a steep power-law profile with α > 3, indicating that formation of dense structures are suppressed.

Combining information from multiple flood projections in a hierarchical Bayesian framework

NASA Astrophysics Data System (ADS)

Le Vine, Nataliya

2016-04-01

This study demonstrates, in the context of flood frequency analysis, the potential of a recently proposed hierarchical Bayesian approach to combine information from multiple models. The approach explicitly accommodates shared multimodel discrepancy as well as the probabilistic nature of the flood estimates, and treats the available models as a sample from a hypothetical complete (but unobserved) set of models. The methodology is applied to flood estimates from multiple hydrological projections (the Future Flows Hydrology data set) for 135 catchments in the UK. The advantages of the approach are shown to be: (1) to ensure adequate "baseline" with which to compare future changes; (2) to reduce flood estimate uncertainty; (3) to maximize use of statistical information in circumstances where multiple weak predictions individually lack power, but collectively provide meaningful information; (4) to diminish the importance of model consistency when model biases are large; and (5) to explicitly consider the influence of the (model performance) stationarity assumption. Moreover, the analysis indicates that reducing shared model discrepancy is the key to further reduction of uncertainty in the flood frequency analysis. The findings are of value regarding how conclusions about changing exposure to flooding are drawn, and to flood frequency change attribution studies.

A Bayesian hierarchical approach to comparative audit for carotid surgery.

PubMed

Kuhan, G; Marshall, E C; Abidia, A F; Chetter, I C; McCollum, P T

2002-12-01

the aim of this study was to illustrate how a Bayesian hierarchical modelling approach can aid the reliable comparison of outcome rates between surgeons. retrospective analysis of prospective and retrospective data. binary outcome data (death/stroke within 30 days), together with information on 15 possible risk factors specific for CEA were available on 836 CEAs performed by four vascular surgeons from 1992-99. The median patient age was 68 (range 38-86) years and 60% were men. the model was developed using the WinBUGS software. After adjusting for patient-level risk factors, a cross-validatory approach was adopted to identify "divergent" performance. A ranking exercise was also carried out. the overall observed 30-day stroke/death rate was 3.9% (33/836). The model found diabetes, stroke and heart disease to be significant risk factors. There was no significant difference between the predicted and observed outcome rates for any surgeon (Bayesian p -value>0.05). Each surgeon had a median rank of 3 with associated 95% CI 1.0-5.0, despite the variability of observed stroke/death rate from 2.9-4.4%. After risk adjustment, there was very little residual between-surgeon variability in outcome rate. Bayesian hierarchical models can help to accurately quantify the uncertainty associated with surgeons' performance and rank.

Compromise decision support problems for hierarchical design involving uncertainty

NASA Astrophysics Data System (ADS)

Vadde, S.; Allen, J. K.; Mistree, F.

1994-08-01

In this paper an extension to the traditional compromise Decision Support Problem (DSP) formulation is presented. Bayesian statistics is used in the formulation to model uncertainties associated with the information being used. In an earlier paper a compromise DSP that accounts for uncertainty using fuzzy set theory was introduced. The Bayesian Decision Support Problem is described in this paper. The method for hierarchical design is demonstrated by using this formulation to design a portal frame. The results are discussed and comparisons are made with those obtained using the fuzzy DSP. Finally, the efficacy of incorporating Bayesian statistics into the traditional compromise DSP formulation is discussed and some pending research issues are described. Our emphasis in this paper is on the method rather than the results per se.

HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python.

PubMed

Wiecki, Thomas V; Sofer, Imri; Frank, Michael J

2013-01-01

The diffusion model is a commonly used tool to infer latent psychological processes underlying decision-making, and to link them to neural mechanisms based on response times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of response time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model), which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject/condition than non-hierarchical methods, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g., fMRI) influence decision-making parameters. This paper will first describe the theoretical background of the drift diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the χ(2)-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs/

A Hierarchical Bayesian Model for Crowd Emotions

PubMed Central

Urizar, Oscar J.; Baig, Mirza S.; Barakova, Emilia I.; Regazzoni, Carlo S.; Marcenaro, Lucio; Rauterberg, Matthias

2016-01-01

Estimation of emotions is an essential aspect in developing intelligent systems intended for crowded environments. However, emotion estimation in crowds remains a challenging problem due to the complexity in which human emotions are manifested and the capability of a system to perceive them in such conditions. This paper proposes a hierarchical Bayesian model to learn in unsupervised manner the behavior of individuals and of the crowd as a single entity, and explore the relation between behavior and emotions to infer emotional states. Information about the motion patterns of individuals are described using a self-organizing map, and a hierarchical Bayesian network builds probabilistic models to identify behaviors and infer the emotional state of individuals and the crowd. This model is trained and tested using data produced from simulated scenarios that resemble real-life environments. The conducted experiments tested the efficiency of our method to learn, detect and associate behaviors with emotional states yielding accuracy levels of 74% for individuals and 81% for the crowd, similar in performance with existing methods for pedestrian behavior detection but with novel concepts regarding the analysis of crowds. PMID:27458366

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…

Bayesian hierarchical modeling for detecting safety signals in clinical trials.

PubMed

Xia, H Amy; Ma, Haijun; Carlin, Bradley P

2011-09-01

Detection of safety signals from clinical trial adverse event data is critical in drug development, but carries a challenging statistical multiplicity problem. Bayesian hierarchical mixture modeling is appealing for its ability to borrow strength across subgroups in the data, as well as moderate extreme findings most likely due merely to chance. We implement such a model for subject incidence (Berry and Berry, 2004 ) using a binomial likelihood, and extend it to subject-year adjusted incidence rate estimation under a Poisson likelihood. We use simulation to choose a signal detection threshold, and illustrate some effective graphics for displaying the flagged signals.

Transdimensional, hierarchical, Bayesian inversion of ambient seismic noise: Australia

NASA Astrophysics Data System (ADS)

Crowder, E.; Rawlinson, N.; Cornwell, D. G.

2017-12-01

We present models of crustal velocity structure in southeastern Australia using a novel, transdimensional and hierarchical, Bayesian inversion approach. The inversion is applied to long-time ambient noise cross-correlations. The study area of SE Australia is thought to represent the eastern margin of Gondwana. Conflicting tectonic models have been proposed to explain the formation of eastern Gondwana and the enigmatic geological relationships in Bass Strait, which separates Tasmania and the mainland. A geologically complex area of crustal accretion, Bass Strait may contain part of an exotic continental block entrained in colliding crusts. Ambient noise data recorded by an array of 24 seismometers is used to produce a high resolution, 3D shear wave velocity model of Bass Strait. Phase velocity maps in the period range 2-30 s are produced and subsequently inverted for 3D shear wave velocity structure. The transdimensional, hierarchical Bayesian, inversion technique is used. This technique proves far superior to linearised inversion. The inversion model is dynamically parameterised during the process, implicitly controlled by the data, and noise is treated as an inversion unknown. The resulting shear wave velocity model shows three sedimentary basins in Bass Strait constrained by slow shear velocities (2.4-2.9 km/s) at 2-10 km depth. These failed rift basins from the breakup of Australia-Antartica appear to be overlying thinned crust, where typical mantle velocities of 3.8-4.0 km/s occur at depths greater than 20 km. High shear wave velocities ( 3.7-3.8 km/s) in our new model also match well with regions of high magnetic and gravity anomalies. Furthermore, we use both Rayleigh and Love wave phase data to to construct Vsv and Vsh maps. These are used to estimate crustal radial anisotropy in the Bass Strait. We interpret that structures delineated by our velocity models support the presence and extent of the exotic Precambrian micro-continent (the Selwyn Block) that was most likely entrained during crustal accretion.

A FAST BAYESIAN METHOD FOR UPDATING AND FORECASTING HOURLY OZONE LEVELS

EPA Science Inventory

A Bayesian hierarchical space-time model is proposed by combining information from real-time ambient AIRNow air monitoring data, and output from a computer simulation model known as the Community Multi-scale Air Quality (Eta-CMAQ) forecast model. A model validation analysis shows...

A hierarchical Bayesian method for vibration-based time domain force reconstruction problems

NASA Astrophysics Data System (ADS)

Li, Qiaofeng; Lu, Qiuhai

2018-05-01

Traditional force reconstruction techniques require prior knowledge on the force nature to determine the regularization term. When such information is unavailable, the inappropriate term is easily chosen and the reconstruction result becomes unsatisfactory. In this paper, we propose a novel method to automatically determine the appropriate q as in ℓq regularization and reconstruct the force history. The method incorporates all to-be-determined variables such as the force history, precision parameters and q into a hierarchical Bayesian formulation. The posterior distributions of variables are evaluated by a Metropolis-within-Gibbs sampler. The point estimates of variables and their uncertainties are given. Simulations of a cantilever beam and a space truss under various loading conditions validate the proposed method in providing adaptive determination of q and better reconstruction performance than existing Bayesian methods.

Profile-Based LC-MS Data Alignment—A Bayesian Approach

PubMed Central

Tsai, Tsung-Heng; Tadesse, Mahlet G.; Wang, Yue; Ressom, Habtom W.

2014-01-01

A Bayesian alignment model (BAM) is proposed for alignment of liquid chromatography-mass spectrometry (LC-MS) data. BAM belongs to the category of profile-based approaches, which are composed of two major components: a prototype function and a set of mapping functions. Appropriate estimation of these functions is crucial for good alignment results. BAM uses Markov chain Monte Carlo (MCMC) methods to draw inference on the model parameters and improves on existing MCMC-based alignment methods through 1) the implementation of an efficient MCMC sampler and 2) an adaptive selection of knots. A block Metropolis-Hastings algorithm that mitigates the problem of the MCMC sampler getting stuck at local modes of the posterior distribution is used for the update of the mapping function coefficients. In addition, a stochastic search variable selection (SSVS) methodology is used to determine the number and positions of knots. We applied BAM to a simulated data set, an LC-MS proteomic data set, and two LC-MS metabolomic data sets, and compared its performance with the Bayesian hierarchical curve registration (BHCR) model, the dynamic time-warping (DTW) model, and the continuous profile model (CPM). The advantage of applying appropriate profile-based retention time correction prior to performing a feature-based approach is also demonstrated through the metabolomic data sets. PMID:23929872

Assessing Local Model Adequacy in Bayesian Hierarchical Models Using the Partitioned Deviance Information Criterion

PubMed Central

Wheeler, David C.; Hickson, DeMarc A.; Waller, Lance A.

2010-01-01

Many diagnostic tools and goodness-of-fit measures, such as the Akaike information criterion (AIC) and the Bayesian deviance information criterion (DIC), are available to evaluate the overall adequacy of linear regression models. In addition, visually assessing adequacy in models has become an essential part of any regression analysis. In this paper, we focus on a spatial consideration of the local DIC measure for model selection and goodness-of-fit evaluation. We use a partitioning of the DIC into the local DIC, leverage, and deviance residuals to assess local model fit and influence for both individual observations and groups of observations in a Bayesian framework. We use visualization of the local DIC and differences in local DIC between models to assist in model selection and to visualize the global and local impacts of adding covariates or model parameters. We demonstrate the utility of the local DIC in assessing model adequacy using HIV prevalence data from pregnant women in the Butare province of Rwanda during 1989-1993 using a range of linear model specifications, from global effects only to spatially varying coefficient models, and a set of covariates related to sexual behavior. Results of applying the diagnostic visualization approach include more refined model selection and greater understanding of the models as applied to the data. PMID:21243121

Constructive Epistemic Modeling: A Hierarchical Bayesian Model Averaging Method

NASA Astrophysics Data System (ADS)

Tsai, F. T. C.; Elshall, A. S.

2014-12-01

Constructive epistemic modeling is the idea that our understanding of a natural system through a scientific model is a mental construct that continually develops through learning about and from the model. Using the hierarchical Bayesian model averaging (HBMA) method [1], this study shows that segregating different uncertain model components through a BMA tree of posterior model probabilities, model prediction, within-model variance, between-model variance and total model variance serves as a learning tool [2]. First, the BMA tree of posterior model probabilities permits the comparative evaluation of the candidate propositions of each uncertain model component. Second, systemic model dissection is imperative for understanding the individual contribution of each uncertain model component to the model prediction and variance. Third, the hierarchical representation of the between-model variance facilitates the prioritization of the contribution of each uncertain model component to the overall model uncertainty. We illustrate these concepts using the groundwater modeling of a siliciclastic aquifer-fault system. The sources of uncertainty considered are from geological architecture, formation dip, boundary conditions and model parameters. The study shows that the HBMA analysis helps in advancing knowledge about the model rather than forcing the model to fit a particularly understanding or merely averaging several candidate models. [1] Tsai, F. T.-C., and A. S. Elshall (2013), Hierarchical Bayesian model averaging for hydrostratigraphic modeling: Uncertainty segregation and comparative evaluation. Water Resources Research, 49, 5520-5536, doi:10.1002/wrcr.20428. [2] Elshall, A.S., and F. T.-C. Tsai (2014). Constructive epistemic modeling of groundwater flow with geological architecture and boundary condition uncertainty under Bayesian paradigm, Journal of Hydrology, 517, 105-119, doi: 10.1016/j.jhydrol.2014.05.027.

Using a Data-Driven Approach to Understand the Interaction between Catchment Characteristics and Water Quality Responses

NASA Astrophysics Data System (ADS)

Western, A. W.; Lintern, A.; Liu, S.; Ryu, D.; Webb, J. A.; Leahy, P.; Wilson, P.; Waters, D.; Bende-Michl, U.; Watson, M.

2016-12-01

Many streams, lakes and estuaries are experiencing increasing concentrations and loads of nutrient and sediments. Models that can predict the spatial and temporal variability in water quality of aquatic systems are required to help guide the management and restoration of polluted aquatic systems. We propose that a Bayesian hierarchical modelling framework could be used to predict water quality responses over varying spatial and temporal scales. Stream water quality data and spatial data of catchment characteristics collected throughout Victoria and Queensland (in Australia) over two decades will be used to develop this Bayesian hierarchical model. In this paper, we present the preliminary exploratory data analysis required for the development of the Bayesian hierarchical model. Specifically, we present the results of exploratory data analysis of Total Nitrogen (TN) concentrations in rivers in Victoria (in South-East Australia) to illustrate the catchment characteristics that appear to be influencing spatial variability in (1) mean concentrations of TN; and (2) the relationship between discharge and TN throughout the state. These important catchment characteristics were identified using: (1) monthly TN concentrations measured at 28 water quality gauging stations and (2) climate, land use, topographic and geologic characteristics of the catchments of these 28 sites. Spatial variability in TN concentrations had a positive correlation to fertiliser use in the catchment and average temperature. There were negative correlations between TN concentrations and catchment forest cover, annual runoff, runoff perenniality, soil erosivity and catchment slope. The relationship between discharge and TN concentrations showed spatial variability, possibly resulting from climatic and topographic differences between the sites. The results of this study will feed into the hierarchical Bayesian model of river water quality.

Determining Crust and Upper Mantle Structure by Bayesian Joint Inversion of Receiver Functions and Surface Wave Dispersion at a Single Station: Preparation for Data from the InSight Mission

NASA Astrophysics Data System (ADS)

Jia, M.; Panning, M. P.; Lekic, V.; Gao, C.

2017-12-01

The InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission will deploy a geophysical station on Mars in 2018. Using seismology to explore the interior structure of the Mars is one of the main targets, and as part of the mission, we will use 3-component seismic data to constrain the crust and upper mantle structure including P and S wave velocities and densities underneath the station. We will apply a reversible jump Markov chain Monte Carlo algorithm in the transdimensional hierarchical Bayesian inversion framework, in which the number of parameters in the model space and the noise level of the observed data are also treated as unknowns in the inversion process. Bayesian based methods produce an ensemble of models which can be analyzed to quantify uncertainties and trade-offs of the model parameters. In order to get better resolution, we will simultaneously invert three different types of seismic data: receiver functions, surface wave dispersion (SWD), and ZH ratios. Because the InSight mission will only deliver a single seismic station to Mars, and both the source location and the interior structure will be unknown, we will jointly invert the ray parameter in our approach. In preparation for this work, we first verify our approach by using a set of synthetic data. We find that SWD can constrain the absolute value of velocities while receiver functions constrain the discontinuities. By joint inversion, the velocity structure in the crust and upper mantle is well recovered. Then, we apply our approach to real data from an earth-based seismic station BFO located in Black Forest Observatory in Germany, as already used in a demonstration study for single station location methods. From the comparison of the results, our hierarchical treatment shows its advantage over the conventional method in which the noise level of observed data is fixed as a prior.

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.

Advances in statistics

Treesearch

Howard Stauffer; Nadav Nur

2005-01-01

The papers included in the Advances in Statistics section of the Partners in Flight (PIF) 2002 Proceedings represent a small sample of statistical topics of current importance to Partners In Flight research scientists: hierarchical modeling, estimation of detection probabilities, and Bayesian applications. Sauer et al. (this volume) examines a hierarchical model...

Sparse Event Modeling with Hierarchical Bayesian Kernel Methods

DTIC Science & Technology

2016-01-05

SECURITY CLASSIFICATION OF: The research objective of this proposal was to develop a predictive Bayesian kernel approach to model count data based on...several predictive variables. Such an approach, which we refer to as the Poisson Bayesian kernel model , is able to model the rate of occurrence of...which adds specificity to the model and can make nonlinear data more manageable. Early results show that the 1. REPORT DATE (DD-MM-YYYY) 4. TITLE

Model-based inference for small area estimation with sampling weights

PubMed Central

Vandendijck, Y.; Faes, C.; Kirby, R.S.; Lawson, A.; Hens, N.

2017-01-01

Obtaining reliable estimates about health outcomes for areas or domains where only few to no samples are available is the goal of small area estimation (SAE). Often, we rely on health surveys to obtain information about health outcomes. Such surveys are often characterised by a complex design, stratification, and unequal sampling weights as common features. Hierarchical Bayesian models are well recognised in SAE as a spatial smoothing method, but often ignore the sampling weights that reflect the complex sampling design. In this paper, we focus on data obtained from a health survey where the sampling weights of the sampled individuals are the only information available about the design. We develop a predictive model-based approach to estimate the prevalence of a binary outcome for both the sampled and non-sampled individuals, using hierarchical Bayesian models that take into account the sampling weights. A simulation study is carried out to compare the performance of our proposed method with other established methods. The results indicate that our proposed method achieves great reductions in mean squared error when compared with standard approaches. It performs equally well or better when compared with more elaborate methods when there is a relationship between the responses and the sampling weights. The proposed method is applied to estimate asthma prevalence across districts. PMID:28989860

Recent global methane trends: an investigation using hierarchical Bayesian methods

NASA Astrophysics Data System (ADS)

Rigby, M. L.; Stavert, A.; Ganesan, A.; Lunt, M. F.

2014-12-01

Following a decade with little growth, methane concentrations began to increase across the globe in 2007, and have continued to rise ever since. The reasons for this renewed growth are currently the subject of much debate. Here, we discuss the recent observed trends, and highlight some of the strengths and weaknesses in current "inverse" methods for quantifying fluxes using observations. In particular, we focus on the outstanding problems of accurately quantifying uncertainties in inverse frameworks. We examine to what extent the recent methane changes can be explained by the current generation of flux models and inventories. We examine the major modes of variability in wetland models along with the Global Fire Emissions Database (GFED) and the Emissions Database for Global Atmospheric Research (EDGAR). Using the Model for Ozone and Related Tracers (MOZART), we determine whether the spatial and temporal atmospheric trends predicted using these emissions can be brought into consistency with in situ atmospheric observations. We use a novel hierarchical Bayesian methodology in which scaling factors applied to the principal components of the flux fields are estimated simultaneously with the uncertainties associated with the a priori fluxes and with model representations of the observations. Using this method, we examine the predictive power of methane flux models for explaining recent fluctuations.

Estimating mono- and bi-phasic regression parameters using a mixture piecewise linear Bayesian hierarchical model

PubMed Central

Zhao, Rui; Catalano, Paul; DeGruttola, Victor G.; Michor, Franziska

2017-01-01

The dynamics of tumor burden, secreted proteins or other biomarkers over time, is often used to evaluate the effectiveness of therapy and to predict outcomes for patients. Many methods have been proposed to investigate longitudinal trends to better characterize patients and to understand disease progression. However, most approaches assume a homogeneous patient population and a uniform response trajectory over time and across patients. Here, we present a mixture piecewise linear Bayesian hierarchical model, which takes into account both population heterogeneity and nonlinear relationships between biomarkers and time. Simulation results show that our method was able to classify subjects according to their patterns of treatment response with greater than 80% accuracy in the three scenarios tested. We then applied our model to a large randomized controlled phase III clinical trial of multiple myeloma patients. Analysis results suggest that the longitudinal tumor burden trajectories in multiple myeloma patients are heterogeneous and nonlinear, even among patients assigned to the same treatment cohort. In addition, between cohorts, there are distinct differences in terms of the regression parameters and the distributions among categories in the mixture. Those results imply that longitudinal data from clinical trials may harbor unobserved subgroups and nonlinear relationships; accounting for both may be important for analyzing longitudinal data. PMID:28723910

Bayesian hierarchical modeling for subject-level response classification in peptide microarray immunoassays

PubMed Central

Imholte, Gregory; Gottardo, Raphael

2017-01-01

Summary The peptide microarray immunoassay simultaneously screens sample serum against thousands of peptides, determining the presence of antibodies bound to array probes. Peptide microarrays tiling immunogenic regions of pathogens (e.g. envelope proteins of a virus) are an important high throughput tool for querying and mapping antibody binding. Because of the assay’s many steps, from probe synthesis to incubation, peptide microarray data can be noisy with extreme outliers. In addition, subjects may produce different antibody profiles in response to an identical vaccine stimulus or infection, due to variability among subjects’ immune systems. We present a robust Bayesian hierarchical model for peptide microarray experiments, pepBayes, to estimate the probability of antibody response for each subject/peptide combination. Heavy-tailed error distributions accommodate outliers and extreme responses, and tailored random effect terms automatically incorporate technical effects prevalent in the assay. We apply our model to two vaccine trial datasets to demonstrate model performance. Our approach enjoys high sensitivity and specificity when detecting vaccine induced antibody responses. A simulation study shows an adaptive thresholding classification method has appropriate false discovery rate control with high sensitivity, and receiver operating characteristics generated on vaccine trial data suggest that pepBayes clearly separates responses from non-responses. PMID:27061097

Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes.

PubMed

Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon

2017-12-01

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. © 2017, The International Biometric Society.

UNSUPERVISED TRANSIENT LIGHT CURVE ANALYSIS VIA HIERARCHICAL BAYESIAN INFERENCE

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

Sanders, N. E.; Soderberg, A. M.; Betancourt, M., E-mail: nsanders@cfa.harvard.edu

2015-02-10

Historically, light curve studies of supernovae (SNe) and other transient classes have focused on individual objects with copious and high signal-to-noise observations. In the nascent era of wide field transient searches, objects with detailed observations are decreasing as a fraction of the overall known SN population, and this strategy sacrifices the majority of the information contained in the data about the underlying population of transients. A population level modeling approach, simultaneously fitting all available observations of objects in a transient sub-class of interest, fully mines the data to infer the properties of the population and avoids certain systematic biases. Wemore » present a novel hierarchical Bayesian statistical model for population level modeling of transient light curves, and discuss its implementation using an efficient Hamiltonian Monte Carlo technique. As a test case, we apply this model to the Type IIP SN sample from the Pan-STARRS1 Medium Deep Survey, consisting of 18,837 photometric observations of 76 SNe, corresponding to a joint posterior distribution with 9176 parameters under our model. Our hierarchical model fits provide improved constraints on light curve parameters relevant to the physical properties of their progenitor stars relative to modeling individual light curves alone. Moreover, we directly evaluate the probability for occurrence rates of unseen light curve characteristics from the model hyperparameters, addressing observational biases in survey methodology. We view this modeling framework as an unsupervised machine learning technique with the ability to maximize scientific returns from data to be collected by future wide field transient searches like LSST.« less

Explaining Inference on a Population of Independent Agents Using Bayesian Networks

ERIC Educational Resources Information Center

Sutovsky, Peter

2013-01-01

The main goal of this research is to design, implement, and evaluate a novel explanation method, the hierarchical explanation method (HEM), for explaining Bayesian network (BN) inference when the network is modeling a population of conditionally independent agents, each of which is modeled as a subnetwork. For example, consider disease-outbreak…

Modeling Associations among Multivariate Longitudinal Categorical Variables in Survey Data: A Semiparametric Bayesian Approach

ERIC Educational Resources Information Center

Tchumtchoua, Sylvie; Dey, Dipak K.

2012-01-01

This paper proposes a semiparametric Bayesian framework for the analysis of associations among multivariate longitudinal categorical variables in high-dimensional data settings. This type of data is frequent, especially in the social and behavioral sciences. A semiparametric hierarchical factor analysis model is developed in which the…

Assessment of Matrix Multiplication Learning with a Rule-Based Analytical Model--"A Bayesian Network Representation"

ERIC Educational Resources Information Center

Zhang, Zhidong

2016-01-01

This study explored an alternative assessment procedure to examine learning trajectories of matrix multiplication. It took rule-based analytical and cognitive task analysis methods specifically to break down operation rules for a given matrix multiplication. Based on the analysis results, a hierarchical Bayesian network, an assessment model,…

A Hierarchical Bayesian Procedure for Two-Mode Cluster Analysis

ERIC Educational Resources Information Center

DeSarbo, Wayne S.; Fong, Duncan K. H.; Liechty, John; Saxton, M. Kim

2004-01-01

This manuscript introduces a new Bayesian finite mixture methodology for the joint clustering of row and column stimuli/objects associated with two-mode asymmetric proximity, dominance, or profile data. That is, common clusters are derived which partition both the row and column stimuli/objects simultaneously into the same derived set of clusters.…

Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models

NASA Astrophysics Data System (ADS)

Vakilzadeh, Majid K.; Huang, Yong; Beck, James L.; Abrahamsson, Thomas

2017-02-01

A new multi-level Markov Chain Monte Carlo algorithm for Approximate Bayesian Computation, ABC-SubSim, has recently appeared that exploits the Subset Simulation method for efficient rare-event simulation. ABC-SubSim adaptively creates a nested decreasing sequence of data-approximating regions in the output space that correspond to increasingly closer approximations of the observed output vector in this output space. At each level, multiple samples of the model parameter vector are generated by a component-wise Metropolis algorithm so that the predicted output corresponding to each parameter value falls in the current data-approximating region. Theoretically, if continued to the limit, the sequence of data-approximating regions would converge on to the observed output vector and the approximate posterior distributions, which are conditional on the data-approximation region, would become exact, but this is not practically feasible. In this paper we study the performance of the ABC-SubSim algorithm for Bayesian updating of the parameters of dynamical systems using a general hierarchical state-space model. We note that the ABC methodology gives an approximate posterior distribution that actually corresponds to an exact posterior where a uniformly distributed combined measurement and modeling error is added. We also note that ABC algorithms have a problem with learning the uncertain error variances in a stochastic state-space model and so we treat them as nuisance parameters and analytically integrate them out of the posterior distribution. In addition, the statistical efficiency of the original ABC-SubSim algorithm is improved by developing a novel strategy to regulate the proposal variance for the component-wise Metropolis algorithm at each level. We demonstrate that Self-regulated ABC-SubSim is well suited for Bayesian system identification by first applying it successfully to model updating of a two degree-of-freedom linear structure for three cases: globally, locally and un-identifiable model classes, and then to model updating of a two degree-of-freedom nonlinear structure with Duffing nonlinearities in its interstory force-deflection relationship.

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.

A fast combination method in DSmT and its application to recommender system

PubMed Central

Liu, Yihai

2018-01-01

In many applications involving epistemic uncertainties usually modeled by belief functions, it is often necessary to approximate general (non-Bayesian) basic belief assignments (BBAs) to subjective probabilities (called Bayesian BBAs). This necessity occurs if one needs to embed the fusion result in a system based on the probabilistic framework and Bayesian inference (e.g. tracking systems), or if one needs to make a decision in the decision making problems. In this paper, we present a new fast combination method, called modified rigid coarsening (MRC), to obtain the final Bayesian BBAs based on hierarchical decomposition (coarsening) of the frame of discernment. Regarding this method, focal elements with probabilities are coarsened efficiently to reduce computational complexity in the process of combination by using disagreement vector and a simple dichotomous approach. In order to prove the practicality of our approach, this new approach is applied to combine users’ soft preferences in recommender systems (RSs). Additionally, in order to make a comprehensive performance comparison, the proportional conflict redistribution rule #6 (PCR6) is regarded as a baseline in a range of experiments. According to the results of experiments, MRC is more effective in accuracy of recommendations compared to original Rigid Coarsening (RC) method and comparable in computational time. PMID:29351297

Receptive Field Inference with Localized Priors

PubMed Central

Park, Mijung; Pillow, Jonathan W.

2011-01-01

The linear receptive field describes a mapping from sensory stimuli to a one-dimensional variable governing a neuron's spike response. However, traditional receptive field estimators such as the spike-triggered average converge slowly and often require large amounts of data. Bayesian methods seek to overcome this problem by biasing estimates towards solutions that are more likely a priori, typically those with small, smooth, or sparse coefficients. Here we introduce a novel Bayesian receptive field estimator designed to incorporate locality, a powerful form of prior information about receptive field structure. The key to our approach is a hierarchical receptive field model that flexibly adapts to localized structure in both spacetime and spatiotemporal frequency, using an inference method known as empirical Bayes. We refer to our method as automatic locality determination (ALD), and show that it can accurately recover various types of smooth, sparse, and localized receptive fields. We apply ALD to neural data from retinal ganglion cells and V1 simple cells, and find it achieves error rates several times lower than standard estimators. Thus, estimates of comparable accuracy can be achieved with substantially less data. Finally, we introduce a computationally efficient Markov Chain Monte Carlo (MCMC) algorithm for fully Bayesian inference under the ALD prior, yielding accurate Bayesian confidence intervals for small or noisy datasets. PMID:22046110

A hierarchical Bayesian approach to adaptive vision testing: A case study with the contrast sensitivity function.

PubMed

Gu, Hairong; Kim, Woojae; Hou, Fang; Lesmes, Luis Andres; Pitt, Mark A; Lu, Zhong-Lin; Myung, Jay I

2016-01-01

Measurement efficiency is of concern when a large number of observations are required to obtain reliable estimates for parametric models of vision. The standard entropy-based Bayesian adaptive testing procedures addressed the issue by selecting the most informative stimulus in sequential experimental trials. Noninformative, diffuse priors were commonly used in those tests. Hierarchical adaptive design optimization (HADO; Kim, Pitt, Lu, Steyvers, & Myung, 2014) further improves the efficiency of the standard Bayesian adaptive testing procedures by constructing an informative prior using data from observers who have already participated in the experiment. The present study represents an empirical validation of HADO in estimating the human contrast sensitivity function. The results show that HADO significantly improves the accuracy and precision of parameter estimates, and therefore requires many fewer observations to obtain reliable inference about contrast sensitivity, compared to the method of quick contrast sensitivity function (Lesmes, Lu, Baek, & Albright, 2010), which uses the standard Bayesian procedure. The improvement with HADO was maintained even when the prior was constructed from heterogeneous populations or a relatively small number of observers. These results of this case study support the conclusion that HADO can be used in Bayesian adaptive testing by replacing noninformative, diffuse priors with statistically justified informative priors without introducing unwanted bias.

A hierarchical Bayesian approach to adaptive vision testing: A case study with the contrast sensitivity function

PubMed Central

Gu, Hairong; Kim, Woojae; Hou, Fang; Lesmes, Luis Andres; Pitt, Mark A.; Lu, Zhong-Lin; Myung, Jay I.

2016-01-01

Measurement efficiency is of concern when a large number of observations are required to obtain reliable estimates for parametric models of vision. The standard entropy-based Bayesian adaptive testing procedures addressed the issue by selecting the most informative stimulus in sequential experimental trials. Noninformative, diffuse priors were commonly used in those tests. Hierarchical adaptive design optimization (HADO; Kim, Pitt, Lu, Steyvers, & Myung, 2014) further improves the efficiency of the standard Bayesian adaptive testing procedures by constructing an informative prior using data from observers who have already participated in the experiment. The present study represents an empirical validation of HADO in estimating the human contrast sensitivity function. The results show that HADO significantly improves the accuracy and precision of parameter estimates, and therefore requires many fewer observations to obtain reliable inference about contrast sensitivity, compared to the method of quick contrast sensitivity function (Lesmes, Lu, Baek, & Albright, 2010), which uses the standard Bayesian procedure. The improvement with HADO was maintained even when the prior was constructed from heterogeneous populations or a relatively small number of observers. These results of this case study support the conclusion that HADO can be used in Bayesian adaptive testing by replacing noninformative, diffuse priors with statistically justified informative priors without introducing unwanted bias. PMID:27105061

Social Influence on Information Technology Adoption and Sustained Use in Healthcare: A Hierarchical Bayesian Learning Method Analysis

ERIC Educational Resources Information Center

Hao, Haijing

2013-01-01

Information technology adoption and diffusion is currently a significant challenge in the healthcare delivery setting. This thesis includes three papers that explore social influence on information technology adoption and sustained use in the healthcare delivery environment using conventional regression models and novel hierarchical Bayesian…

Weakly Informative Prior for Point Estimation of Covariance Matrices in Hierarchical Models

ERIC Educational Resources Information Center

Chung, Yeojin; Gelman, Andrew; Rabe-Hesketh, Sophia; Liu, Jingchen; Dorie, Vincent

2015-01-01

When fitting hierarchical regression models, maximum likelihood (ML) estimation has computational (and, for some users, philosophical) advantages compared to full Bayesian inference, but when the number of groups is small, estimates of the covariance matrix (S) of group-level varying coefficients are often degenerate. One can do better, even from…

Hierarchical models of animal abundance and occurrence

USGS Publications Warehouse

Royle, J. Andrew; Dorazio, R.M.

2006-01-01

Much of animal ecology is devoted to studies of abundance and occurrence of species, based on surveys of spatially referenced sample units. These surveys frequently yield sparse counts that are contaminated by imperfect detection, making direct inference about abundance or occurrence based on observational data infeasible. This article describes a flexible hierarchical modeling framework for estimation and inference about animal abundance and occurrence from survey data that are subject to imperfect detection. Within this framework, we specify models of abundance and detectability of animals at the level of the local populations defined by the sample units. Information at the level of the local population is aggregated by specifying models that describe variation in abundance and detection among sites. We describe likelihood-based and Bayesian methods for estimation and inference under the resulting hierarchical model. We provide two examples of the application of hierarchical models to animal survey data, the first based on removal counts of stream fish and the second based on avian quadrat counts. For both examples, we provide a Bayesian analysis of the models using the software WinBUGS.

Quantifying inter- and intra-population niche variability using hierarchical bayesian stable isotope mixing models.

PubMed

Semmens, Brice X; Ward, Eric J; Moore, Jonathan W; Darimont, Chris T

2009-07-09

Variability in resource use defines the width of a trophic niche occupied by a population. Intra-population variability in resource use may occur across hierarchical levels of population structure from individuals to subpopulations. Understanding how levels of population organization contribute to population niche width is critical to ecology and evolution. Here we describe a hierarchical stable isotope mixing model that can simultaneously estimate both the prey composition of a consumer diet and the diet variability among individuals and across levels of population organization. By explicitly estimating variance components for multiple scales, the model can deconstruct the niche width of a consumer population into relevant levels of population structure. We apply this new approach to stable isotope data from a population of gray wolves from coastal British Columbia, and show support for extensive intra-population niche variability among individuals, social groups, and geographically isolated subpopulations. The analytic method we describe improves mixing models by accounting for diet variability, and improves isotope niche width analysis by quantitatively assessing the contribution of levels of organization to the niche width of a population.

Prion Amplification and Hierarchical Bayesian Modeling Refine Detection of Prion Infection

NASA Astrophysics Data System (ADS)

Wyckoff, A. Christy; Galloway, Nathan; Meyerett-Reid, Crystal; Powers, Jenny; Spraker, Terry; Monello, Ryan J.; Pulford, Bruce; Wild, Margaret; Antolin, Michael; Vercauteren, Kurt; Zabel, Mark

2015-02-01

Prions are unique infectious agents that replicate without a genome and cause neurodegenerative diseases that include chronic wasting disease (CWD) of cervids. Immunohistochemistry (IHC) is currently considered the gold standard for diagnosis of a prion infection but may be insensitive to early or sub-clinical CWD that are important to understanding CWD transmission and ecology. We assessed the potential of serial protein misfolding cyclic amplification (sPMCA) to improve detection of CWD prior to the onset of clinical signs. We analyzed tissue samples from free-ranging Rocky Mountain elk (Cervus elaphus nelsoni) and used hierarchical Bayesian analysis to estimate the specificity and sensitivity of IHC and sPMCA conditional on simultaneously estimated disease states. Sensitivity estimates were higher for sPMCA (99.51%, credible interval (CI) 97.15-100%) than IHC of obex (brain stem, 76.56%, CI 57.00-91.46%) or retropharyngeal lymph node (90.06%, CI 74.13-98.70%) tissues, or both (98.99%, CI 90.01-100%). Our hierarchical Bayesian model predicts the prevalence of prion infection in this elk population to be 18.90% (CI 15.50-32.72%), compared to previous estimates of 12.90%. Our data reveal a previously unidentified sub-clinical prion-positive portion of the elk population that could represent silent carriers capable of significantly impacting CWD ecology.

Prion amplification and hierarchical Bayesian modeling refine detection of prion infection.

PubMed

Wyckoff, A Christy; Galloway, Nathan; Meyerett-Reid, Crystal; Powers, Jenny; Spraker, Terry; Monello, Ryan J; Pulford, Bruce; Wild, Margaret; Antolin, Michael; VerCauteren, Kurt; Zabel, Mark

2015-02-10

Prions are unique infectious agents that replicate without a genome and cause neurodegenerative diseases that include chronic wasting disease (CWD) of cervids. Immunohistochemistry (IHC) is currently considered the gold standard for diagnosis of a prion infection but may be insensitive to early or sub-clinical CWD that are important to understanding CWD transmission and ecology. We assessed the potential of serial protein misfolding cyclic amplification (sPMCA) to improve detection of CWD prior to the onset of clinical signs. We analyzed tissue samples from free-ranging Rocky Mountain elk (Cervus elaphus nelsoni) and used hierarchical Bayesian analysis to estimate the specificity and sensitivity of IHC and sPMCA conditional on simultaneously estimated disease states. Sensitivity estimates were higher for sPMCA (99.51%, credible interval (CI) 97.15-100%) than IHC of obex (brain stem, 76.56%, CI 57.00-91.46%) or retropharyngeal lymph node (90.06%, CI 74.13-98.70%) tissues, or both (98.99%, CI 90.01-100%). Our hierarchical Bayesian model predicts the prevalence of prion infection in this elk population to be 18.90% (CI 15.50-32.72%), compared to previous estimates of 12.90%. Our data reveal a previously unidentified sub-clinical prion-positive portion of the elk population that could represent silent carriers capable of significantly impacting CWD ecology.

EVOLUTION OF THE VELOCITY-DISPERSION FUNCTION OF LUMINOUS RED GALAXIES: A HIERARCHICAL BAYESIAN MEASUREMENT

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

Shu Yiping; Bolton, Adam S.; Dawson, Kyle S.

2012-04-15

We present a hierarchical Bayesian determination of the velocity-dispersion function of approximately 430,000 massive luminous red galaxies observed at relatively low spectroscopic signal-to-noise ratio (S/N {approx} 3-5 per 69 km s{sup -1}) by the Baryon Oscillation Spectroscopic Survey (BOSS) of the Sloan Digital Sky Survey III. We marginalize over spectroscopic redshift errors, and use the full velocity-dispersion likelihood function for each galaxy to make a self-consistent determination of the velocity-dispersion distribution parameters as a function of absolute magnitude and redshift, correcting as well for the effects of broadband magnitude errors on our binning. Parameterizing the distribution at each point inmore » the luminosity-redshift plane with a log-normal form, we detect significant evolution in the width of the distribution toward higher intrinsic scatter at higher redshifts. Using a subset of deep re-observations of BOSS galaxies, we demonstrate that our distribution-parameter estimates are unbiased regardless of spectroscopic S/N. We also show through simulation that our method introduces no systematic parameter bias with redshift. We highlight the advantage of the hierarchical Bayesian method over frequentist 'stacking' of spectra, and illustrate how our measured distribution parameters can be adopted as informative priors for velocity-dispersion measurements from individual noisy spectra.« less

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.

An adaptive sparse-grid high-order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling

NASA Astrophysics Data System (ADS)

Zhang, Guannan; Lu, Dan; Ye, Ming; Gunzburger, Max; Webster, Clayton

2013-10-01

Bayesian analysis has become vital to uncertainty quantification in groundwater modeling, but its application has been hindered by the computational cost associated with numerous model executions required by exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, a new approach is developed to improve the computational efficiency of Bayesian inference by constructing a surrogate of the PPDF, using an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, this paper utilizes a compactly supported higher-order hierarchical basis to construct the surrogate system, resulting in a significant reduction in the number of required model executions. In addition, using the hierarchical surplus as an error indicator allows locally adaptive refinement of sparse grids in the parameter space, which further improves computational efficiency. To efficiently build the surrogate system for the PPDF with multiple significant modes, optimization techniques are used to identify the modes, for which high-probability regions are defined and components of the aSG-hSC approximation are constructed. After the surrogate is determined, the PPDF can be evaluated by sampling the surrogate system directly without model execution, resulting in improved efficiency of the surrogate-based MCMC compared with conventional MCMC. The developed method is evaluated using two synthetic groundwater reactive transport models. The first example involves coupled linear reactions and demonstrates the accuracy of our high-order hierarchical basis approach in approximating high-dimensional posteriori distribution. The second example is highly nonlinear because of the reactions of uranium surface complexation, and demonstrates how the iterative aSG-hSC method is able to capture multimodal and non-Gaussian features of PPDF caused by model nonlinearity. Both experiments show that aSG-hSC is an effective and efficient tool for Bayesian inference.

Testing for Divergent Transmission Histories among Cultural Characters: A Study Using Bayesian Phylogenetic Methods and Iranian Tribal Textile Data

PubMed Central

Matthews, Luke J.; Tehrani, Jamie J.; Jordan, Fiona M.; Collard, Mark; Nunn, Charles L.

2011-01-01

Background Archaeologists and anthropologists have long recognized that different cultural complexes may have distinct descent histories, but they have lacked analytical techniques capable of easily identifying such incongruence. Here, we show how Bayesian phylogenetic analysis can be used to identify incongruent cultural histories. We employ the approach to investigate Iranian tribal textile traditions. Methods We used Bayes factor comparisons in a phylogenetic framework to test two models of cultural evolution: the hierarchically integrated system hypothesis and the multiple coherent units hypothesis. In the hierarchically integrated system hypothesis, a core tradition of characters evolves through descent with modification and characters peripheral to the core are exchanged among contemporaneous populations. In the multiple coherent units hypothesis, a core tradition does not exist. Rather, there are several cultural units consisting of sets of characters that have different histories of descent. Results For the Iranian textiles, the Bayesian phylogenetic analyses supported the multiple coherent units hypothesis over the hierarchically integrated system hypothesis. Our analyses suggest that pile-weave designs represent a distinct cultural unit that has a different phylogenetic history compared to other textile characters. Conclusions The results from the Iranian textiles are consistent with the available ethnographic evidence, which suggests that the commercial rug market has influenced pile-rug designs but not the techniques or designs incorporated in the other textiles produced by the tribes. We anticipate that Bayesian phylogenetic tests for inferring cultural units will be of great value for researchers interested in studying the evolution of cultural traits including language, behavior, and material culture. PMID:21559083

How does aging affect recognition-based inference? A hierarchical Bayesian modeling approach.

PubMed

Horn, Sebastian S; Pachur, Thorsten; Mata, Rui

2015-01-01

The recognition heuristic (RH) is a simple strategy for probabilistic inference according to which recognized objects are judged to score higher on a criterion than unrecognized objects. In this article, a hierarchical Bayesian extension of the multinomial r-model is applied to measure use of the RH on the individual participant level and to re-evaluate differences between younger and older adults' strategy reliance across environments. Further, it is explored how individual r-model parameters relate to alternative measures of the use of recognition and other knowledge, such as adherence rates and indices from signal-detection theory (SDT). Both younger and older adults used the RH substantially more often in an environment with high than low recognition validity, reflecting adaptivity in strategy use across environments. In extension of previous analyses (based on adherence rates), hierarchical modeling revealed that in an environment with low recognition validity, (a) older adults had a stronger tendency than younger adults to rely on the RH and (b) variability in RH use between individuals was larger than in an environment with high recognition validity; variability did not differ between age groups. Further, the r-model parameters correlated moderately with an SDT measure expressing how well people can discriminate cases where the RH leads to a correct vs. incorrect inference; this suggests that the r-model and the SDT measures may offer complementary insights into the use of recognition in decision making. In conclusion, younger and older adults are largely adaptive in their application of the RH, but cognitive aging may be associated with an increased tendency to rely on this strategy. Copyright © 2014 Elsevier B.V. All rights reserved.

Examining driver injury severity outcomes in rural non-interstate roadway crashes using a hierarchical ordered logit model.

PubMed

Chen, Cong; Zhang, Guohui; Huang, Helai; Wang, Jiangfeng; Tarefder, Rafiqul A

2016-11-01

Rural non-interstate crashes induce a significant amount of severe injuries and fatalities. Examination of such injury patterns and the associated contributing factors is of practical importance. Taking into account the ordinal nature of injury severity levels and the hierarchical feature of crash data, this study employs a hierarchical ordered logit model to examine the significant factors in predicting driver injury severities in rural non-interstate crashes based on two-year New Mexico crash records. Bayesian inference is utilized in model estimation procedure and 95% Bayesian Credible Interval (BCI) is applied to testing variable significance. An ordinary ordered logit model omitting the between-crash variance effect is evaluated as well for model performance comparison. Results indicate that the model employed in this study outperforms ordinary ordered logit model in model fit and parameter estimation. Variables regarding crash features, environment conditions, and driver and vehicle characteristics are found to have significant influence on the predictions of driver injury severities in rural non-interstate crashes. Factors such as road segments far from intersection, wet road surface condition, collision with animals, heavy vehicle drivers, male drivers and driver seatbelt used tend to induce less severe driver injury outcomes than the factors such as multiple-vehicle crashes, severe vehicle damage in a crash, motorcyclists, females, senior drivers, driver with alcohol or drug impairment, and other major collision types. Research limitations regarding crash data and model assumptions are also discussed. Overall, this research provides reasonable results and insight in developing effective road safety measures for crash injury severity reduction and prevention. Copyright © 2016 Elsevier Ltd. All rights reserved.

A model-based analysis of impulsivity using a slot-machine gambling paradigm

PubMed Central

Paliwal, Saee; Petzschner, Frederike H.; Schmitz, Anna Katharina; Tittgemeyer, Marc; Stephan, Klaas E.

2014-01-01

Impulsivity plays a key role in decision-making under uncertainty. It is a significant contributor to problem and pathological gambling (PG). Standard assessments of impulsivity by questionnaires, however, have various limitations, partly because impulsivity is a broad, multi-faceted concept. What remains unclear is which of these facets contribute to shaping gambling behavior. In the present study, we investigated impulsivity as expressed in a gambling setting by applying computational modeling to data from 47 healthy male volunteers who played a realistic, virtual slot-machine gambling task. Behaviorally, we found that impulsivity, as measured independently by the 11th revision of the Barratt Impulsiveness Scale (BIS-11), correlated significantly with an aggregate read-out of the following gambling responses: bet increases (BIs), machines switches (MS), casino switches (CS), and double-ups (DUs). Using model comparison, we compared a set of hierarchical Bayesian belief-updating models, i.e., the Hierarchical Gaussian Filter (HGF) and Rescorla–Wagner reinforcement learning (RL) models, with regard to how well they explained different aspects of the behavioral data. We then examined the construct validity of our winning models with multiple regression, relating subject-specific model parameter estimates to the individual BIS-11 total scores. In the most predictive model (a three-level HGF), the two free parameters encoded uncertainty-dependent mechanisms of belief updates and significantly explained BIS-11 variance across subjects. Furthermore, in this model, decision noise was a function of trial-wise uncertainty about winning probability. Collectively, our results provide a proof of concept that hierarchical Bayesian models can characterize the decision-making mechanisms linked to the impulsive traits of an individual. These novel indices of gambling mechanisms unmasked during actual play may be useful for online prevention measures for at-risk players and future assessments of PG. PMID:25071497

Bayesian Decision Support

NASA Astrophysics Data System (ADS)

Berliner, M.

2017-12-01

Bayesian statistical decision theory offers a natural framework for decision-policy making in the presence of uncertainty. Key advantages of the approach include efficient incorporation of information and observations. However, in complicated settings it is very difficult, perhaps essentially impossible, to formalize the mathematical inputs needed in the approach. Nevertheless, using the approach as a template is useful for decision support; that is, organizing and communicating our analyses. Bayesian hierarchical modeling is valuable in quantifying and managing uncertainty such cases. I review some aspects of the idea emphasizing statistical model development and use in the context of sea-level rise.

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

Bayesian Correction for Misclassification in Multilevel Count Data Models.

PubMed

Nelson, Tyler; Song, Joon Jin; Chin, Yoo-Mi; Stamey, James D

2018-01-01

Covariate misclassification is well known to yield biased estimates in single level regression models. The impact on hierarchical count models has been less studied. A fully Bayesian approach to modeling both the misclassified covariate and the hierarchical response is proposed. Models with a single diagnostic test and with multiple diagnostic tests are considered. Simulation studies show the ability of the proposed model to appropriately account for the misclassification by reducing bias and improving performance of interval estimators. A real data example further demonstrated the consequences of ignoring the misclassification. Ignoring misclassification yielded a model that indicated there was a significant, positive impact on the number of children of females who observed spousal abuse between their parents. When the misclassification was accounted for, the relationship switched to negative, but not significant. Ignoring misclassification in standard linear and generalized linear models is well known to lead to biased results. We provide an approach to extend misclassification modeling to the important area of hierarchical generalized linear models.

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

LiDAR based prediction of forest biomass using hierarchical models with spatially varying coefficients

Treesearch

Chad Babcock; Andrew O. Finley; John B. Bradford; Randy Kolka; Richard Birdsey; Michael G. Ryan

2015-01-01

Many studies and production inventory systems have shown the utility of coupling covariates derived from Light Detection and Ranging (LiDAR) data with forest variables measured on georeferenced inventory plots through regression models. The objective of this study was to propose and assess the use of a Bayesian hierarchical modeling framework that accommodates both...

Bayesian Hierarchical Grouping: perceptual grouping as mixture estimation

PubMed Central

Froyen, Vicky; Feldman, Jacob; Singh, Manish

2015-01-01

We propose a novel framework for perceptual grouping based on the idea of mixture models, called Bayesian Hierarchical Grouping (BHG). In BHG we assume that the configuration of image elements is generated by a mixture of distinct objects, each of which generates image elements according to some generative assumptions. Grouping, in this framework, means estimating the number and the parameters of the mixture components that generated the image, including estimating which image elements are “owned” by which objects. We present a tractable implementation of the framework, based on the hierarchical clustering approach of Heller and Ghahramani (2005). We illustrate it with examples drawn from a number of classical perceptual grouping problems, including dot clustering, contour integration, and part decomposition. Our approach yields an intuitive hierarchical representation of image elements, giving an explicit decomposition of the image into mixture components, along with estimates of the probability of various candidate decompositions. We show that BHG accounts well for a diverse range of empirical data drawn from the literature. Because BHG provides a principled quantification of the plausibility of grouping interpretations over a wide range of grouping problems, we argue that it provides an appealing unifying account of the elusive Gestalt notion of Prägnanz. PMID:26322548

A bayesian hierarchical model for spatio-temporal prediction and uncertainty assessment using repeat LiDAR acquisitions for the Kenai Peninsula, AK, USA

Treesearch

Chad Babcock; Hans Andersen; Andrew O. Finley; Bruce D. Cook

2015-01-01

Models leveraging repeat LiDAR and field collection campaigns may be one possible mechanism to monitor carbon flux in remote forested regions. Here, we look to the spatio-temporally data-rich Kenai Peninsula in Alaska, USA to examine the potential for Bayesian spatio-temporal mapping of terrestrial forest carbon storage and uncertainty.

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.

Maximum likelihood Bayesian model averaging and its predictive analysis for groundwater reactive transport models

USGS Publications Warehouse

Curtis, Gary P.; Lu, Dan; Ye, Ming

2015-01-01

While Bayesian model averaging (BMA) has been widely used in groundwater modeling, it is infrequently applied to groundwater reactive transport modeling because of multiple sources of uncertainty in the coupled hydrogeochemical processes and because of the long execution time of each model run. To resolve these problems, this study analyzed different levels of uncertainty in a hierarchical way, and used the maximum likelihood version of BMA, i.e., MLBMA, to improve the computational efficiency. This study demonstrates the applicability of MLBMA to groundwater reactive transport modeling in a synthetic case in which twenty-seven reactive transport models were designed to predict the reactive transport of hexavalent uranium (U(VI)) based on observations at a former uranium mill site near Naturita, CO. These reactive transport models contain three uncertain model components, i.e., parameterization of hydraulic conductivity, configuration of model boundary, and surface complexation reactions that simulate U(VI) adsorption. These uncertain model components were aggregated into the alternative models by integrating a hierarchical structure into MLBMA. The modeling results of the individual models and MLBMA were analyzed to investigate their predictive performance. The predictive logscore results show that MLBMA generally outperforms the best model, suggesting that using MLBMA is a sound strategy to achieve more robust model predictions relative to a single model. MLBMA works best when the alternative models are structurally distinct and have diverse model predictions. When correlation in model structure exists, two strategies were used to improve predictive performance by retaining structurally distinct models or assigning smaller prior model probabilities to correlated models. Since the synthetic models were designed using data from the Naturita site, the results of this study are expected to provide guidance for real-world modeling. Limitations of applying MLBMA to the synthetic study and future real-world modeling are discussed.

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.

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.

A Bayesian Hierarchical Modeling Scheme for Estimating Erosion Rates Under Current Climate Conditions

NASA Astrophysics Data System (ADS)

Lowman, L.; Barros, A. P.

2014-12-01

Computational modeling of surface erosion processes is inherently difficult because of the four-dimensional nature of the problem and the multiple temporal and spatial scales that govern individual mechanisms. Landscapes are modified via surface and fluvial erosion and exhumation, each of which takes place over a range of time scales. Traditional field measurements of erosion/exhumation rates are scale dependent, often valid for a single point-wise location or averaging over large aerial extents and periods with intense and mild erosion. We present a method of remotely estimating erosion rates using a Bayesian hierarchical model based upon the stream power erosion law (SPEL). A Bayesian approach allows for estimating erosion rates using the deterministic relationship given by the SPEL and data on channel slopes and precipitation at the basin and sub-basin scale. The spatial scale associated with this framework is the elevation class, where each class is characterized by distinct morphologic behavior observed through different modes in the distribution of basin outlet elevations. Interestingly, the distributions of first-order outlets are similar in shape and extent to the distribution of precipitation events (i.e. individual storms) over a 14-year period between 1998-2011. We demonstrate an application of the Bayesian hierarchical modeling framework for five basins and one intermontane basin located in the central Andes between 5S and 20S. Using remotely sensed data of current annual precipitation rates from the Tropical Rainfall Measuring Mission (TRMM) and topography from a high resolution (3 arc-seconds) digital elevation map (DEM), our erosion rate estimates are consistent with decadal-scale estimates based on landslide mapping and sediment flux observations and 1-2 orders of magnitude larger than most millennial and million year timescale estimates from thermochronology and cosmogenic nuclides.

Tracing the influence of land-use change on water quality and coral reefs using a Bayesian model.

PubMed

Brown, Christopher J; Jupiter, Stacy D; Albert, Simon; Klein, Carissa J; Mangubhai, Sangeeta; Maina, Joseph M; Mumby, Peter; Olley, Jon; Stewart-Koster, Ben; Tulloch, Vivitskaia; Wenger, Amelia

2017-07-06

Coastal ecosystems can be degraded by poor water quality. Tracing the causes of poor water quality back to land-use change is necessary to target catchment management for coastal zone management. However, existing models for tracing the sources of pollution require extensive data-sets which are not available for many of the world's coral reef regions that may have severe water quality issues. Here we develop a hierarchical Bayesian model that uses freely available satellite data to infer the connection between land-uses in catchments and water clarity in coastal oceans. We apply the model to estimate the influence of land-use change on water clarity in Fiji. We tested the model's predictions against underwater surveys, finding that predictions of poor water quality are consistent with observations of high siltation and low coverage of sediment-sensitive coral genera. The model thus provides a means to link land-use change to declines in coastal water quality.

Learning coefficient of generalization error in Bayesian estimation and vandermonde matrix-type singularity.

PubMed

Aoyagi, Miki; Nagata, Kenji

2012-06-01

The term algebraic statistics arises from the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry (Sturmfels, 2009 ). The purpose of our study is to consider the generalization error and stochastic complexity in learning theory by using the log-canonical threshold in algebraic geometry. Such thresholds correspond to the main term of the generalization error in Bayesian estimation, which is called a learning coefficient (Watanabe, 2001a , 2001b ). The learning coefficient serves to measure the learning efficiencies in hierarchical learning models. In this letter, we consider learning coefficients for Vandermonde matrix-type singularities, by using a new approach: focusing on the generators of the ideal, which defines singularities. We give tight new bound values of learning coefficients for the Vandermonde matrix-type singularities and the explicit values with certain conditions. By applying our results, we can show the learning coefficients of three-layered neural networks and normal mixture models.

Hierarchical Bayesian modelling of mobility metrics for hazard model input calibration

NASA Astrophysics Data System (ADS)

Calder, Eliza; Ogburn, Sarah; Spiller, Elaine; Rutarindwa, Regis; Berger, Jim

2015-04-01

In this work we present a method to constrain flow mobility input parameters for pyroclastic flow models using hierarchical Bayes modeling of standard mobility metrics such as H/L and flow volume etc. The advantage of hierarchical modeling is that it can leverage the information in global dataset for a particular mobility metric in order to reduce the uncertainty in modeling of an individual volcano, especially important where individual volcanoes have only sparse datasets. We use compiled pyroclastic flow runout data from Colima, Merapi, Soufriere Hills, Unzen and Semeru volcanoes, presented in an open-source database FlowDat (https://vhub.org/groups/massflowdatabase). While the exact relationship between flow volume and friction varies somewhat between volcanoes, dome collapse flows originating from the same volcano exhibit similar mobility relationships. Instead of fitting separate regression models for each volcano dataset, we use a variation of the hierarchical linear model (Kass and Steffey, 1989). The model presents a hierarchical structure with two levels; all dome collapse flows and dome collapse flows at specific volcanoes. The hierarchical model allows us to assume that the flows at specific volcanoes share a common distribution of regression slopes, then solves for that distribution. We present comparisons of the 95% confidence intervals on the individual regression lines for the data set from each volcano as well as those obtained from the hierarchical model. The results clearly demonstrate the advantage of considering global datasets using this technique. The technique developed is demonstrated here for mobility metrics, but can be applied to many other global datasets of volcanic parameters. In particular, such methods can provide a means to better contain parameters for volcanoes for which we only have sparse data, a ubiquitous problem in volcanology.

Spatio-temporal hierarchical modeling of rates and variability of Holocene sea-level changes in the western North Atlantic and the Caribbean

NASA Astrophysics Data System (ADS)

Ashe, E.; Kopp, R. E.; Khan, N.; Horton, B.; Engelhart, S. E.

2016-12-01

Sea level varies over of both space and time. Prior to the instrumental period, the sea-level record depends upon geological reconstructions that contain vertical and temporal uncertainty. Spatio-temporal statistical models enable the interpretation of RSL and rates of change as well as the reconstruction of the entire sea-level field from such noisy data. Hierarchical models explicitly distinguish between a process level, which characterizes the spatio-temporal field, and a data level, by which sparse proxy data and its noise is recorded. A hyperparameter level depicts prior expectations about the structure of variability in the spatio-temporal field. Spatio-temporal hierarchical models are amenable to several analysis approaches, with tradeoffs regarding computational efficiency and comprehensiveness of uncertainty characterization. A fully-Bayesian hierarchical model (BHM), which places prior probability distributions upon the hyperparameters, is more computationally intensive than an empirical hierarchical model (EHM), which uses point estimates of hyperparameters, derived from the data [1]. Here, we assess the sensitivity of posterior estimates of relative sea level (RSL) and rates to different statistical approaches by varying prior assumptions about the spatial and temporal structure of sea-level variability and applying multiple analytical approaches to Holocene sea-level proxies along the Atlantic coast of North American and the Caribbean [2]. References: 1. N Cressie, Wikle CK (2011) Statistics for spatio-temporal data (John Wiley & Sons). 2. Kahn N et al. (2016). Quaternary Science Reviews (in revision).

What are hierarchical models and how do we analyze them?

USGS Publications Warehouse

Royle, Andy

2016-01-01

In this chapter we provide a basic definition of hierarchical models and introduce the two canonical hierarchical models in this book: site occupancy and N-mixture models. The former is a hierarchical extension of logistic regression and the latter is a hierarchical extension of Poisson regression. We introduce basic concepts of probability modeling and statistical inference including likelihood and Bayesian perspectives. We go through the mechanics of maximizing the likelihood and characterizing the posterior distribution by Markov chain Monte Carlo (MCMC) methods. We give a general perspective on topics such as model selection and assessment of model fit, although we demonstrate these topics in practice in later chapters (especially Chapters 5, 6, 7, and 10 Chapter 5 Chapter 6 Chapter 7 Chapter 10)

Bayesian model reduction and empirical Bayes for group (DCM) studies

PubMed Central

Friston, Karl J.; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E.; van Wijk, Bernadette C.M.; Ziegler, Gabriel; Zeidman, Peter

2016-01-01

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level – e.g., dynamic causal models – and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. PMID:26569570

Investigating different approaches to develop informative priors in hierarchical Bayesian safety performance functions.

PubMed

Yu, Rongjie; Abdel-Aty, Mohamed

2013-07-01

The Bayesian inference method has been frequently adopted to develop safety performance functions. One advantage of the Bayesian inference is that prior information for the independent variables can be included in the inference procedures. However, there are few studies that discussed how to formulate informative priors for the independent variables and evaluated the effects of incorporating informative priors in developing safety performance functions. This paper addresses this deficiency by introducing four approaches of developing informative priors for the independent variables based on historical data and expert experience. Merits of these informative priors have been tested along with two types of Bayesian hierarchical models (Poisson-gamma and Poisson-lognormal models). Deviance information criterion (DIC), R-square values, and coefficients of variance for the estimations were utilized as evaluation measures to select the best model(s). Comparison across the models indicated that the Poisson-gamma model is superior with a better model fit and it is much more robust with the informative priors. Moreover, the two-stage Bayesian updating informative priors provided the best goodness-of-fit and coefficient estimation accuracies. Furthermore, informative priors for the inverse dispersion parameter have also been introduced and tested. Different types of informative priors' effects on the model estimations and goodness-of-fit have been compared and concluded. Finally, based on the results, recommendations for future research topics and study applications have been made. Copyright © 2013 Elsevier Ltd. All rights reserved.

Multinomial Bayesian learning for modeling classical and nonclassical receptive field properties.

PubMed

Hosoya, Haruo

2012-08-01

We study the interplay of Bayesian inference and natural image learning in a hierarchical vision system, in relation to the response properties of early visual cortex. We particularly focus on a Bayesian network with multinomial variables that can represent discrete feature spaces similar to hypercolumns combining minicolumns, enforce sparsity of activation to learn efficient representations, and explain divisive normalization. We demonstrate that maximal-likelihood learning using sampling-based Bayesian inference gives rise to classical receptive field properties similar to V1 simple cells and V2 cells, while inference performed on the trained network yields nonclassical context-dependent response properties such as cross-orientation suppression and filling in. Comparison with known physiological properties reveals some qualitative and quantitative similarities.

INFERRING THE ECCENTRICITY DISTRIBUTION

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

Hogg, David W.; Bovy, Jo; Myers, Adam D., E-mail: david.hogg@nyu.ed

2010-12-20

Standard maximum-likelihood estimators for binary-star and exoplanet eccentricities are biased high, in the sense that the estimated eccentricity tends to be larger than the true eccentricity. As with most non-trivial observables, a simple histogram of estimated eccentricities is not a good estimate of the true eccentricity distribution. Here, we develop and test a hierarchical probabilistic method for performing the relevant meta-analysis, that is, inferring the true eccentricity distribution, taking as input the likelihood functions for the individual star eccentricities, or samplings of the posterior probability distributions for the eccentricities (under a given, uninformative prior). The method is a simple implementationmore » of a hierarchical Bayesian model; it can also be seen as a kind of heteroscedastic deconvolution. It can be applied to any quantity measured with finite precision-other orbital parameters, or indeed any astronomical measurements of any kind, including magnitudes, distances, or photometric redshifts-so long as the measurements have been communicated as a likelihood function or a posterior sampling.« less

Mapping brucellosis increases relative to elk density using hierarchical Bayesian models

USGS Publications Warehouse

Cross, Paul C.; Heisey, Dennis M.; Scurlock, Brandon M.; Edwards, William H.; Brennan, Angela; Ebinger, Michael R.

2010-01-01

The relationship between host density and parasite transmission is central to the effectiveness of many disease management strategies. Few studies, however, have empirically estimated this relationship particularly in large mammals. We applied hierarchical Bayesian methods to a 19-year dataset of over 6400 brucellosis tests of adult female elk (Cervus elaphus) in northwestern Wyoming. Management captures that occurred from January to March were over two times more likely to be seropositive than hunted elk that were killed in September to December, while accounting for site and year effects. Areas with supplemental feeding grounds for elk had higher seroprevalence in 1991 than other regions, but by 2009 many areas distant from the feeding grounds were of comparable seroprevalence. The increases in brucellosis seroprevalence were correlated with elk densities at the elk management unit, or hunt area, scale (mean 2070 km2; range = [95–10237]). The data, however, could not differentiate among linear and non-linear effects of host density. Therefore, control efforts that focus on reducing elk densities at a broad spatial scale were only weakly supported. Additional research on how a few, large groups within a region may be driving disease dynamics is needed for more targeted and effective management interventions. Brucellosis appears to be expanding its range into new regions and elk populations, which is likely to further complicate the United States brucellosis eradication program. This study is an example of how the dynamics of host populations can affect their ability to serve as disease reservoirs.

Modeling Heterogeneity in Relationships between Initial Status and Rates of Change: Latent Variable Regression in a Three-Level Hierarchical Model. CSE Report 647

ERIC Educational Resources Information Center

Choi, Kilchan; Seltzer, Michael

2005-01-01

In studies of change in education and numerous other fields, interest often centers on how differences in the status of individuals at the start of a time period of substantive interest relate to differences in subsequent change. This report presents a fully Bayesian approach to estimating three-level hierarchical models in which latent variable…

A hierarchical model for spatial capture-recapture data

USGS Publications Warehouse

Royle, J. Andrew; Young, K.V.

2008-01-01

Estimating density is a fundamental objective of many animal population studies. Application of methods for estimating population size from ostensibly closed populations is widespread, but ineffective for estimating absolute density because most populations are subject to short-term movements or so-called temporary emigration. This phenomenon invalidates the resulting estimates because the effective sample area is unknown. A number of methods involving the adjustment of estimates based on heuristic considerations are in widespread use. In this paper, a hierarchical model of spatially indexed capture recapture data is proposed for sampling based on area searches of spatial sample units subject to uniform sampling intensity. The hierarchical model contains explicit models for the distribution of individuals and their movements, in addition to an observation model that is conditional on the location of individuals during sampling. Bayesian analysis of the hierarchical model is achieved by the use of data augmentation, which allows for a straightforward implementation in the freely available software WinBUGS. We present results of a simulation study that was carried out to evaluate the operating characteristics of the Bayesian estimator under variable densities and movement patterns of individuals. An application of the model is presented for survey data on the flat-tailed horned lizard (Phrynosoma mcallii) in Arizona, USA.

Improving Hierarchical Models Using Historical Data with Applications in High-Throughput Genomics Data Analysis.

PubMed

Li, Ben; Li, Yunxiao; Qin, Zhaohui S

2017-06-01

Modern high-throughput biotechnologies such as microarray and next generation sequencing produce a massive amount of information for each sample assayed. However, in a typical high-throughput experiment, only limited amount of data are observed for each individual feature, thus the classical 'large p , small n ' problem. Bayesian hierarchical model, capable of borrowing strength across features within the same dataset, has been recognized as an effective tool in analyzing such data. However, the shrinkage effect, the most prominent feature of hierarchical features, can lead to undesirable over-correction for some features. In this work, we discuss possible causes of the over-correction problem and propose several alternative solutions. Our strategy is rooted in the fact that in the Big Data era, large amount of historical data are available which should be taken advantage of. Our strategy presents a new framework to enhance the Bayesian hierarchical model. Through simulation and real data analysis, we demonstrated superior performance of the proposed strategy. Our new strategy also enables borrowing information across different platforms which could be extremely useful with emergence of new technologies and accumulation of data from different platforms in the Big Data era. Our method has been implemented in R package "adaptiveHM", which is freely available from https://github.com/benliemory/adaptiveHM.

Improving Hierarchical Models Using Historical Data with Applications in High-Throughput Genomics Data Analysis

PubMed Central

Li, Ben; Li, Yunxiao; Qin, Zhaohui S.

2016-01-01

Modern high-throughput biotechnologies such as microarray and next generation sequencing produce a massive amount of information for each sample assayed. However, in a typical high-throughput experiment, only limited amount of data are observed for each individual feature, thus the classical ‘large p, small n’ problem. Bayesian hierarchical model, capable of borrowing strength across features within the same dataset, has been recognized as an effective tool in analyzing such data. However, the shrinkage effect, the most prominent feature of hierarchical features, can lead to undesirable over-correction for some features. In this work, we discuss possible causes of the over-correction problem and propose several alternative solutions. Our strategy is rooted in the fact that in the Big Data era, large amount of historical data are available which should be taken advantage of. Our strategy presents a new framework to enhance the Bayesian hierarchical model. Through simulation and real data analysis, we demonstrated superior performance of the proposed strategy. Our new strategy also enables borrowing information across different platforms which could be extremely useful with emergence of new technologies and accumulation of data from different platforms in the Big Data era. Our method has been implemented in R package “adaptiveHM”, which is freely available from https://github.com/benliemory/adaptiveHM. PMID:28919931

Bayesian Hierarchical Random Intercept Model Based on Three Parameter Gamma Distribution

NASA Astrophysics Data System (ADS)

Wirawati, Ika; Iriawan, Nur; Irhamah

2017-06-01

Hierarchical data structures are common throughout many areas of research. Beforehand, the existence of this type of data was less noticed in the analysis. The appropriate statistical analysis to handle this type of data is the hierarchical linear model (HLM). This article will focus only on random intercept model (RIM), as a subclass of HLM. This model assumes that the intercept of models in the lowest level are varied among those models, and their slopes are fixed. The differences of intercepts were suspected affected by some variables in the upper level. These intercepts, therefore, are regressed against those upper level variables as predictors. The purpose of this paper would demonstrate a proven work of the proposed two level RIM of the modeling on per capita household expenditure in Maluku Utara, which has five characteristics in the first level and three characteristics of districts/cities in the second level. The per capita household expenditure data in the first level were captured by the three parameters Gamma distribution. The model, therefore, would be more complex due to interaction of many parameters for representing the hierarchical structure and distribution pattern of the data. To simplify the estimation processes of parameters, the computational Bayesian method couple with Markov Chain Monte Carlo (MCMC) algorithm and its Gibbs Sampling are employed.

Hierarchical Bayesian Approach To Reduce Uncertainty in the Aquatic Effect Assessment of Realistic Chemical Mixtures.

PubMed

Oldenkamp, Rik; Hendriks, Harrie W M; van de Meent, Dik; Ragas, Ad M J

2015-09-01

Species in the aquatic environment differ in their toxicological sensitivity to the various chemicals they encounter. In aquatic risk assessment, this interspecies variation is often quantified via species sensitivity distributions. Because the information available for the characterization of these distributions is typically limited, optimal use of information is essential to reduce uncertainty involved in the assessment. In the present study, we show that the credibility intervals on the estimated potentially affected fraction of species after exposure to a mixture of chemicals at environmentally relevant surface water concentrations can be extremely wide if a classical approach is followed, in which each chemical in the mixture is considered in isolation. As an alternative, we propose a hierarchical Bayesian approach, in which knowledge on the toxicity of chemicals other than those assessed is incorporated. A case study with a mixture of 13 pharmaceuticals demonstrates that this hierarchical approach results in more realistic estimations of the potentially affected fraction, as a result of reduced uncertainty in species sensitivity distributions for data-poor chemicals.

A Development of Nonstationary Regional Frequency Analysis Model with Large-scale Climate Information: Its Application to Korean Watershed

NASA Astrophysics Data System (ADS)

Kim, Jin-Young; Kwon, Hyun-Han; Kim, Hung-Soo

2015-04-01

The existing regional frequency analysis has disadvantages in that it is difficult to consider geographical characteristics in estimating areal rainfall. In this regard, this study aims to develop a hierarchical Bayesian model based nonstationary regional frequency analysis in that spatial patterns of the design rainfall with geographical information (e.g. latitude, longitude and altitude) are explicitly incorporated. This study assumes that the parameters of Gumbel (or GEV distribution) are a function of geographical characteristics within a general linear regression framework. Posterior distribution of the regression parameters are estimated by Bayesian Markov Chain Monte Carlo (MCMC) method, and the identified functional relationship is used to spatially interpolate the parameters of the distributions by using digital elevation models (DEM) as inputs. The proposed model is applied to derive design rainfalls over the entire Han-river watershed. It was found that the proposed Bayesian regional frequency analysis model showed similar results compared to L-moment based regional frequency analysis. In addition, the model showed an advantage in terms of quantifying uncertainty of the design rainfall and estimating the area rainfall considering geographical information. Finally, comprehensive discussion on design rainfall in the context of nonstationary will be presented. KEYWORDS: Regional frequency analysis, Nonstationary, Spatial information, Bayesian Acknowledgement This research was supported by a grant (14AWMP-B082564-01) from Advanced Water Management Research Program funded by Ministry of Land, Infrastructure and Transport of Korean government.

A hierarchical Bayesian GEV model for improving local and regional flood quantile estimates

NASA Astrophysics Data System (ADS)

Lima, Carlos H. R.; Lall, Upmanu; Troy, Tara; Devineni, Naresh

2016-10-01

We estimate local and regional Generalized Extreme Value (GEV) distribution parameters for flood frequency analysis in a multilevel, hierarchical Bayesian framework, to explicitly model and reduce uncertainties. As prior information for the model, we assume that the GEV location and scale parameters for each site come from independent log-normal distributions, whose mean parameter scales with the drainage area. From empirical and theoretical arguments, the shape parameter for each site is shrunk towards a common mean. Non-informative prior distributions are assumed for the hyperparameters and the MCMC method is used to sample from the joint posterior distribution. The model is tested using annual maximum series from 20 streamflow gauges located in an 83,000 km2 flood prone basin in Southeast Brazil. The results show a significant reduction of uncertainty estimates of flood quantile estimates over the traditional GEV model, particularly for sites with shorter records. For return periods within the range of the data (around 50 years), the Bayesian credible intervals for the flood quantiles tend to be narrower than the classical confidence limits based on the delta method. As the return period increases beyond the range of the data, the confidence limits from the delta method become unreliable and the Bayesian credible intervals provide a way to estimate satisfactory confidence bands for the flood quantiles considering parameter uncertainties and regional information. In order to evaluate the applicability of the proposed hierarchical Bayesian model for regional flood frequency analysis, we estimate flood quantiles for three randomly chosen out-of-sample sites and compare with classical estimates using the index flood method. The posterior distributions of the scaling law coefficients are used to define the predictive distributions of the GEV location and scale parameters for the out-of-sample sites given only their drainage areas and the posterior distribution of the average shape parameter is taken as the regional predictive distribution for this parameter. While the index flood method does not provide a straightforward way to consider the uncertainties in the index flood and in the regional parameters, the results obtained here show that the proposed Bayesian method is able to produce adequate credible intervals for flood quantiles that are in accordance with empirical estimates.

Variational learning and bits-back coding: an information-theoretic view to Bayesian learning.

PubMed

Honkela, Antti; Valpola, Harri

2004-07-01

The bits-back coding first introduced by Wallace in 1990 and later by Hinton and van Camp in 1993 provides an interesting link between Bayesian learning and information-theoretic minimum-description-length (MDL) learning approaches. The bits-back coding allows interpreting the cost function used in the variational Bayesian method called ensemble learning as a code length in addition to the Bayesian view of misfit of the posterior approximation and a lower bound of model evidence. Combining these two viewpoints provides interesting insights to the learning process and the functions of different parts of the model. In this paper, the problem of variational Bayesian learning of hierarchical latent variable models is used to demonstrate the benefits of the two views. The code-length interpretation provides new views to many parts of the problem such as model comparison and pruning and helps explain many phenomena occurring in learning.

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.

Multimethod, multistate Bayesian hierarchical modeling approach for use in regional monitoring of wolves.

PubMed

Jiménez, José; García, Emilio J; Llaneza, Luis; Palacios, Vicente; González, Luis Mariano; García-Domínguez, Francisco; Múñoz-Igualada, Jaime; López-Bao, José Vicente

2016-08-01

In many cases, the first step in large-carnivore management is to obtain objective, reliable, and cost-effective estimates of population parameters through procedures that are reproducible over time. However, monitoring predators over large areas is difficult, and the data have a high level of uncertainty. We devised a practical multimethod and multistate modeling approach based on Bayesian hierarchical-site-occupancy models that combined multiple survey methods to estimate different population states for use in monitoring large predators at a regional scale. We used wolves (Canis lupus) as our model species and generated reliable estimates of the number of sites with wolf reproduction (presence of pups). We used 2 wolf data sets from Spain (Western Galicia in 2013 and Asturias in 2004) to test the approach. Based on howling surveys, the naïve estimation (i.e., estimate based only on observations) of the number of sites with reproduction was 9 and 25 sites in Western Galicia and Asturias, respectively. Our model showed 33.4 (SD 9.6) and 34.4 (3.9) sites with wolf reproduction, respectively. The number of occupied sites with wolf reproduction was 0.67 (SD 0.19) and 0.76 (0.11), respectively. This approach can be used to design more cost-effective monitoring programs (i.e., to define the sampling effort needed per site). Our approach should inspire well-coordinated surveys across multiple administrative borders and populations and lead to improved decision making for management of large carnivores on a landscape level. The use of this Bayesian framework provides a simple way to visualize the degree of uncertainty around population-parameter estimates and thus provides managers and stakeholders an intuitive approach to interpreting monitoring results. Our approach can be widely applied to large spatial scales in wildlife monitoring where detection probabilities differ between population states and where several methods are being used to estimate different population parameters. © 2016 Society for Conservation Biology.

Modeling Heterogeneity in Relationships between Initial Status and Rates of Change: Treating Latent Variable Regression Coefficients as Random Coefficients in a Three-Level Hierarchical Model

ERIC Educational Resources Information Center

Choi, Kilchan; Seltzer, Michael

2010-01-01

In studies of change in education and numerous other fields, interest often centers on how differences in the status of individuals at the start of a period of substantive interest relate to differences in subsequent change. In this article, the authors present a fully Bayesian approach to estimating three-level Hierarchical Models in which latent…

Bayesian model reduction and empirical Bayes for group (DCM) studies.

PubMed

Friston, Karl J; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E; van Wijk, Bernadette C M; Ziegler, Gabriel; Zeidman, Peter

2016-03-01

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level - e.g., dynamic causal models - and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

A Bayesian hierarchical model for accident and injury surveillance.

PubMed

MacNab, Ying C

2003-01-01

This article presents a recent study which applies Bayesian hierarchical methodology to model and analyse accident and injury surveillance data. A hierarchical Poisson random effects spatio-temporal model is introduced and an analysis of inter-regional variations and regional trends in hospitalisations due to motor vehicle accident injuries to boys aged 0-24 in the province of British Columbia, Canada, is presented. The objective of this article is to illustrate how the modelling technique can be implemented as part of an accident and injury surveillance and prevention system where transportation and/or health authorities may routinely examine accidents, injuries, and hospitalisations to target high-risk regions for prevention programs, to evaluate prevention strategies, and to assist in health planning and resource allocation. The innovation of the methodology is its ability to uncover and highlight important underlying structure of the data. Between 1987 and 1996, British Columbia hospital separation registry registered 10,599 motor vehicle traffic injury related hospitalisations among boys aged 0-24 who resided in British Columbia, of which majority (89%) of the injuries occurred to boys aged 15-24. The injuries were aggregated by three age groups (0-4, 5-14, and 15-24), 20 health regions (based of place-of-residence), and 10 calendar years (1987 to 1996) and the corresponding mid-year population estimates were used as 'at risk' population. An empirical Bayes inference technique using penalised quasi-likelihood estimation was implemented to model both rates and counts, with spline smoothing accommodating non-linear temporal effects. The results show that (a) crude rates and ratios at health region level are unstable, (b) the models with spline smoothing enable us to explore possible shapes of injury trends at both the provincial level and the regional level, and (c) the fitted models provide a wealth of information about the patterns (both over space and time) of the injury counts, rates and ratios. During the 10-year period, high injury risk ratios evolved from northwest to central-interior and the southeast [corrected].

A Bayesian Hierarchical Modeling Approach to Predicting Flow in Ungauged Basins

NASA Astrophysics Data System (ADS)

Gronewold, A.; Alameddine, I.; Anderson, R. M.

2009-12-01

Recent innovative approaches to identifying and applying regression-based relationships between land use patterns (such as increasing impervious surface area and decreasing vegetative cover) and rainfall-runoff model parameters represent novel and promising improvements to predicting flow from ungauged basins. In particular, these approaches allow for predicting flows under uncertain and potentially variable future conditions due to rapid land cover changes, variable climate conditions, and other factors. Despite the broad range of literature on estimating rainfall-runoff model parameters, however, the absence of a robust set of modeling tools for identifying and quantifying uncertainties in (and correlation between) rainfall-runoff model parameters represents a significant gap in current hydrological modeling research. Here, we build upon a series of recent publications promoting novel Bayesian and probabilistic modeling strategies for quantifying rainfall-runoff model parameter estimation uncertainty. Our approach applies alternative measures of rainfall-runoff model parameter joint likelihood (including Nash-Sutcliffe efficiency, among others) to simulate samples from the joint parameter posterior probability density function. We then use these correlated samples as response variables in a Bayesian hierarchical model with land use coverage data as predictor variables in order to develop a robust land use-based tool for forecasting flow in ungauged basins while accounting for, and explicitly acknowledging, parameter estimation uncertainty. We apply this modeling strategy to low-relief coastal watersheds of Eastern North Carolina, an area representative of coastal resource waters throughout the world because of its sensitive embayments and because of the abundant (but currently threatened) natural resources it hosts. Consequently, this area is the subject of several ongoing studies and large-scale planning initiatives, including those conducted through the United States Environmental Protection Agency (USEPA) total maximum daily load (TMDL) program, as well as those addressing coastal population dynamics and sea level rise. Our approach has several advantages, including the propagation of parameter uncertainty through a nonparametric probability distribution which avoids common pitfalls of fitting parameters and model error structure to a predetermined parametric distribution function. In addition, by explicitly acknowledging correlation between model parameters (and reflecting those correlations in our predictive model) our model yields relatively efficient prediction intervals (unlike those in the current literature which are often unnecessarily large, and may lead to overly-conservative management actions). Finally, our model helps improve understanding of the rainfall-runoff process by identifying model parameters (and associated catchment attributes) which are most sensitive to current and future land use change patterns. Disclaimer: Although this work was reviewed by EPA and approved for publication, it may not necessarily reflect official Agency policy.

Hierarchical Bayesian Spatio–Temporal Analysis of Climatic and Socio–Economic Determinants of Rocky Mountain Spotted Fever

PubMed Central

Raghavan, Ram K.; Goodin, Douglas G.; Neises, Daniel; Anderson, Gary A.; Ganta, Roman R.

2016-01-01

This study aims to examine the spatio-temporal dynamics of Rocky Mountain spotted fever (RMSF) prevalence in four contiguous states of Midwestern United States, and to determine the impact of environmental and socio–economic factors associated with this disease. Bayesian hierarchical models were used to quantify space and time only trends and spatio–temporal interaction effect in the case reports submitted to the state health departments in the region. Various socio–economic, environmental and climatic covariates screened a priori in a bivariate procedure were added to a main–effects Bayesian model in progressive steps to evaluate important drivers of RMSF space-time patterns in the region. Our results show a steady increase in RMSF incidence over the study period to newer geographic areas, and the posterior probabilities of county-specific trends indicate clustering of high risk counties in the central and southern parts of the study region. At the spatial scale of a county, the prevalence levels of RMSF is influenced by poverty status, average relative humidity, and average land surface temperature (>35°C) in the region, and the relevance of these factors in the context of climate–change impacts on tick–borne diseases are discussed. PMID:26942604

Hierarchical Bayesian Spatio-Temporal Analysis of Climatic and Socio-Economic Determinants of Rocky Mountain Spotted Fever.

PubMed

Raghavan, Ram K; Goodin, Douglas G; Neises, Daniel; Anderson, Gary A; Ganta, Roman R

2016-01-01

This study aims to examine the spatio-temporal dynamics of Rocky Mountain spotted fever (RMSF) prevalence in four contiguous states of Midwestern United States, and to determine the impact of environmental and socio-economic factors associated with this disease. Bayesian hierarchical models were used to quantify space and time only trends and spatio-temporal interaction effect in the case reports submitted to the state health departments in the region. Various socio-economic, environmental and climatic covariates screened a priori in a bivariate procedure were added to a main-effects Bayesian model in progressive steps to evaluate important drivers of RMSF space-time patterns in the region. Our results show a steady increase in RMSF incidence over the study period to newer geographic areas, and the posterior probabilities of county-specific trends indicate clustering of high risk counties in the central and southern parts of the study region. At the spatial scale of a county, the prevalence levels of RMSF is influenced by poverty status, average relative humidity, and average land surface temperature (>35°C) in the region, and the relevance of these factors in the context of climate-change impacts on tick-borne diseases are discussed.

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

Traffic & safety statewide model and GIS modeling.

DOT National Transportation Integrated Search

2012-07-01

Several steps have been taken over the past two years to advance the Utah Department of Transportation (UDOT) safety initiative. Previous research projects began the development of a hierarchical Bayesian model to analyze crashes on Utah roadways. De...

Sampling-free Bayesian inversion with adaptive hierarchical tensor representations

NASA Astrophysics Data System (ADS)

Eigel, Martin; Marschall, Manuel; Schneider, Reinhold

2018-03-01

A sampling-free approach to Bayesian inversion with an explicit polynomial representation of the parameter densities is developed, based on an affine-parametric representation of a linear forward model. This becomes feasible due to the complete treatment in function spaces, which requires an efficient model reduction technique for numerical computations. The advocated perspective yields the crucial benefit that error bounds can be derived for all occuring approximations, leading to provable convergence subject to the discretization parameters. Moreover, it enables a fully adaptive a posteriori control with automatic problem-dependent adjustments of the employed discretizations. The method is discussed in the context of modern hierarchical tensor representations, which are used for the evaluation of a random PDE (the forward model) and the subsequent high-dimensional quadrature of the log-likelihood, alleviating the ‘curse of dimensionality’. Numerical experiments demonstrate the performance and confirm the theoretical results.

Bayesian hierarchical models for smoothing in two-phase studies, with application to small area estimation.

PubMed

Ross, Michelle; Wakefield, Jon

2015-10-01

Two-phase study designs are appealing since they allow for the oversampling of rare sub-populations which improves efficiency. In this paper we describe a Bayesian hierarchical model for the analysis of two-phase data. Such a model is particularly appealing in a spatial setting in which random effects are introduced to model between-area variability. In such a situation, one may be interested in estimating regression coefficients or, in the context of small area estimation, in reconstructing the population totals by strata. The efficiency gains of the two-phase sampling scheme are compared to standard approaches using 2011 birth data from the research triangle area of North Carolina. We show that the proposed method can overcome small sample difficulties and improve on existing techniques. We conclude that the two-phase design is an attractive approach for small area estimation.

Laminar fMRI and computational theories of brain function.

PubMed

Stephan, K E; Petzschner, F H; Kasper, L; Bayer, J; Wellstein, K V; Stefanics, G; Pruessmann, K P; Heinzle, J

2017-11-02

Recently developed methods for functional MRI at the resolution of cortical layers (laminar fMRI) offer a novel window into neurophysiological mechanisms of cortical activity. Beyond physiology, laminar fMRI also offers an unprecedented opportunity to test influential theories of brain function. Specifically, hierarchical Bayesian theories of brain function, such as predictive coding, assign specific computational roles to different cortical layers. Combined with computational models, laminar fMRI offers a unique opportunity to test these proposals noninvasively in humans. This review provides a brief overview of predictive coding and related hierarchical Bayesian theories, summarises their predictions with regard to layered cortical computations, examines how these predictions could be tested by laminar fMRI, and considers methodological challenges. We conclude by discussing the potential of laminar fMRI for clinically useful computational assays of layer-specific information processing. Copyright © 2017 Elsevier Inc. All rights reserved.

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

A Bayesian hierarchical model with spatial variable selection: the effect of weather on insurance claims

PubMed Central

Scheel, Ida; Ferkingstad, Egil; Frigessi, Arnoldo; Haug, Ola; Hinnerichsen, Mikkel; Meze-Hausken, Elisabeth

2013-01-01

Climate change will affect the insurance industry. We develop a Bayesian hierarchical statistical approach to explain and predict insurance losses due to weather events at a local geographic scale. The number of weather-related insurance claims is modelled by combining generalized linear models with spatially smoothed variable selection. Using Gibbs sampling and reversible jump Markov chain Monte Carlo methods, this model is fitted on daily weather and insurance data from each of the 319 municipalities which constitute southern and central Norway for the period 1997–2006. Precise out-of-sample predictions validate the model. Our results show interesting regional patterns in the effect of different weather covariates. In addition to being useful for insurance pricing, our model can be used for short-term predictions based on weather forecasts and for long-term predictions based on downscaled climate models. PMID:23396890

A Flexible Hierarchical Bayesian Modeling Technique for Risk Analysis of Major Accidents.

PubMed

Yu, Hongyang; Khan, Faisal; Veitch, Brian

2017-09-01

Safety analysis of rare events with potentially catastrophic consequences is challenged by data scarcity and uncertainty. Traditional causation-based approaches, such as fault tree and event tree (used to model rare event), suffer from a number of weaknesses. These include the static structure of the event causation, lack of event occurrence data, and need for reliable prior information. In this study, a new hierarchical Bayesian modeling based technique is proposed to overcome these drawbacks. The proposed technique can be used as a flexible technique for risk analysis of major accidents. It enables both forward and backward analysis in quantitative reasoning and the treatment of interdependence among the model parameters. Source-to-source variability in data sources is also taken into account through a robust probabilistic safety analysis. The applicability of the proposed technique has been demonstrated through a case study in marine and offshore industry. © 2017 Society for Risk Analysis.

Generative models for discovering sparse distributed representations.

PubMed Central

Hinton, G E; Ghahramani, Z

1997-01-01

We describe a hierarchical, generative model that can be viewed as a nonlinear generalization of factor analysis and can be implemented in a neural network. The model uses bottom-up, top-down and lateral connections to perform Bayesian perceptual inference correctly. Once perceptual inference has been performed the connection strengths can be updated using a very simple learning rule that only requires locally available information. We demonstrate that the network learns to extract sparse, distributed, hierarchical representations. PMID:9304685

Novelty and Inductive Generalization in Human Reinforcement Learning.

PubMed

Gershman, Samuel J; Niv, Yael

2015-07-01

In reinforcement learning (RL), a decision maker searching for the most rewarding option is often faced with the question: What is the value of an option that has never been tried before? One way to frame this question is as an inductive problem: How can I generalize my previous experience with one set of options to a novel option? We show how hierarchical Bayesian inference can be used to solve this problem, and we describe an equivalence between the Bayesian model and temporal difference learning algorithms that have been proposed as models of RL in humans and animals. According to our view, the search for the best option is guided by abstract knowledge about the relationships between different options in an environment, resulting in greater search efficiency compared to traditional RL algorithms previously applied to human cognition. In two behavioral experiments, we test several predictions of our model, providing evidence that humans learn and exploit structured inductive knowledge to make predictions about novel options. In light of this model, we suggest a new interpretation of dopaminergic responses to novelty. Copyright © 2015 Cognitive Science Society, Inc.

Novelty and Inductive Generalization in Human Reinforcement Learning

PubMed Central

Gershman, Samuel J.; Niv, Yael

2015-01-01

In reinforcement learning, a decision maker searching for the most rewarding option is often faced with the question: what is the value of an option that has never been tried before? One way to frame this question is as an inductive problem: how can I generalize my previous experience with one set of options to a novel option? We show how hierarchical Bayesian inference can be used to solve this problem, and describe an equivalence between the Bayesian model and temporal difference learning algorithms that have been proposed as models of reinforcement learning in humans and animals. According to our view, the search for the best option is guided by abstract knowledge about the relationships between different options in an environment, resulting in greater search efficiency compared to traditional reinforcement learning algorithms previously applied to human cognition. In two behavioral experiments, we test several predictions of our model, providing evidence that humans learn and exploit structured inductive knowledge to make predictions about novel options. In light of this model, we suggest a new interpretation of dopaminergic responses to novelty. PMID:25808176

Spatial Bayesian Latent Factor Regression Modeling of Coordinate-based Meta-analysis Data

PubMed Central

Montagna, Silvia; Wager, Tor; Barrett, Lisa Feldman; Johnson, Timothy D.; Nichols, Thomas E.

2017-01-01

Summary Now over 20 years old, functional MRI (fMRI) has a large and growing literature that is best synthesised with meta-analytic tools. As most authors do not share image data, only the peak activation coordinates (foci) reported in the paper are available for Coordinate-Based Meta-Analysis (CBMA). Neuroimaging meta-analysis is used to 1) identify areas of consistent activation; and 2) build a predictive model of task type or cognitive process for new studies (reverse inference). To simultaneously address these aims, we propose a Bayesian point process hierarchical model for CBMA. We model the foci from each study as a doubly stochastic Poisson process, where the study-specific log intensity function is characterised as a linear combination of a high-dimensional basis set. A sparse representation of the intensities is guaranteed through latent factor modeling of the basis coefficients. Within our framework, it is also possible to account for the effect of study-level covariates (meta-regression), significantly expanding the capabilities of the current neuroimaging meta-analysis methods available. We apply our methodology to synthetic data and neuroimaging meta-analysis datasets. PMID:28498564

Supernova Cosmology Inference with Probabilistic Photometric Redshifts (SCIPPR)

NASA Astrophysics Data System (ADS)

Peters, Christina; Malz, Alex; Hlozek, Renée

2018-01-01

The Bayesian Estimation Applied to Multiple Species (BEAMS) framework employs probabilistic supernova type classifications to do photometric SN cosmology. This work extends BEAMS to replace high-confidence spectroscopic redshifts with photometric redshift probability density functions, a capability that will be essential in the era the Large Synoptic Survey Telescope and other next-generation photometric surveys where it will not be possible to perform spectroscopic follow up on every SN. We present the Supernova Cosmology Inference with Probabilistic Photometric Redshifts (SCIPPR) Bayesian hierarchical model for constraining the cosmological parameters from photometric lightcurves and host galaxy photometry, which includes selection effects and is extensible to uncertainty in the redshift-dependent supernova type proportions. We create a pair of realistic mock catalogs of joint posteriors over supernova type, redshift, and distance modulus informed by photometric supernova lightcurves and over redshift from simulated host galaxy photometry. We perform inference under our model to obtain a joint posterior probability distribution over the cosmological parameters and compare our results with other methods, namely: a spectroscopic subset, a subset of high probability photometrically classified supernovae, and reducing the photometric redshift probability to a single measurement and error bar.

Hierarchical Bayesian method for mapping biogeochemical hot spots using induced polarization imaging

DOE PAGES

Wainwright, Haruko M.; Flores Orozco, Adrian; Bucker, Matthias; ...

2016-01-29

In floodplain environments, a naturally reduced zone (NRZ) is considered to be a common biogeochemical hot spot, having distinct microbial and geochemical characteristics. Although important for understanding their role in mediating floodplain biogeochemical processes, mapping the subsurface distribution of NRZs over the dimensions of a floodplain is challenging, as conventional wellbore data are typically spatially limited and the distribution of NRZs is heterogeneous. In this work, we present an innovative methodology for the probabilistic mapping of NRZs within a three-dimensional (3-D) subsurface domain using induced polarization imaging, which is a noninvasive geophysical technique. Measurements consist of surface geophysical surveys andmore » drilling-recovered sediments at the U.S. Department of Energy field site near Rifle, CO (USA). Inversion of surface time domain-induced polarization (TDIP) data yielded 3-D images of the complex electrical resistivity, in terms of magnitude and phase, which are associated with mineral precipitation and other lithological properties. By extracting the TDIP data values colocated with wellbore lithological logs, we found that the NRZs have a different distribution of resistivity and polarization from the other aquifer sediments. To estimate the spatial distribution of NRZs, we developed a Bayesian hierarchical model to integrate the geophysical and wellbore data. In addition, the resistivity images were used to estimate hydrostratigraphic interfaces under the floodplain. Validation results showed that the integration of electrical imaging and wellbore data using a Bayesian hierarchical model was capable of mapping spatially heterogeneous interfaces and NRZ distributions thereby providing a minimally invasive means to parameterize a hydrobiogeochemical model of the floodplain.« less

Hierarchical Bayesian Markov switching models with application to predicting spawning success of shovelnose sturgeon

USGS Publications Warehouse

Holan, S.H.; Davis, G.M.; Wildhaber, M.L.; DeLonay, A.J.; Papoulias, D.M.

2009-01-01

The timing of spawning in fish is tightly linked to environmental factors; however, these factors are not very well understood for many species. Specifically, little information is available to guide recruitment efforts for endangered species such as the sturgeon. Therefore, we propose a Bayesian hierarchical model for predicting the success of spawning of the shovelnose sturgeon which uses both biological and behavioural (longitudinal) data. In particular, we use data that were produced from a tracking study that was conducted in the Lower Missouri River. The data that were produced from this study consist of biological variables associated with readiness to spawn along with longitudinal behavioural data collected by using telemetry and archival data storage tags. These high frequency data are complex both biologically and in the underlying behavioural process. To accommodate such complexity we developed a hierarchical linear regression model that uses an eigenvalue predictor, derived from the transition probability matrix of a two-state Markov switching model with generalized auto-regressive conditional heteroscedastic dynamics. Finally, to minimize the computational burden that is associated with estimation of this model, a parallel computing approach is proposed. ?? Journal compilation 2009 Royal Statistical Society.

Hierarchical models for estimating density from DNA mark-recapture studies

USGS Publications Warehouse

Gardner, B.; Royle, J. Andrew; Wegan, M.T.

2009-01-01

Genetic sampling is increasingly used as a tool by wildlife biologists and managers to estimate abundance and density of species. Typically, DNA is used to identify individuals captured in an array of traps ( e. g., baited hair snares) from which individual encounter histories are derived. Standard methods for estimating the size of a closed population can be applied to such data. However, due to the movement of individuals on and off the trapping array during sampling, the area over which individuals are exposed to trapping is unknown, and so obtaining unbiased estimates of density has proved difficult. We propose a hierarchical spatial capture-recapture model which contains explicit models for the spatial point process governing the distribution of individuals and their exposure to (via movement) and detection by traps. Detection probability is modeled as a function of each individual's distance to the trap. We applied this model to a black bear (Ursus americanus) study conducted in 2006 using a hair-snare trap array in the Adirondack region of New York, USA. We estimated the density of bears to be 0.159 bears/km2, which is lower than the estimated density (0.410 bears/km2) based on standard closed population techniques. A Bayesian analysis of the model is fully implemented in the software program WinBUGS.

Subjective value of risky foods for individual domestic chicks: a hierarchical Bayesian model.

PubMed

Kawamori, Ai; Matsushima, Toshiya

2010-05-01

For animals to decide which prey to attack, the gain and delay of the food item must be integrated in a value function. However, the subjective value is not obtained by expected profitability when it is accompanied by risk. To estimate the subjective value, we examined choices in a cross-shaped maze with two colored feeders in domestic chicks. When tested by a reversal in food amount or delay, chicks changed choices similarly in both conditions (experiment 1). We therefore examined risk sensitivity for amount and delay (experiment 2) by supplying one feeder with food of fixed profitability and the alternative feeder with high- or low-profitability food at equal probability. Profitability varied in amount (groups 1 and 2 at high and low variance) or in delay (group 3). To find the equilibrium, the amount (groups 1 and 2) or delay (group 3) of the food in the fixed feeder was adjusted in a total of 18 blocks. The Markov chain Monte Carlo method was applied to a hierarchical Bayesian model to estimate the subjective value. Chicks undervalued the variable feeder in group 1 and were indifferent in group 2 but overvalued the variable feeder in group 3 at a population level. Re-examination without the titration procedure (experiment 3) suggested that the subjective value was not absolute for each option. When the delay was varied, the variable option was often given a paradoxically high value depending on fixed alternative. Therefore, the basic assumption of the uniquely determined value function might be questioned.

Cosmological parameters, shear maps and power spectra from CFHTLenS using Bayesian hierarchical inference

NASA Astrophysics Data System (ADS)

Alsing, Justin; Heavens, Alan; Jaffe, Andrew H.

2017-04-01

We apply two Bayesian hierarchical inference schemes to infer shear power spectra, shear maps and cosmological parameters from the Canada-France-Hawaii Telescope (CFHTLenS) weak lensing survey - the first application of this method to data. In the first approach, we sample the joint posterior distribution of the shear maps and power spectra by Gibbs sampling, with minimal model assumptions. In the second approach, we sample the joint posterior of the shear maps and cosmological parameters, providing a new, accurate and principled approach to cosmological parameter inference from cosmic shear data. As a first demonstration on data, we perform a two-bin tomographic analysis to constrain cosmological parameters and investigate the possibility of photometric redshift bias in the CFHTLenS data. Under the baseline ΛCDM (Λ cold dark matter) model, we constrain S_8 = σ _8(Ω _m/0.3)^{0.5} = 0.67+0.03-0.03 (68 per cent), consistent with previous CFHTLenS analyses but in tension with Planck. Adding neutrino mass as a free parameter, we are able to constrain ∑mν < 4.6 eV (95 per cent) using CFHTLenS data alone. Including a linear redshift-dependent photo-z bias Δz = p2(z - p1), we find p_1=-0.25+0.53-0.60 and p_2 = -0.15+0.17-0.15, and tension with Planck is only alleviated under very conservative prior assumptions. Neither the non-minimal neutrino mass nor photo-z bias models are significantly preferred by the CFHTLenS (two-bin tomography) data.

Maximum likelihood Bayesian model averaging and its predictive analysis for groundwater reactive transport models

DOE PAGES

Lu, Dan; Ye, Ming; Curtis, Gary P.

2015-08-01

While Bayesian model averaging (BMA) has been widely used in groundwater modeling, it is infrequently applied to groundwater reactive transport modeling because of multiple sources of uncertainty in the coupled hydrogeochemical processes and because of the long execution time of each model run. To resolve these problems, this study analyzed different levels of uncertainty in a hierarchical way, and used the maximum likelihood version of BMA, i.e., MLBMA, to improve the computational efficiency. Our study demonstrates the applicability of MLBMA to groundwater reactive transport modeling in a synthetic case in which twenty-seven reactive transport models were designed to predict themore » reactive transport of hexavalent uranium (U(VI)) based on observations at a former uranium mill site near Naturita, CO. Moreover, these reactive transport models contain three uncertain model components, i.e., parameterization of hydraulic conductivity, configuration of model boundary, and surface complexation reactions that simulate U(VI) adsorption. These uncertain model components were aggregated into the alternative models by integrating a hierarchical structure into MLBMA. The modeling results of the individual models and MLBMA were analyzed to investigate their predictive performance. The predictive logscore results show that MLBMA generally outperforms the best model, suggesting that using MLBMA is a sound strategy to achieve more robust model predictions relative to a single model. MLBMA works best when the alternative models are structurally distinct and have diverse model predictions. When correlation in model structure exists, two strategies were used to improve predictive performance by retaining structurally distinct models or assigning smaller prior model probabilities to correlated models. Since the synthetic models were designed using data from the Naturita site, the results of this study are expected to provide guidance for real-world modeling. Finally, limitations of applying MLBMA to the synthetic study and future real-world modeling are discussed.« less

Decoding of Ankle Flexion and Extension from Cortical Current Sources Estimated from Non-invasive Brain Activity Recording Methods.

PubMed

Mejia Tobar, Alejandra; Hyoudou, Rikiya; Kita, Kahori; Nakamura, Tatsuhiro; Kambara, Hiroyuki; Ogata, Yousuke; Hanakawa, Takashi; Koike, Yasuharu; Yoshimura, Natsue

2017-01-01

The classification of ankle movements from non-invasive brain recordings can be applied to a brain-computer interface (BCI) to control exoskeletons, prosthesis, and functional electrical stimulators for the benefit of patients with walking impairments. In this research, ankle flexion and extension tasks at two force levels in both legs, were classified from cortical current sources estimated by a hierarchical variational Bayesian method, using electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) recordings. The hierarchical prior for the current source estimation from EEG was obtained from activated brain areas and their intensities from an fMRI group (second-level) analysis. The fMRI group analysis was performed on regions of interest defined over the primary motor cortex, the supplementary motor area, and the somatosensory area, which are well-known to contribute to movement control. A sparse logistic regression method was applied for a nine-class classification (eight active tasks and a resting control task) obtaining a mean accuracy of 65.64% for time series of current sources, estimated from the EEG and the fMRI signals using a variational Bayesian method, and a mean accuracy of 22.19% for the classification of the pre-processed of EEG sensor signals, with a chance level of 11.11%. The higher classification accuracy of current sources, when compared to EEG classification accuracy, was attributed to the high number of sources and the different signal patterns obtained in the same vertex for different motor tasks. Since the inverse filter estimation for current sources can be done offline with the present method, the present method is applicable to real-time BCIs. Finally, due to the highly enhanced spatial distribution of current sources over the brain cortex, this method has the potential to identify activation patterns to design BCIs for the control of an affected limb in patients with stroke, or BCIs from motor imagery in patients with spinal cord injury.

Uncertainty and inference in the world of paleoecological data

NASA Astrophysics Data System (ADS)

McLachlan, J. S.; Dawson, A.; Dietze, M.; Finley, M.; Hooten, M.; Itter, M.; Jackson, S. T.; Marlon, J. R.; Raiho, A.; Tipton, J.; Williams, J.

2017-12-01

Proxy data in paleoecology and paleoclimatology share a common set of biases and uncertainties: spatiotemporal error associated with the taphonomic processes of deposition, preservation, and dating; calibration error between proxy data and the ecosystem states of interest; and error in the interpolation of calibrated estimates across space and time. Researchers often account for this daunting suite of challenges by applying qualitave expert judgment: inferring the past states of ecosystems and assessing the level of uncertainty in those states subjectively. The effectiveness of this approach can be seen by the extent to which future observations confirm previous assertions. Hierarchical Bayesian (HB) statistical approaches allow an alternative approach to accounting for multiple uncertainties in paleo data. HB estimates of ecosystem state formally account for each of the common uncertainties listed above. HB approaches can readily incorporate additional data, and data of different types into estimates of ecosystem state. And HB estimates of ecosystem state, with associated uncertainty, can be used to constrain forecasts of ecosystem dynamics based on mechanistic ecosystem models using data assimilation. Decisions about how to structure an HB model are also subjective, which creates a parallel framework for deciding how to interpret data from the deep past.Our group, the Paleoecological Observatory Network (PalEON), has applied hierarchical Bayesian statistics to formally account for uncertainties in proxy based estimates of past climate, fire, primary productivity, biomass, and vegetation composition. Our estimates often reveal new patterns of past ecosystem change, which is an unambiguously good thing, but we also often estimate a level of uncertainty that is uncomfortably high for many researchers. High levels of uncertainty are due to several features of the HB approach: spatiotemporal smoothing, the formal aggregation of multiple types of uncertainty, and a coarseness in statistical models of taphonomic process. Each of these features provides useful opportunities for statisticians and data-generating researchers to assess what we know about the signal and the noise in paleo data and to improve inference about past changes in ecosystem state.

HIV Trends in the United States: Diagnoses and Estimated Incidence

PubMed Central

Song, Ruiguang; Tang, Tian; An, Qian; Prejean, Joseph; Dietz, Patricia; Hernandez, Angela L; Green, Timothy; Harris, Norma; McCray, Eugene; Mermin, Jonathan

2017-01-01

Background The best indicator of the impact of human immunodeficiency virus (HIV) prevention programs is the incidence of infection; however, HIV is a chronic infection and HIV diagnoses may include infections that occurred years before diagnosis. Alternative methods to estimate incidence use diagnoses, stage of disease, and laboratory assays of infection recency. Using a consistent, accurate method would allow for timely interpretation of HIV trends. Objective The objective of our study was to assess the recent progress toward reducing HIV infections in the United States overall and among selected population segments with available incidence estimation methods. Methods Data on cases of HIV infection reported to national surveillance for 2008-2013 were used to compare trends in HIV diagnoses, unadjusted and adjusted for reporting delay, and model-based incidence for the US population aged ≥13 years. Incidence was estimated using a biomarker for recency of infection (stratified extrapolation approach) and 2 back-calculation models (CD4 and Bayesian hierarchical models). HIV testing trends were determined from behavioral surveys for persons aged ≥18 years. Analyses were stratified by sex, race or ethnicity (black, Hispanic or Latino, and white), and transmission category (men who have sex with men, MSM). Results On average, HIV diagnoses decreased 4.0% per year from 48,309 in 2008 to 39,270 in 2013 (P<.001). Adjusting for reporting delays, diagnoses decreased 3.1% per year (P<.001). The CD4 model estimated an annual decrease in incidence of 4.6% (P<.001) and the Bayesian hierarchical model 2.6% (P<.001); the stratified extrapolation approach estimated a stable incidence. During these years, overall, the percentage of persons who ever had received an HIV test or had had a test within the past year remained stable; among MSM testing increased. For women, all 3 incidence models corroborated the decreasing trend in HIV diagnoses, and HIV diagnoses and 2 incidence models indicated decreases among blacks and whites. The CD4 and Bayesian hierarchical models, but not the stratified extrapolation approach, indicated decreases in incidence among MSM. Conclusions HIV diagnoses and CD4 and Bayesian hierarchical model estimates indicated decreases in HIV incidence overall, among both sexes and all race or ethnicity groups. Further progress depends on effectively reducing HIV incidence among MSM, among whom the majority of new infections occur. PMID:28159730

Air toxics and birth defects: a Bayesian hierarchical approach to evaluate multiple pollutants and spina bifida.

PubMed

Swartz, Michael D; Cai, Yi; Chan, Wenyaw; Symanski, Elaine; Mitchell, Laura E; Danysh, Heather E; Langlois, Peter H; Lupo, Philip J

2015-02-09

While there is evidence that maternal exposure to benzene is associated with spina bifida in offspring, to our knowledge there have been no assessments to evaluate the role of multiple hazardous air pollutants (HAPs) simultaneously on the risk of this relatively common birth defect. In the current study, we evaluated the association between maternal exposure to HAPs identified by the United States Environmental Protection Agency (U.S. EPA) and spina bifida in offspring using hierarchical Bayesian modeling that includes Stochastic Search Variable Selection (SSVS). The Texas Birth Defects Registry provided data on spina bifida cases delivered between 1999 and 2004. The control group was a random sample of unaffected live births, frequency matched to cases on year of birth. Census tract-level estimates of annual HAP levels were obtained from the U.S. EPA's 1999 Assessment System for Population Exposure Nationwide. Using the distribution among controls, exposure was categorized as high exposure (>95(th) percentile), medium exposure (5(th)-95(th) percentile), and low exposure (<5(th) percentile, reference). We used hierarchical Bayesian logistic regression models with SSVS to evaluate the association between HAPs and spina bifida by computing an odds ratio (OR) for each HAP using the posterior mean, and a 95% credible interval (CI) using the 2.5(th) and 97.5(th) quantiles of the posterior samples. Based on previous assessments, any pollutant with a Bayes factor greater than 1 was selected for inclusion in a final model. Twenty-five HAPs were selected in the final analysis to represent "bins" of highly correlated HAPs (ρ > 0.80). We identified two out of 25 HAPs with a Bayes factor greater than 1: quinoline (ORhigh = 2.06, 95% CI: 1.11-3.87, Bayes factor = 1.01) and trichloroethylene (ORmedium = 2.00, 95% CI: 1.14-3.61, Bayes factor = 3.79). Overall there is evidence that quinoline and trichloroethylene may be significant contributors to the risk of spina bifida. Additionally, the use of Bayesian hierarchical models with SSVS is an alternative approach in the evaluation of multiple environmental pollutants on disease risk. This approach can be easily extended to environmental exposures, where novel approaches are needed in the context of multi-pollutant modeling.

multi-dice: r package for comparative population genomic inference under hierarchical co-demographic models of independent single-population size changes.

PubMed

Xue, Alexander T; Hickerson, Michael J

2017-11-01

Population genetic data from multiple taxa can address comparative phylogeographic questions about community-scale response to environmental shifts, and a useful strategy to this end is to employ hierarchical co-demographic models that directly test multi-taxa hypotheses within a single, unified analysis. This approach has been applied to classical phylogeographic data sets such as mitochondrial barcodes as well as reduced-genome polymorphism data sets that can yield 10,000s of SNPs, produced by emergent technologies such as RAD-seq and GBS. A strategy for the latter had been accomplished by adapting the site frequency spectrum to a novel summarization of population genomic data across multiple taxa called the aggregate site frequency spectrum (aSFS), which potentially can be deployed under various inferential frameworks including approximate Bayesian computation, random forest and composite likelihood optimization. Here, we introduce the r package multi-dice, a wrapper program that exploits existing simulation software for flexible execution of hierarchical model-based inference using the aSFS, which is derived from reduced genome data, as well as mitochondrial data. We validate several novel software features such as applying alternative inferential frameworks, enforcing a minimal threshold of time surrounding co-demographic pulses and specifying flexible hyperprior distributions. In sum, multi-dice provides comparative analysis within the familiar R environment while allowing a high degree of user customization, and will thus serve as a tool for comparative phylogeography and population genomics. © 2017 The Authors. Molecular Ecology Resources Published by John Wiley & Sons Ltd.

Characterization and Quantification of Uncertainty in the NARCCAP Regional Climate Model Ensemble and Application to Impacts on Water Systems

NASA Astrophysics Data System (ADS)

Mearns, L. O.; Sain, S. R.; McGinnis, S. A.; Steinschneider, S.; Brown, C. M.

2015-12-01

In this talk we present the development of a joint Bayesian Probabilistic Model for the climate change results of the North American Regional Climate Change Assessment Program (NARCCAP) that uses a unique prior in the model formulation. We use the climate change results (joint distribution of seasonal temperature and precipitation changes (future vs. current)) from the global climate models (GCMs) that provided boundary conditions for the six different regional climate models used in the program as informative priors for the bivariate Bayesian Model. The two variables involved are seasonal temperature and precipitation over sub-regions (i.e., Bukovsky Regions) of the full NARCCAP domain. The basic approach to the joint Bayesian hierarchical model follows the approach of Tebaldi and Sansó (2009). We compare model results using informative (i.e., GCM information) as well as uninformative priors. We apply these results to the Water Evaluation and Planning System (WEAP) model for the Colorado Springs Utility in Colorado. We investigate the layout of the joint pdfs in the context of the water model sensitivities to ranges of temperature and precipitation results to determine the likelihoods of future climate conditions that cannot be accommodated by possible adaptation options. Comparisons may also be made with joint pdfs formed from the CMIP5 collection of global climate models and empirically downscaled to the region of interest.

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.

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

Nonparametric Hierarchical Bayesian Model for Functional Brain Parcellation

PubMed Central

Lashkari, Danial; Sridharan, Ramesh; Vul, Edward; Hsieh, Po-Jang; Kanwisher, Nancy; Golland, Polina

2011-01-01

We develop a method for unsupervised analysis of functional brain images that learns group-level patterns of functional response. Our algorithm is based on a generative model that comprises two main layers. At the lower level, we express the functional brain response to each stimulus as a binary activation variable. At the next level, we define a prior over the sets of activation variables in all subjects. We use a Hierarchical Dirichlet Process as the prior in order to simultaneously learn the patterns of response that are shared across the group, and to estimate the number of these patterns supported by data. Inference based on this model enables automatic discovery and characterization of salient and consistent patterns in functional signals. We apply our method to data from a study that explores the response of the visual cortex to a collection of images. The discovered profiles of activation correspond to selectivity to a number of image categories such as faces, bodies, and scenes. More generally, our results appear superior to the results of alternative data-driven methods in capturing the category structure in the space of stimuli. PMID:21841977

Modeling Menstrual Cycle Length and Variability at the Approach of Menopause Using Hierarchical Change Point Models

PubMed Central

Huang, Xiaobi; Elliott, Michael R.; Harlow, Siobán D.

2013-01-01

SUMMARY As women approach menopause, the patterns of their menstrual cycle lengths change. To study these changes, we need to jointly model both the mean and variability of cycle length. Our proposed model incorporates separate mean and variance change points for each woman and a hierarchical model to link them together, along with regression components to include predictors of menopausal onset such as age at menarche and parity. Additional complexity arises from the fact that the calendar data have substantial missingness due to hormone use, surgery, and failure to report. We integrate multiple imputation and time-to event modeling in a Bayesian estimation framework to deal with different forms of the missingness. Posterior predictive model checks are applied to evaluate the model fit. Our method successfully models patterns of women’s menstrual cycle trajectories throughout their late reproductive life and identifies change points for mean and variability of segment length, providing insight into the menopausal process. More generally, our model points the way toward increasing use of joint mean-variance models to predict health outcomes and better understand disease processes. PMID:24729638

Modeling abundance using hierarchical distance sampling

USGS Publications Warehouse

Royle, Andy; Kery, Marc

2016-01-01

In this chapter, we provide an introduction to classical distance sampling ideas for point and line transect data, and for continuous and binned distance data. We introduce the conditional and the full likelihood, and we discuss Bayesian analysis of these models in BUGS using the idea of data augmentation, which we discussed in Chapter 7. We then extend the basic ideas to the problem of hierarchical distance sampling (HDS), where we have multiple point or transect sample units in space (or possibly in time). The benefit of HDS in practice is that it allows us to directly model spatial variation in population size among these sample units. This is a preeminent concern of most field studies that use distance sampling methods, but it is not a problem that has received much attention in the literature. We show how to analyze HDS models in both the unmarked package and in the BUGS language for point and line transects, and for continuous and binned distance data. We provide a case study of HDS applied to a survey of the island scrub-jay on Santa Cruz Island, California.

Improving Water Quality Assessments through a HierarchicalBayesian Analysis of Variability

EPA Science Inventory

Water quality measurement error and variability, while well-documented in laboratory-scale studies, is rarely acknowledged or explicitly resolved in most water body assessments, including those conducted in compliance with the United States Environmental Protection Agency (USEPA)...

Identification of lung cancer histology-specific variants applying Bayesian framework variant prioritization approaches within the TRICL and ILCCO consortia

PubMed Central

Brenner, Darren R.; Amos, Christopher I.; Brhane, Yonathan; Timofeeva, Maria N.; Caporaso, Neil; Wang, Yufei; Christiani, David C.; Bickeböller, Heike; Yang, Ping; Albanes, Demetrius; Stevens, Victoria L.; Gapstur, Susan; McKay, James; Boffetta, Paolo; Zaridze, David; Szeszenia-Dabrowska, Neonilia; Lissowska, Jolanta; Rudnai, Peter; Fabianova, Eleonora; Mates, Dana; Bencko, Vladimir; Foretova, Lenka; Janout, Vladimir; Krokan, Hans E.; Skorpen, Frank; Gabrielsen, Maiken E.; Vatten, Lars; Njølstad, Inger; Chen, Chu; Goodman, Gary; Lathrop, Mark; Vooder, Tõnu; Välk, Kristjan; Nelis, Mari; Metspalu, Andres; Broderick, Peter; Eisen, Timothy; Wu, Xifeng; Zhang, Di; Chen, Wei; Spitz, Margaret R.; Wei, Yongyue; Su, Li; Xie, Dong; She, Jun; Matsuo, Keitaro; Matsuda, Fumihiko; Ito, Hidemi; Risch, Angela; Heinrich, Joachim; Rosenberger, Albert; Muley, Thomas; Dienemann, Hendrik; Field, John K.; Raji, Olaide; Chen, Ying; Gosney, John; Liloglou, Triantafillos; Davies, Michael P.A.; Marcus, Michael; McLaughlin, John; Orlow, Irene; Han, Younghun; Li, Yafang; Zong, Xuchen; Johansson, Mattias; Liu, Geoffrey; Tworoger, Shelley S.; Le Marchand, Loic; Henderson, Brian E.; Wilkens, Lynne R.; Dai, Juncheng; Shen, Hongbing; Houlston, Richard S.; Landi, Maria T.; Brennan, Paul; Hung, Rayjean J.

2015-01-01

Large-scale genome-wide association studies (GWAS) have likely uncovered all common variants at the GWAS significance level. Additional variants within the suggestive range (0.0001> P > 5×10−8) are, however, still of interest for identifying causal associations. This analysis aimed to apply novel variant prioritization approaches to identify additional lung cancer variants that may not reach the GWAS level. Effects were combined across studies with a total of 33456 controls and 6756 adenocarcinoma (AC; 13 studies), 5061 squamous cell carcinoma (SCC; 12 studies) and 2216 small cell lung cancer cases (9 studies). Based on prior information such as variant physical properties and functional significance, we applied stratified false discovery rates, hierarchical modeling and Bayesian false discovery probabilities for variant prioritization. We conducted a fine mapping analysis as validation of our methods by examining top-ranking novel variants in six independent populations with a total of 3128 cases and 2966 controls. Three novel loci in the suggestive range were identified based on our Bayesian framework analyses: KCNIP4 at 4p15.2 (rs6448050, P = 4.6×10−7) and MTMR2 at 11q21 (rs10501831, P = 3.1×10−6) with SCC, as well as GAREM at 18q12.1 (rs11662168, P = 3.4×10−7) with AC. Use of our prioritization methods validated two of the top three loci associated with SCC (P = 1.05×10−4 for KCNIP4, represented by rs9799795) and AC (P = 2.16×10−4 for GAREM, represented by rs3786309) in the independent fine mapping populations. This study highlights the utility of using prior functional data for sequence variants in prioritization analyses to search for robust signals in the suggestive range. PMID:26363033

Identification of lung cancer histology-specific variants applying Bayesian framework variant prioritization approaches within the TRICL and ILCCO consortia.

PubMed

Brenner, Darren R; Amos, Christopher I; Brhane, Yonathan; Timofeeva, Maria N; Caporaso, Neil; Wang, Yufei; Christiani, David C; Bickeböller, Heike; Yang, Ping; Albanes, Demetrius; Stevens, Victoria L; Gapstur, Susan; McKay, James; Boffetta, Paolo; Zaridze, David; Szeszenia-Dabrowska, Neonilia; Lissowska, Jolanta; Rudnai, Peter; Fabianova, Eleonora; Mates, Dana; Bencko, Vladimir; Foretova, Lenka; Janout, Vladimir; Krokan, Hans E; Skorpen, Frank; Gabrielsen, Maiken E; Vatten, Lars; Njølstad, Inger; Chen, Chu; Goodman, Gary; Lathrop, Mark; Vooder, Tõnu; Välk, Kristjan; Nelis, Mari; Metspalu, Andres; Broderick, Peter; Eisen, Timothy; Wu, Xifeng; Zhang, Di; Chen, Wei; Spitz, Margaret R; Wei, Yongyue; Su, Li; Xie, Dong; She, Jun; Matsuo, Keitaro; Matsuda, Fumihiko; Ito, Hidemi; Risch, Angela; Heinrich, Joachim; Rosenberger, Albert; Muley, Thomas; Dienemann, Hendrik; Field, John K; Raji, Olaide; Chen, Ying; Gosney, John; Liloglou, Triantafillos; Davies, Michael P A; Marcus, Michael; McLaughlin, John; Orlow, Irene; Han, Younghun; Li, Yafang; Zong, Xuchen; Johansson, Mattias; Liu, Geoffrey; Tworoger, Shelley S; Le Marchand, Loic; Henderson, Brian E; Wilkens, Lynne R; Dai, Juncheng; Shen, Hongbing; Houlston, Richard S; Landi, Maria T; Brennan, Paul; Hung, Rayjean J

2015-11-01

Large-scale genome-wide association studies (GWAS) have likely uncovered all common variants at the GWAS significance level. Additional variants within the suggestive range (0.0001> P > 5×10(-8)) are, however, still of interest for identifying causal associations. This analysis aimed to apply novel variant prioritization approaches to identify additional lung cancer variants that may not reach the GWAS level. Effects were combined across studies with a total of 33456 controls and 6756 adenocarcinoma (AC; 13 studies), 5061 squamous cell carcinoma (SCC; 12 studies) and 2216 small cell lung cancer cases (9 studies). Based on prior information such as variant physical properties and functional significance, we applied stratified false discovery rates, hierarchical modeling and Bayesian false discovery probabilities for variant prioritization. We conducted a fine mapping analysis as validation of our methods by examining top-ranking novel variants in six independent populations with a total of 3128 cases and 2966 controls. Three novel loci in the suggestive range were identified based on our Bayesian framework analyses: KCNIP4 at 4p15.2 (rs6448050, P = 4.6×10(-7)) and MTMR2 at 11q21 (rs10501831, P = 3.1×10(-6)) with SCC, as well as GAREM at 18q12.1 (rs11662168, P = 3.4×10(-7)) with AC. Use of our prioritization methods validated two of the top three loci associated with SCC (P = 1.05×10(-4) for KCNIP4, represented by rs9799795) and AC (P = 2.16×10(-4) for GAREM, represented by rs3786309) in the independent fine mapping populations. This study highlights the utility of using prior functional data for sequence variants in prioritization analyses to search for robust signals in the suggestive range. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

An evaluation of the Bayesian approach to fitting the N-mixture model for use with pseudo-replicated count data

USGS Publications Warehouse

Toribo, S.G.; Gray, B.R.; Liang, S.

2011-01-01

The N-mixture model proposed by Royle in 2004 may be used to approximate the abundance and detection probability of animal species in a given region. In 2006, Royle and Dorazio discussed the advantages of using a Bayesian approach in modelling animal abundance and occurrence using a hierarchical N-mixture model. N-mixture models assume replication on sampling sites, an assumption that may be violated when the site is not closed to changes in abundance during the survey period or when nominal replicates are defined spatially. In this paper, we studied the robustness of a Bayesian approach to fitting the N-mixture model for pseudo-replicated count data. Our simulation results showed that the Bayesian estimates for abundance and detection probability are slightly biased when the actual detection probability is small and are sensitive to the presence of extra variability within local sites.

Bayesian Group Bridge for Bi-level Variable Selection.

PubMed

Mallick, Himel; Yi, Nengjun

2017-06-01

A Bayesian bi-level variable selection method (BAGB: Bayesian Analysis of Group Bridge) is developed for regularized regression and classification. This new development is motivated by grouped data, where generic variables can be divided into multiple groups, with variables in the same group being mechanistically related or statistically correlated. As an alternative to frequentist group variable selection methods, BAGB incorporates structural information among predictors through a group-wise shrinkage prior. Posterior computation proceeds via an efficient MCMC algorithm. In addition to the usual ease-of-interpretation of hierarchical linear models, the Bayesian formulation produces valid standard errors, a feature that is notably absent in the frequentist framework. Empirical evidence of the attractiveness of the method is illustrated by extensive Monte Carlo simulations and real data analysis. Finally, several extensions of this new approach are presented, providing a unified framework for bi-level variable selection in general models with flexible penalties.

Bayesian learning of visual chunks by human observers

PubMed Central

Orbán, Gergő; Fiser, József; Aslin, Richard N.; Lengyel, Máté

2008-01-01

Efficient and versatile processing of any hierarchically structured information requires a learning mechanism that combines lower-level features into higher-level chunks. We investigated this chunking mechanism in humans with a visual pattern-learning paradigm. We developed an ideal learner based on Bayesian model comparison that extracts and stores only those chunks of information that are minimally sufficient to encode a set of visual scenes. Our ideal Bayesian chunk learner not only reproduced the results of a large set of previous empirical findings in the domain of human pattern learning but also made a key prediction that we confirmed experimentally. In accordance with Bayesian learning but contrary to associative learning, human performance was well above chance when pair-wise statistics in the exemplars contained no relevant information. Thus, humans extract chunks from complex visual patterns by generating accurate yet economical representations and not by encoding the full correlational structure of the input. PMID:18268353

Bayesian analysis of non-homogeneous Markov chains: application to mental health data.

PubMed

Sung, Minje; Soyer, Refik; Nhan, Nguyen

2007-07-10

In this paper we present a formal treatment of non-homogeneous Markov chains by introducing a hierarchical Bayesian framework. Our work is motivated by the analysis of correlated categorical data which arise in assessment of psychiatric treatment programs. In our development, we introduce a Markovian structure to describe the non-homogeneity of transition patterns. In doing so, we introduce a logistic regression set-up for Markov chains and incorporate covariates in our model. We present a Bayesian model using Markov chain Monte Carlo methods and develop inference procedures to address issues encountered in the analyses of data from psychiatric treatment programs. Our model and inference procedures are implemented to some real data from a psychiatric treatment study. Copyright 2006 John Wiley & Sons, Ltd.

Bayesian Hierarchical Modeling of Cardiac Response to Particulate Matter Exposure

EPA Science Inventory

Studies have linked increased levels of particulate air pollution to decreased autonomic control, as measured by heart rate variability (HRV), particularly in populations such as the elderly. In this study, we use data obtained from the 1998 USEPA epidemiology-exposure longitudin...

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.

Predicting individual brain functional connectivity using a Bayesian hierarchical model.

PubMed

Dai, Tian; Guo, Ying

2017-02-15

Network-oriented analysis of functional magnetic resonance imaging (fMRI), especially resting-state fMRI, has revealed important association between abnormal connectivity and brain disorders such as schizophrenia, major depression and Alzheimer's disease. Imaging-based brain connectivity measures have become a useful tool for investigating the pathophysiology, progression and treatment response of psychiatric disorders and neurodegenerative diseases. Recent studies have started to explore the possibility of using functional neuroimaging to help predict disease progression and guide treatment selection for individual patients. These studies provide the impetus to develop statistical methodology that would help provide predictive information on disease progression-related or treatment-related changes in neural connectivity. To this end, we propose a prediction method based on Bayesian hierarchical model that uses individual's baseline fMRI scans, coupled with relevant subject characteristics, to predict the individual's future functional connectivity. A key advantage of the proposed method is that it can improve the accuracy of individualized prediction of connectivity by combining information from both group-level connectivity patterns that are common to subjects with similar characteristics as well as individual-level connectivity features that are particular to the specific subject. Furthermore, our method also offers statistical inference tools such as predictive intervals that help quantify the uncertainty or variability of the predicted outcomes. The proposed prediction method could be a useful approach to predict the changes in individual patient's brain connectivity with the progression of a disease. It can also be used to predict a patient's post-treatment brain connectivity after a specified treatment regimen. Another utility of the proposed method is that it can be applied to test-retest imaging data to develop a more reliable estimator for individual functional connectivity. We show there exists a nice connection between our proposed estimator and a recently developed shrinkage estimator of connectivity measures in the neuroimaging community. We develop an expectation-maximization (EM) algorithm for estimation of the proposed Bayesian hierarchical model. Simulations studies are performed to evaluate the accuracy of our proposed prediction methods. We illustrate the application of the methods with two data examples: the longitudinal resting-state fMRI from ADNI2 study and the test-retest fMRI data from Kirby21 study. In both the simulation studies and the fMRI data applications, we demonstrate that the proposed methods provide more accurate prediction and more reliable estimation of individual functional connectivity as compared with alternative methods. Copyright © 2017 Elsevier Inc. All rights reserved.

High-Dimensional Bayesian Geostatistics

PubMed Central

Banerjee, Sudipto

2017-01-01

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and time points. Over the last decade, hierarchical spatiotemporal process models have become widely deployed statistical tools for researchers to better understand the complex nature of spatial and temporal variability. However, fitting hierarchical spatiotemporal models often involves expensive matrix computations with complexity increasing in cubic order for the number of spatial locations and temporal points. This renders such models unfeasible for large data sets. This article offers a focused review of two methods for constructing well-defined highly scalable spatiotemporal stochastic processes. Both these processes can be used as “priors” for spatiotemporal random fields. The first approach constructs a low-rank process operating on a lower-dimensional subspace. The second approach constructs a Nearest-Neighbor Gaussian Process (NNGP) that ensures sparse precision matrices for its finite realizations. Both processes can be exploited as a scalable prior embedded within a rich hierarchical modeling framework to deliver full Bayesian inference. These approaches can be described as model-based solutions for big spatiotemporal datasets. The models ensure that the algorithmic complexity has ~ n floating point operations (flops), where n the number of spatial locations (per iteration). We compare these methods and provide some insight into their methodological underpinnings. PMID:29391920

Hierarchical imputation of systematically and sporadically missing data: An approximate Bayesian approach using chained equations.

PubMed

Jolani, Shahab

2018-03-01

In health and medical sciences, multiple imputation (MI) is now becoming popular to obtain valid inferences in the presence of missing data. However, MI of clustered data such as multicenter studies and individual participant data meta-analysis requires advanced imputation routines that preserve the hierarchical structure of data. In clustered data, a specific challenge is the presence of systematically missing data, when a variable is completely missing in some clusters, and sporadically missing data, when it is partly missing in some clusters. Unfortunately, little is known about how to perform MI when both types of missing data occur simultaneously. We develop a new class of hierarchical imputation approach based on chained equations methodology that simultaneously imputes systematically and sporadically missing data while allowing for arbitrary patterns of missingness among them. Here, we use a random effect imputation model and adopt a simplification over fully Bayesian techniques such as Gibbs sampler to directly obtain draws of parameters within each step of the chained equations. We justify through theoretical arguments and extensive simulation studies that the proposed imputation methodology has good statistical properties in terms of bias and coverage rates of parameter estimates. An illustration is given in a case study with eight individual participant datasets. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

High-Dimensional Bayesian Geostatistics.

PubMed

Banerjee, Sudipto

2017-06-01

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and time points. Over the last decade, hierarchical spatiotemporal process models have become widely deployed statistical tools for researchers to better understand the complex nature of spatial and temporal variability. However, fitting hierarchical spatiotemporal models often involves expensive matrix computations with complexity increasing in cubic order for the number of spatial locations and temporal points. This renders such models unfeasible for large data sets. This article offers a focused review of two methods for constructing well-defined highly scalable spatiotemporal stochastic processes. Both these processes can be used as "priors" for spatiotemporal random fields. The first approach constructs a low-rank process operating on a lower-dimensional subspace. The second approach constructs a Nearest-Neighbor Gaussian Process (NNGP) that ensures sparse precision matrices for its finite realizations. Both processes can be exploited as a scalable prior embedded within a rich hierarchical modeling framework to deliver full Bayesian inference. These approaches can be described as model-based solutions for big spatiotemporal datasets. The models ensure that the algorithmic complexity has ~ n floating point operations (flops), where n the number of spatial locations (per iteration). We compare these methods and provide some insight into their methodological underpinnings.

INACTIVATION OF BACILLUS GLOBIGII BY CHLORINATION: A HIERARCHICAL BAYESIAN MODEL

EPA Science Inventory

Recent events where spores of Bacillus anthracis have been used as a bioterrorist weapon have prompted interest in determining the resistance of this organism to commonly used disinfectants, such as chlorine, chlorine dioxide and ozone. This work was undertaken to study ...

Implications of Nonlinear Concentration Response Curve for Ozone related Mortality on Health Burden Assessment

EPA Science Inventory

We characterize the sensitivity of the ozone attributable health burden assessment with respect to different modeling strategies of concentration-response function. For this purpose, we develop a flexible Bayesian hierarchical model allowing for a nonlinear ozone risk curve with ...

BAYESIAN HIERARCHICAL MODELING OF PERSONAL EXPOSURE TO PARTICULATE MATTER

EPA Science Inventory

In the US EPA's 1998 Baltimore Epidemiology-Exposure Panel Study, a group of 21 residents of a single building retirement community wore personal monitors recording personal fine particulate air pollution concentrations (PM_2.5) for 27 days, while other monitors recorde...

Evaluation of spatio-temporal Bayesian models for the spread of infectious diseases in oil palm.

PubMed

Denis, Marie; Cochard, Benoît; Syahputra, Indra; de Franqueville, Hubert; Tisné, Sébastien

2018-02-01

In the field of epidemiology, studies are often focused on mapping diseases in relation to time and space. Hierarchical modeling is a common flexible and effective tool for modeling problems related to disease spread. In the context of oil palm plantations infected by the fungal pathogen Ganoderma boninense, we propose and compare two spatio-temporal hierarchical Bayesian models addressing the lack of information on propagation modes and transmission vectors. We investigate two alternative process models to study the unobserved mechanism driving the infection process. The models help gain insight into the spatio-temporal dynamic of the infection by identifying a genetic component in the disease spread and by highlighting a spatial component acting at the end of the experiment. In this challenging context, we propose models that provide assumptions on the unobserved mechanism driving the infection process while making short-term predictions using ready-to-use software. Copyright © 2018 Elsevier Ltd. All rights reserved.

Bayesian multivariate hierarchical transformation models for ROC analysis.

PubMed

O'Malley, A James; Zou, Kelly H

2006-02-15

A Bayesian multivariate hierarchical transformation model (BMHTM) is developed for receiver operating characteristic (ROC) curve analysis based on clustered continuous diagnostic outcome data with covariates. Two special features of this model are that it incorporates non-linear monotone transformations of the outcomes and that multiple correlated outcomes may be analysed. The mean, variance, and transformation components are all modelled parametrically, enabling a wide range of inferences. The general framework is illustrated by focusing on two problems: (1) analysis of the diagnostic accuracy of a covariate-dependent univariate test outcome requiring a Box-Cox transformation within each cluster to map the test outcomes to a common family of distributions; (2) development of an optimal composite diagnostic test using multivariate clustered outcome data. In the second problem, the composite test is estimated using discriminant function analysis and compared to the test derived from logistic regression analysis where the gold standard is a binary outcome. The proposed methodology is illustrated on prostate cancer biopsy data from a multi-centre clinical trial.

Bayesian multivariate hierarchical transformation models for ROC analysis

PubMed Central

O'Malley, A. James; Zou, Kelly H.

2006-01-01

SUMMARY A Bayesian multivariate hierarchical transformation model (BMHTM) is developed for receiver operating characteristic (ROC) curve analysis based on clustered continuous diagnostic outcome data with covariates. Two special features of this model are that it incorporates non-linear monotone transformations of the outcomes and that multiple correlated outcomes may be analysed. The mean, variance, and transformation components are all modelled parametrically, enabling a wide range of inferences. The general framework is illustrated by focusing on two problems: (1) analysis of the diagnostic accuracy of a covariate-dependent univariate test outcome requiring a Box–Cox transformation within each cluster to map the test outcomes to a common family of distributions; (2) development of an optimal composite diagnostic test using multivariate clustered outcome data. In the second problem, the composite test is estimated using discriminant function analysis and compared to the test derived from logistic regression analysis where the gold standard is a binary outcome. The proposed methodology is illustrated on prostate cancer biopsy data from a multi-centre clinical trial. PMID:16217836

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.

Bayesian hierarchical modelling of North Atlantic windiness

NASA Astrophysics Data System (ADS)

Vanem, E.; Breivik, O. N.

2013-03-01

Extreme weather conditions represent serious natural hazards to ship operations and may be the direct cause or contributing factor to maritime accidents. Such severe environmental conditions can be taken into account in ship design and operational windows can be defined that limits hazardous operations to less extreme conditions. Nevertheless, possible changes in the statistics of extreme weather conditions, possibly due to anthropogenic climate change, represent an additional hazard to ship operations that is less straightforward to account for in a consistent way. Obviously, there are large uncertainties as to how future climate change will affect the extreme weather conditions at sea and there is a need for stochastic models that can describe the variability in both space and time at various scales of the environmental conditions. Previously, Bayesian hierarchical space-time models have been developed to describe the variability and complex dependence structures of significant wave height in space and time. These models were found to perform reasonably well and provided some interesting results, in particular, pertaining to long-term trends in the wave climate. In this paper, a similar framework is applied to oceanic windiness and the spatial and temporal variability of the 10-m wind speed over an area in the North Atlantic ocean is investigated. When the results from the model for North Atlantic windiness is compared to the results for significant wave height over the same area, it is interesting to observe that whereas an increasing trend in significant wave height was identified, no statistically significant long-term trend was estimated in windiness. This may indicate that the increase in significant wave height is not due to an increase in locally generated wind waves, but rather to increased swell. This observation is also consistent with studies that have suggested a poleward shift of the main storm tracks.

Bayesian Models for Streamflow and River Network Reconstruction using Tree Rings

NASA Astrophysics Data System (ADS)

Ravindranath, A.; Devineni, N.

2016-12-01

Water systems face non-stationary, dynamically shifting risks due to shifting societal conditions and systematic long-term variations in climate manifesting as quasi-periodic behavior on multi-decadal time scales. Water systems are thus vulnerable to long periods of wet or dry hydroclimatic conditions. Streamflow is a major component of water systems and a primary means by which water is transported to serve ecosystems' and human needs. Thus, our concern is in understanding streamflow variability. Climate variability and impacts on water resources are crucial factors affecting streamflow, and multi-scale variability increases risk to water sustainability and systems. Dam operations are necessary for collecting water brought by streamflow while maintaining downstream ecological health. Rules governing dam operations are based on streamflow records that are woefully short compared to periods of systematic variation present in the climatic factors driving streamflow variability and non-stationarity. We use hierarchical Bayesian regression methods in order to reconstruct paleo-streamflow records for dams within a basin using paleoclimate proxies (e.g. tree rings) to guide the reconstructions. The riverine flow network for the entire basin is subsequently modeled hierarchically using feeder stream and tributary flows. This is a starting point in analyzing streamflow variability and risks to water systems, and developing a scientifically-informed dynamic risk management framework for formulating dam operations and water policies to best hedge such risks. We will apply this work to the Missouri and Delaware River Basins (DRB). Preliminary results of streamflow reconstructions for eight dams in the upper DRB using standard Gaussian regression with regional tree ring chronologies give streamflow records that now span two to two and a half centuries, and modestly smoothed versions of these reconstructed flows indicate physically-justifiable trends in the time series.

Reclaiming the past: Using hierarchical Bayesian analysis to fill missing values in the tide gauge mean sea level record, with application to extreme value analysis

NASA Astrophysics Data System (ADS)

Piecuch, C. G.; Huybers, P. J.; Tingley, M.

2015-12-01

Tide gauge records of mean sea level are some of the most valuable instrumental time series of oceanic variability and change. Yet these time series sometimes have short record lengths and intermittently missing values. Such issues can limit the utility of the data, for example, precluding rigorous analyses of return periods of extreme mean sea level events and whether they are unprecedented. With a view to filling gaps in the tide gauge mean sea level time series, we describe a hierarchical Bayesian modeling approach. The model, which is predicated on the notion of conditional probabilities, comprises three levels: a process level, which casts mean sea level as a field with spatiotemporal covariance; a data level, which represents tide gauge observations as noisy, biased versions of the true process; and a prior level, which gives prior functional forms to model parameters. Using Bayes' rule, this technique gives estimates of the posterior probability of the process and the parameters given the observations. To demonstrate the approach, we apply it to 2,967 station-years of annual mean sea level observations over 1856-2013 from 70 tide gauges along the United States East Coast from Florida to Maine (i.e., 26.8% record completeness). The model overcomes the data paucity by sharing information across space and time. The result is an ensemble of realizations, each member of which is a possible history of sea level changes at these locations over this period, which is consistent with and equally likely given the tide gauge data and underlying model assumptions. Using the ensemble of histories furnished by the Bayesian model, we identify extreme events of mean sea level change in the tide gauge time series. Specifically, we use the model to address the particular hypothesis (with rigorous uncertainty quantification) that a recently reported interannual sea level rise during 2008-2010 was unprecedented in the instrumental record along the northeast coast of North America, and that it had a return period of 850 years. Preliminary analysis suggests that this event was likely unprecedented on the coast of Maine in the last century.

Robust, Adaptive Functional Regression in Functional Mixed Model Framework.

PubMed

Zhu, Hongxiao; Brown, Philip J; Morris, Jeffrey S

2011-09-01

Functional data are increasingly encountered in scientific studies, and their high dimensionality and complexity lead to many analytical challenges. Various methods for functional data analysis have been developed, including functional response regression methods that involve regression of a functional response on univariate/multivariate predictors with nonparametrically represented functional coefficients. In existing methods, however, the functional regression can be sensitive to outlying curves and outlying regions of curves, so is not robust. In this paper, we introduce a new Bayesian method, robust functional mixed models (R-FMM), for performing robust functional regression within the general functional mixed model framework, which includes multiple continuous or categorical predictors and random effect functions accommodating potential between-function correlation induced by the experimental design. The underlying model involves a hierarchical scale mixture model for the fixed effects, random effect and residual error functions. These modeling assumptions across curves result in robust nonparametric estimators of the fixed and random effect functions which down-weight outlying curves and regions of curves, and produce statistics that can be used to flag global and local outliers. These assumptions also lead to distributions across wavelet coefficients that have outstanding sparsity and adaptive shrinkage properties, with great flexibility for the data to determine the sparsity and the heaviness of the tails. Together with the down-weighting of outliers, these within-curve properties lead to fixed and random effect function estimates that appear in our simulations to be remarkably adaptive in their ability to remove spurious features yet retain true features of the functions. We have developed general code to implement this fully Bayesian method that is automatic, requiring the user to only provide the functional data and design matrices. It is efficient enough to handle large data sets, and yields posterior samples of all model parameters that can be used to perform desired Bayesian estimation and inference. Although we present details for a specific implementation of the R-FMM using specific distributional choices in the hierarchical model, 1D functions, and wavelet transforms, the method can be applied more generally using other heavy-tailed distributions, higher dimensional functions (e.g. images), and using other invertible transformations as alternatives to wavelets.

Robust, Adaptive Functional Regression in Functional Mixed Model Framework

PubMed Central

Zhu, Hongxiao; Brown, Philip J.; Morris, Jeffrey S.

2012-01-01

Functional data are increasingly encountered in scientific studies, and their high dimensionality and complexity lead to many analytical challenges. Various methods for functional data analysis have been developed, including functional response regression methods that involve regression of a functional response on univariate/multivariate predictors with nonparametrically represented functional coefficients. In existing methods, however, the functional regression can be sensitive to outlying curves and outlying regions of curves, so is not robust. In this paper, we introduce a new Bayesian method, robust functional mixed models (R-FMM), for performing robust functional regression within the general functional mixed model framework, which includes multiple continuous or categorical predictors and random effect functions accommodating potential between-function correlation induced by the experimental design. The underlying model involves a hierarchical scale mixture model for the fixed effects, random effect and residual error functions. These modeling assumptions across curves result in robust nonparametric estimators of the fixed and random effect functions which down-weight outlying curves and regions of curves, and produce statistics that can be used to flag global and local outliers. These assumptions also lead to distributions across wavelet coefficients that have outstanding sparsity and adaptive shrinkage properties, with great flexibility for the data to determine the sparsity and the heaviness of the tails. Together with the down-weighting of outliers, these within-curve properties lead to fixed and random effect function estimates that appear in our simulations to be remarkably adaptive in their ability to remove spurious features yet retain true features of the functions. We have developed general code to implement this fully Bayesian method that is automatic, requiring the user to only provide the functional data and design matrices. It is efficient enough to handle large data sets, and yields posterior samples of all model parameters that can be used to perform desired Bayesian estimation and inference. Although we present details for a specific implementation of the R-FMM using specific distributional choices in the hierarchical model, 1D functions, and wavelet transforms, the method can be applied more generally using other heavy-tailed distributions, higher dimensional functions (e.g. images), and using other invertible transformations as alternatives to wavelets. PMID:22308015

Benefits of Applying Hierarchical Models to the Empirical Green's Function Approach

NASA Astrophysics Data System (ADS)

Denolle, M.; Van Houtte, C.

2017-12-01

Stress drops calculated from source spectral studies currently show larger variability than what is implied by empirical ground motion models. One of the potential origins of the inflated variability is the simplified model-fitting techniques used in most source spectral studies. This study improves upon these existing methods, and shows that the fitting method may explain some of the discrepancy. In particular, Bayesian hierarchical modelling is shown to be a method that can reduce bias, better quantify uncertainties and allow additional effects to be resolved. The method is applied to the Mw7.1 Kumamoto, Japan earthquake, and other global, moderate-magnitude, strike-slip earthquakes between Mw5 and Mw7.5. It is shown that the variation of the corner frequency, fc, and the falloff rate, n, across the focal sphere can be reliably retrieved without overfitting the data. Additionally, it is shown that methods commonly used to calculate corner frequencies can give substantial biases. In particular, if fc were calculated for the Kumamoto earthquake using a model with a falloff rate fixed at 2 instead of the best fit 1.6, the obtained fc would be as large as twice its realistic value. The reliable retrieval of the falloff rate allows deeper examination of this parameter for a suite of global, strike-slip earthquakes, and its scaling with magnitude. The earthquake sequences considered in this study are from Japan, New Zealand, Haiti and California.

HIV Trends in the United States: Diagnoses and Estimated Incidence.

PubMed

Hall, H Irene; Song, Ruiguang; Tang, Tian; An, Qian; Prejean, Joseph; Dietz, Patricia; Hernandez, Angela L; Green, Timothy; Harris, Norma; McCray, Eugene; Mermin, Jonathan

2017-02-03

The best indicator of the impact of human immunodeficiency virus (HIV) prevention programs is the incidence of infection; however, HIV is a chronic infection and HIV diagnoses may include infections that occurred years before diagnosis. Alternative methods to estimate incidence use diagnoses, stage of disease, and laboratory assays of infection recency. Using a consistent, accurate method would allow for timely interpretation of HIV trends. The objective of our study was to assess the recent progress toward reducing HIV infections in the United States overall and among selected population segments with available incidence estimation methods. Data on cases of HIV infection reported to national surveillance for 2008-2013 were used to compare trends in HIV diagnoses, unadjusted and adjusted for reporting delay, and model-based incidence for the US population aged ≥13 years. Incidence was estimated using a biomarker for recency of infection (stratified extrapolation approach) and 2 back-calculation models (CD4 and Bayesian hierarchical models). HIV testing trends were determined from behavioral surveys for persons aged ≥18 years. Analyses were stratified by sex, race or ethnicity (black, Hispanic or Latino, and white), and transmission category (men who have sex with men, MSM). On average, HIV diagnoses decreased 4.0% per year from 48,309 in 2008 to 39,270 in 2013 (P<.001). Adjusting for reporting delays, diagnoses decreased 3.1% per year (P<.001). The CD4 model estimated an annual decrease in incidence of 4.6% (P<.001) and the Bayesian hierarchical model 2.6% (P<.001); the stratified extrapolation approach estimated a stable incidence. During these years, overall, the percentage of persons who ever had received an HIV test or had had a test within the past year remained stable; among MSM testing increased. For women, all 3 incidence models corroborated the decreasing trend in HIV diagnoses, and HIV diagnoses and 2 incidence models indicated decreases among blacks and whites. The CD4 and Bayesian hierarchical models, but not the stratified extrapolation approach, indicated decreases in incidence among MSM. HIV diagnoses and CD4 and Bayesian hierarchical model estimates indicated decreases in HIV incidence overall, among both sexes and all race or ethnicity groups. Further progress depends on effectively reducing HIV incidence among MSM, among whom the majority of new infections occur. ©H Irene Hall, Ruiguang Song, Tian Tang, Qian An, Joseph Prejean, Patricia Dietz, Angela L Hernandez, Timothy Green, Norma Harris, Eugene McCray, Jonathan Mermin. Originally published in JMIR Public Health and Surveillance (http://publichealth.jmir.org), 03.02.2017.

Manual hierarchical clustering of regional geochemical data using a Bayesian finite mixture model

USGS Publications Warehouse

Ellefsen, Karl J.; Smith, David

2016-01-01

Interpretation of regional scale, multivariate geochemical data is aided by a statistical technique called “clustering.” We investigate a particular clustering procedure by applying it to geochemical data collected in the State of Colorado, United States of America. The clustering procedure partitions the field samples for the entire survey area into two clusters. The field samples in each cluster are partitioned again to create two subclusters, and so on. This manual procedure generates a hierarchy of clusters, and the different levels of the hierarchy show geochemical and geological processes occurring at different spatial scales. Although there are many different clustering methods, we use Bayesian finite mixture modeling with two probability distributions, which yields two clusters. The model parameters are estimated with Hamiltonian Monte Carlo sampling of the posterior probability density function, which usually has multiple modes. Each mode has its own set of model parameters; each set is checked to ensure that it is consistent both with the data and with independent geologic knowledge. The set of model parameters that is most consistent with the independent geologic knowledge is selected for detailed interpretation and partitioning of the field samples.

Bayesian inference in camera trapping studies for a class of spatial capture-recapture models

USGS Publications Warehouse

Royle, J. Andrew; Karanth, K. Ullas; Gopalaswamy, Arjun M.; Kumar, N. Samba

2009-01-01

We develop a class of models for inference about abundance or density using spatial capture-recapture data from studies based on camera trapping and related methods. The model is a hierarchical model composed of two components: a point process model describing the distribution of individuals in space (or their home range centers) and a model describing the observation of individuals in traps. We suppose that trap- and individual-specific capture probabilities are a function of distance between individual home range centers and trap locations. We show that the models can be regarded as generalized linear mixed models, where the individual home range centers are random effects. We adopt a Bayesian framework for inference under these models using a formulation based on data augmentation. We apply the models to camera trapping data on tigers from the Nagarahole Reserve, India, collected over 48 nights in 2006. For this study, 120 camera locations were used, but cameras were only operational at 30 locations during any given sample occasion. Movement of traps is common in many camera-trapping studies and represents an important feature of the observation model that we address explicitly in our application.

Spatial Bayesian latent factor regression modeling of coordinate-based meta-analysis data.

PubMed

Montagna, Silvia; Wager, Tor; Barrett, Lisa Feldman; Johnson, Timothy D; Nichols, Thomas E

2018-03-01

Now over 20 years old, functional MRI (fMRI) has a large and growing literature that is best synthesised with meta-analytic tools. As most authors do not share image data, only the peak activation coordinates (foci) reported in the article are available for Coordinate-Based Meta-Analysis (CBMA). Neuroimaging meta-analysis is used to (i) identify areas of consistent activation; and (ii) build a predictive model of task type or cognitive process for new studies (reverse inference). To simultaneously address these aims, we propose a Bayesian point process hierarchical model for CBMA. We model the foci from each study as a doubly stochastic Poisson process, where the study-specific log intensity function is characterized as a linear combination of a high-dimensional basis set. A sparse representation of the intensities is guaranteed through latent factor modeling of the basis coefficients. Within our framework, it is also possible to account for the effect of study-level covariates (meta-regression), significantly expanding the capabilities of the current neuroimaging meta-analysis methods available. We apply our methodology to synthetic data and neuroimaging meta-analysis datasets. © 2017, The International Biometric Society.

Parameter Estimation of Partial Differential Equation Models.

PubMed

Xun, Xiaolei; Cao, Jiguo; Mallick, Bani; Carroll, Raymond J; Maity, Arnab

2013-01-01

Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE, and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from LIDAR data.

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 modelling of lung function data from multiple-breath washout tests.

PubMed

Mahar, Robert K; Carlin, John B; Ranganathan, Sarath; Ponsonby, Anne-Louise; Vuillermin, Peter; Vukcevic, Damjan

2018-05-30

Paediatric respiratory researchers have widely adopted the multiple-breath washout (MBW) test because it allows assessment of lung function in unsedated infants and is well suited to longitudinal studies of lung development and disease. However, a substantial proportion of MBW tests in infants fail current acceptability criteria. We hypothesised that a model-based approach to analysing the data, in place of traditional simple empirical summaries, would enable more efficient use of these tests. We therefore developed a novel statistical model for infant MBW data and applied it to 1197 tests from 432 individuals from a large birth cohort study. We focus on Bayesian estimation of the lung clearance index, the most commonly used summary of lung function from MBW tests. Our results show that the model provides an excellent fit to the data and shed further light on statistical properties of the standard empirical approach. Furthermore, the modelling approach enables the lung clearance index to be estimated by using tests with different degrees of completeness, something not possible with the standard approach. Our model therefore allows previously unused data to be used rather than discarded, as well as routine use of shorter tests without significant loss of precision. Beyond our specific application, our work illustrates a number of important aspects of Bayesian modelling in practice, such as the importance of hierarchical specifications to account for repeated measurements and the value of model checking via posterior predictive distributions. Copyright © 2018 John Wiley & Sons, Ltd.

Hierarchical Bayesian Model Averaging for Non-Uniqueness and Uncertainty Analysis of Artificial Neural Networks

NASA Astrophysics Data System (ADS)

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

2012-12-01

Artificial Neural Networks (ANNs) have been widely used to estimate concentration of chemicals in groundwater systems. However, estimation uncertainty is rarely discussed in the literature. Uncertainty in ANN output stems from three sources: ANN inputs, ANN parameters (weights and biases), and ANN structures. Uncertainty in ANN inputs may come from input data selection and/or input data error. ANN parameters are naturally uncertain because they are maximum-likelihood estimated. ANN structure is also uncertain because there is no unique ANN model given a specific case. Therefore, multiple plausible AI models are generally resulted for a study. One might ask why good models have to be ignored in favor of the best model in traditional estimation. What is the ANN estimation variance? How do the variances from different ANN models accumulate to the total estimation variance? To answer these questions we propose a Hierarchical Bayesian Model Averaging (HBMA) framework. Instead of choosing one ANN model (the best ANN model) for estimation, HBMA averages outputs of all plausible ANN models. The model weights are based on the evidence of data. Therefore, the HBMA avoids overconfidence on the single best ANN model. In addition, HBMA is able to analyze uncertainty propagation through aggregation of ANN models in a hierarchy framework. This method is applied for estimation of fluoride concentration in the Poldasht plain and the Bazargan plain in Iran. Unusually high fluoride concentration in the Poldasht and Bazargan plains has caused negative effects on the public health. Management of this anomaly requires estimation of fluoride concentration distribution in the area. The results show that the HBMA provides a knowledge-decision-based framework that facilitates analyzing and quantifying ANN estimation uncertainties from different sources. In addition HBMA allows comparative evaluation of the realizations for each source of uncertainty by segregating the uncertainty sources in a hierarchical framework. Fluoride concentration estimation using the HBMA method shows better agreement to the observation data in the test step because they are not based on a single model with a non-dominate weights.

A Bayesian analysis of the impact of air pollution episodes on cardio-respiratory hospital admissions in the Greater London area.

PubMed

Blangiardo, Marta; Richardson, Sylvia; Gulliver, John; Hansell, Anna

2011-02-01

In this paper, we present a Bayesian hierarchical model to evaluate the effect of long-range and local range PM(10) during air pollution episodes on hospital admissions for cardio-respiratory diseases in Greater London. These episodes in 2003 are matched with the same periods during the previous year, used as a control. A baseline dose-response function is estimated for the controls and carried forward in the episodes, which are characterised by an additional component that estimates their specific effect on the health outcome.

Hierarchical Adaptive Regression Kernels for Regression with Functional Predictors.

PubMed

Woodard, Dawn B; Crainiceanu, Ciprian; Ruppert, David

2013-01-01

We propose a new method for regression using a parsimonious and scientifically interpretable representation of functional predictors. Our approach is designed for data that exhibit features such as spikes, dips, and plateaus whose frequency, location, size, and shape varies stochastically across subjects. We propose Bayesian inference of the joint functional and exposure models, and give a method for efficient computation. We contrast our approach with existing state-of-the-art methods for regression with functional predictors, and show that our method is more effective and efficient for data that include features occurring at varying locations. We apply our methodology to a large and complex dataset from the Sleep Heart Health Study, to quantify the association between sleep characteristics and health outcomes. Software and technical appendices are provided in online supplemental materials.

Estimating temporal trend in the presence of spatial complexity: A Bayesian hierarchical model for a wetland plant population undergoing restoration

USGS Publications Warehouse

Rodhouse, T.J.; Irvine, K.M.; Vierling, K.T.; Vierling, L.A.

2011-01-01

Monitoring programs that evaluate restoration and inform adaptive management are important for addressing environmental degradation. These efforts may be well served by spatially explicit hierarchical approaches to modeling because of unavoidable spatial structure inherited from past land use patterns and other factors. We developed Bayesian hierarchical models to estimate trends from annual density counts observed in a spatially structured wetland forb (Camassia quamash [camas]) population following the cessation of grazing and mowing on the study area, and in a separate reference population of camas. The restoration site was bisected by roads and drainage ditches, resulting in distinct subpopulations ("zones") with different land use histories. We modeled this spatial structure by fitting zone-specific intercepts and slopes. We allowed spatial covariance parameters in the model to vary by zone, as in stratified kriging, accommodating anisotropy and improving computation and biological interpretation. Trend estimates provided evidence of a positive effect of passive restoration, and the strength of evidence was influenced by the amount of spatial structure in the model. Allowing trends to vary among zones and accounting for topographic heterogeneity increased precision of trend estimates. Accounting for spatial autocorrelation shifted parameter coefficients in ways that varied among zones depending on strength of statistical shrinkage, autocorrelation and topographic heterogeneity-a phenomenon not widely described. Spatially explicit estimates of trend from hierarchical models will generally be more useful to land managers than pooled regional estimates and provide more realistic assessments of uncertainty. The ability to grapple with historical contingency is an appealing benefit of this approach.

Theory Learning as Stochastic Search in the Language of Thought

ERIC Educational Resources Information Center

Ullman, Tomer D.; Goodman, Noah D.; Tenenbaum, Joshua B.

2012-01-01

We present an algorithmic model for the development of children's intuitive theories within a hierarchical Bayesian framework, where theories are described as sets of logical laws generated by a probabilistic context-free grammar. We contrast our approach with connectionist and other emergentist approaches to modeling cognitive development. While…

Why environmental scientists are becoming Bayesians

Treesearch

James S. Clark

2005-01-01

Advances in computational statistics provide a general framework for the high dimensional models typically needed for ecological inference and prediction. Hierarchical Bayes (HB) represents a modelling structure with capacity to exploit diverse sources of information, to accommodate influences that are unknown (or unknowable), and to draw inference on large numbers of...

RISK ASSESSMENT FOR CRYPTOSPORIDIUM: A HIERARCHICAL BAYESIAN ANALYSIS OF HUMAN DOSE-RESPONSE DATA. (R828035)

EPA Science Inventory

Three dose_¯response studies were conducted with healthy volunteers using different Cryptosporidium parvum isolates (IOWA, TAMU, and UCP). The study data were previously analyzed for median infectious dose (ID₅₀) using a simple cumulative perce...

RISK ASSESSMENT FOR CRYPTOSPORIDIUM: A HIERARCHICAL BAYESIAN ANALYSIS OF HUMAN DOSE-RESPONSE DATA. (R829180)

EPA Science Inventory

Three dose–response studies were conducted with healthy volunteers using different Cryptosporidium parvum isolates (IOWA, TAMU, and UCP). The study data were previously analyzed for median infectious dose (ID₅₀) using a simple cumulative percent endpoi...

Transportation safety data and analysis : Volume 2, Calibration of the highway safety manual and development of new safety performance functions.

DOT National Transportation Integrated Search

2011-03-01

This report documents the calibration of the Highway Safety Manual (HSM) safety performance function (SPF) : for rural two-lane two-way roadway segments in Utah and the development of new models using negative : binomial and hierarchical Bayesian mod...

Testing Adaptive Toolbox Models: A Bayesian Hierarchical Approach

ERIC Educational Resources Information Center

Scheibehenne, Benjamin; Rieskamp, Jorg; Wagenmakers, Eric-Jan

2013-01-01

Many theories of human cognition postulate that people are equipped with a repertoire of strategies to solve the tasks they face. This theoretical framework of a cognitive toolbox provides a plausible account of intra- and interindividual differences in human behavior. Unfortunately, it is often unclear how to rigorously test the toolbox…

A Survey of Model Evaluation Approaches with a Tutorial on Hierarchical Bayesian Methods

ERIC Educational Resources Information Center

Shiffrin, Richard M.; Lee, Michael D.; Kim, Woojae; Wagenmakers, Eric-Jan

2008-01-01

This article reviews current methods for evaluating models in the cognitive sciences, including theoretically based approaches, such as Bayes factors and minimum description length measures; simulation approaches, including model mimicry evaluations; and practical approaches, such as validation and generalization measures. This article argues…

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.

Bayesian Analysis of the Association between Family-Level Factors and Siblings' Dental Caries.

PubMed

Wen, A; Weyant, R J; McNeil, D W; Crout, R J; Neiswanger, K; Marazita, M L; Foxman, B

2017-07-01

We conducted a Bayesian analysis of the association between family-level socioeconomic status and smoking and the prevalence of dental caries among siblings (children from infant to 14 y) among children living in rural and urban Northern Appalachia using data from the Center for Oral Health Research in Appalachia (COHRA). The observed proportion of siblings sharing caries was significantly different from predicted assuming siblings' caries status was independent. Using a Bayesian hierarchical model, we found the inclusion of a household factor significantly improved the goodness of fit. Other findings showed an inverse association between parental education and siblings' caries and a positive association between households with smokers and siblings' caries. Our study strengthens existing evidence suggesting that increased parental education and decreased parental cigarette smoking are associated with reduced childhood caries in the household. Our results also demonstrate the value of a Bayesian approach, which allows us to include household as a random effect, thereby providing more accurate estimates than obtained using generalized linear mixed models.

Modeling responses of large-river fish populations to global climate change through downscaling and incorporation of predictive uncertainty

USGS Publications Warehouse

Wildhaber, Mark L.; Wikle, Christopher K.; Anderson, Christopher J.; Franz, Kristie J.; Moran, Edward H.; Dey, Rima; Mader, Helmut; Kraml, Julia

2012-01-01

Climate change operates over a broad range of spatial and temporal scales. Understanding its effects on ecosystems requires multi-scale models. For understanding effects on fish populations of riverine ecosystems, climate predicted by coarse-resolution Global Climate Models must be downscaled to Regional Climate Models to watersheds to river hydrology to population response. An additional challenge is quantifying sources of uncertainty given the highly nonlinear nature of interactions between climate variables and community level processes. We present a modeling approach for understanding and accomodating uncertainty by applying multi-scale climate models and a hierarchical Bayesian modeling framework to Midwest fish population dynamics and by linking models for system components together by formal rules of probability. The proposed hierarchical modeling approach will account for sources of uncertainty in forecasts of community or population response. The goal is to evaluate the potential distributional changes in an ecological system, given distributional changes implied by a series of linked climate and system models under various emissions/use scenarios. This understanding will aid evaluation of management options for coping with global climate change. In our initial analyses, we found that predicted pallid sturgeon population responses were dependent on the climate scenario considered.

A hierarchical spatial model for well yield in complex aquifers

NASA Astrophysics Data System (ADS)

Montgomery, J.; O'sullivan, F.

2017-12-01

Efficiently siting and managing groundwater wells requires reliable estimates of the amount of water that can be produced, or the well yield. This can be challenging to predict in highly complex, heterogeneous fractured aquifers due to the uncertainty around local hydraulic properties. Promising statistical approaches have been advanced in recent years. For instance, kriging and multivariate regression analysis have been applied to well test data with limited but encouraging levels of prediction accuracy. Additionally, some analytical solutions to diffusion in homogeneous porous media have been used to infer "effective" properties consistent with observed flow rates or drawdown. However, this is an under-specified inverse problem with substantial and irreducible uncertainty. We describe a flexible machine learning approach capable of combining diverse datasets with constraining physical and geostatistical models for improved well yield prediction accuracy and uncertainty quantification. Our approach can be implemented within a hierarchical Bayesian framework using Markov Chain Monte Carlo, which allows for additional sources of information to be incorporated in priors to further constrain and improve predictions and reduce the model order. We demonstrate the usefulness of this approach using data from over 7,000 wells in a fractured bedrock aquifer.

Hierarchical spatiotemporal matrix models for characterizing invasions

USGS Publications Warehouse

Hooten, M.B.; Wikle, C.K.; Dorazio, R.M.; Royle, J. Andrew

2007-01-01

The growth and dispersal of biotic organisms is an important subject in ecology. Ecologists are able to accurately describe survival and fecundity in plant and animal populations and have developed quantitative approaches to study the dynamics of dispersal and population size. Of particular interest are the dynamics of invasive species. Such nonindigenous animals and plants can levy significant impacts on native biotic communities. Effective models for relative abundance have been developed; however, a better understanding of the dynamics of actual population size (as opposed to relative abundance) in an invasion would be beneficial to all branches of ecology. In this article, we adopt a hierarchical Bayesian framework for modeling the invasion of such species while addressing the discrete nature of the data and uncertainty associated with the probability of detection. The nonlinear dynamics between discrete time points are intuitively modeled through an embedded deterministic population model with density-dependent growth and dispersal components. Additionally, we illustrate the importance of accommodating spatially varying dispersal rates. The method is applied to the specific case of the Eurasian Collared-Dove, an invasive species at mid-invasion in the United States at the time of this writing.

Hierarchical spatiotemporal matrix models for characterizing invasions

USGS Publications Warehouse

Hooten, M.B.; Wikle, C.K.; Dorazio, R.M.; Royle, J. Andrew

2007-01-01

The growth and dispersal of biotic organisms is an important subject in ecology. Ecologists are able to accurately describe survival and fecundity in plant and animal populations and have developed quantitative approaches to study the dynamics of dispersal and population size. Of particular interest are the dynamics of invasive species. Such nonindigenous animals and plants can levy significant impacts on native biotic communities. Effective models for relative abundance have been developed; however, a better understanding of the dynamics of actual population size (as opposed to relative abundance) in an invasion would be beneficial to all branches of ecology. In this article, we adopt a hierarchical Bayesian framework for modeling the invasion of such species while addressing the discrete nature of the data and uncertainty associated with the probability of detection. The nonlinear dynamics between discrete time points are intuitively modeled through an embedded deterministic population model with density-dependent growth and dispersal components. Additionally, we illustrate the importance of accommodating spatially varying dispersal rates. The method is applied to the specific case of the Eurasian Collared-Dove, an invasive species at mid-invasion in the United States at the time of this writing. ?? 2006, The International Biometric Society.

Hierarchical Bayesian spatial models for predicting multiple forest variables using waveform LiDAR, hyperspectral imagery, and large inventory datasets

USGS Publications Warehouse

Finley, Andrew O.; Banerjee, Sudipto; Cook, Bruce D.; Bradford, John B.

2013-01-01

In this paper we detail a multivariate spatial regression model that couples LiDAR, hyperspectral and forest inventory data to predict forest outcome variables at a high spatial resolution. The proposed model is used to analyze forest inventory data collected on the US Forest Service Penobscot Experimental Forest (PEF), ME, USA. In addition to helping meet the regression model's assumptions, results from the PEF analysis suggest that the addition of multivariate spatial random effects improves model fit and predictive ability, compared with two commonly applied modeling approaches. This improvement results from explicitly modeling the covariation among forest outcome variables and spatial dependence among observations through the random effects. Direct application of such multivariate models to even moderately large datasets is often computationally infeasible because of cubic order matrix algorithms involved in estimation. We apply a spatial dimension reduction technique to help overcome this computational hurdle without sacrificing richness in modeling.

An Improved Statistical Solution for Global Seismicity by the HIST-ETAS Approach

NASA Astrophysics Data System (ADS)

Chu, A.; Ogata, Y.; Katsura, K.

2010-12-01

For long-term global seismic model fitting, recent work by Chu et al. (2010) applied the spatial-temporal ETAS model (Ogata 1998) and analyzed global data partitioned into tectonic zones based on geophysical characteristics (Bird 2003), and it has shown tremendous improvements of model fitting compared with one overall global model. While the ordinary ETAS model assumes constant parameter values across the complete region analyzed, the hierarchical space-time ETAS model (HIST-ETAS, Ogata 2004) is a newly introduced approach by proposing regional distinctions of the parameters for more accurate seismic prediction. As the HIST-ETAS model has been fit to regional data of Japan (Ogata 2010), our work applies the model to describe global seismicity. Employing the Akaike's Bayesian Information Criterion (ABIC) as an assessment method, we compare the MLE results with zone divisions considered to results obtained by an overall global model. Location dependent parameters of the model and Gutenberg-Richter b-values are optimized, and seismological interpretations are discussed.

A measure of uncertainty regarding the interval constraint of normal mean elicited by two stages of a prior hierarchy.

PubMed

Kim, Hea-Jung

2014-01-01

This paper considers a hierarchical screened Gaussian model (HSGM) for Bayesian inference of normal models when an interval constraint in the mean parameter space needs to be incorporated in the modeling but when such a restriction is uncertain. An objective measure of the uncertainty, regarding the interval constraint, accounted for by using the HSGM is proposed for the Bayesian inference. For this purpose, we drive a maximum entropy prior of the normal mean, eliciting the uncertainty regarding the interval constraint, and then obtain the uncertainty measure by considering the relationship between the maximum entropy prior and the marginal prior of the normal mean in HSGM. Bayesian estimation procedure of HSGM is developed and two numerical illustrations pertaining to the properties of the uncertainty measure are provided.

Use of space-time models to investigate the stability of patterns of disease.

PubMed

Abellan, Juan Jose; Richardson, Sylvia; Best, Nicky

2008-08-01

The use of Bayesian hierarchical spatial models has become widespread in disease mapping and ecologic studies of health-environment associations. In this type of study, the data are typically aggregated over an extensive time period, thus neglecting the time dimension. The output of purely spatial disease mapping studies is therefore the average spatial pattern of risk over the period analyzed, but the results do not inform about, for example, whether a high average risk was sustained over time or changed over time. We investigated how including the time dimension in disease-mapping models strengthens the epidemiologic interpretation of the overall pattern of risk. We discuss a class of Bayesian hierarchical models that simultaneously characterize and estimate the stable spatial and temporal patterns as well as departures from these stable components. We show how useful rules for classifying areas as stable can be constructed based on the posterior distribution of the space-time interactions. We carry out a simulation study to investigate the sensitivity and specificity of the decision rules we propose, and we illustrate our approach in a case study of congenital anomalies in England. Our results confirm that extending hierarchical disease-mapping models to models that simultaneously consider space and time leads to a number of benefits in terms of interpretation and potential for detection of localized excesses.

Basics of Bayesian methods.

PubMed

Ghosh, Sujit K

2010-01-01

Bayesian methods are rapidly becoming popular tools for making statistical inference in various fields of science including biology, engineering, finance, and genetics. One of the key aspects of Bayesian inferential method is its logical foundation that provides a coherent framework to utilize not only empirical but also scientific information available to a researcher. Prior knowledge arising from scientific background, expert judgment, or previously collected data is used to build a prior distribution which is then combined with current data via the likelihood function to characterize the current state of knowledge using the so-called posterior distribution. Bayesian methods allow the use of models of complex physical phenomena that were previously too difficult to estimate (e.g., using asymptotic approximations). Bayesian methods offer a means of more fully understanding issues that are central to many practical problems by allowing researchers to build integrated models based on hierarchical conditional distributions that can be estimated even with limited amounts of data. Furthermore, advances in numerical integration methods, particularly those based on Monte Carlo methods, have made it possible to compute the optimal Bayes estimators. However, there is a reasonably wide gap between the background of the empirically trained scientists and the full weight of Bayesian statistical inference. Hence, one of the goals of this chapter is to bridge the gap by offering elementary to advanced concepts that emphasize linkages between standard approaches and full probability modeling via Bayesian methods.

Characterizing regional-scale temporal evolution of air dose rates after the Fukushima Daiichi Nuclear Power Plant accident.

PubMed

Wainwright, Haruko M; Seki, Akiyuki; Mikami, Satoshi; Saito, Kimiaki

2018-09-01

In this study, we quantify the temporal changes of air dose rates in the regional scale around the Fukushima Dai-ichi Nuclear Power Plant in Japan, and predict the spatial distribution of air dose rates in the future. We first apply the Bayesian geostatistical method developed by Wainwright et al. (2017) to integrate multiscale datasets including ground-based walk and car surveys, and airborne surveys, all of which have different scales, resolutions, spatial coverage, and accuracy. This method is based on geostatistics to represent spatial heterogeneous structures, and also on Bayesian hierarchical models to integrate multiscale, multi-type datasets in a consistent manner. We apply this method to the datasets from three years: 2014 to 2016. The temporal changes among the three integrated maps enables us to characterize the spatiotemporal dynamics of radiation air dose rates. The data-driven ecological decay model is then coupled with the integrated map to predict future dose rates. Results show that the air dose rates are decreasing consistently across the region. While slower in the forested region, the decrease is particularly significant in the town area. The decontamination has contributed to significant reduction of air dose rates. By 2026, the air dose rates will continue to decrease, and the area above 3.8 μSv/h will be almost fully contained within the non-residential forested zone. Copyright © 2018 Elsevier Ltd. All rights reserved.

Bayesian randomized clinical trials: From fixed to adaptive design.

PubMed

Yin, Guosheng; Lam, Chi Kin; Shi, Haolun

2017-08-01

Randomized controlled studies are the gold standard for phase III clinical trials. Using α-spending functions to control the overall type I error rate, group sequential methods are well established and have been dominating phase III studies. Bayesian randomized design, on the other hand, can be viewed as a complement instead of competitive approach to the frequentist methods. For the fixed Bayesian design, the hypothesis testing can be cast in the posterior probability or Bayes factor framework, which has a direct link to the frequentist type I error rate. Bayesian group sequential design relies upon Bayesian decision-theoretic approaches based on backward induction, which is often computationally intensive. Compared with the frequentist approaches, Bayesian methods have several advantages. The posterior predictive probability serves as a useful and convenient tool for trial monitoring, and can be updated at any time as the data accrue during the trial. The Bayesian decision-theoretic framework possesses a direct link to the decision making in the practical setting, and can be modeled more realistically to reflect the actual cost-benefit analysis during the drug development process. Other merits include the possibility of hierarchical modeling and the use of informative priors, which would lead to a more comprehensive utilization of information from both historical and longitudinal data. From fixed to adaptive design, we focus on Bayesian randomized controlled clinical trials and make extensive comparisons with frequentist counterparts through numerical studies. Copyright © 2017 Elsevier Inc. All rights reserved.

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...

Calibration of Automatically Generated Items Using Bayesian Hierarchical Modeling.

ERIC Educational Resources Information Center

Johnson, Matthew S.; Sinharay, Sandip

For complex educational assessments, there is an increasing use of "item families," which are groups of related items. However, calibration or scoring for such an assessment requires fitting models that take into account the dependence structure inherent among the items that belong to the same item family. C. Glas and W. van der Linden…

A Hierarchical Bayesian Multidimensional Scaling Methodology for Accommodating Both Structural and Preference Heterogeneity

ERIC Educational Resources Information Center

Park, Joonwook; Desarbo, Wayne S.; Liechty, John

2008-01-01

Multidimensional scaling (MDS) models for the analysis of dominance data have been developed in the psychometric and classification literature to simultaneously capture subjects' "preference heterogeneity" and the underlying dimentional structure for a set of designated stimuli in a parsimonious manner. There are two major types of latent utility…

Variability, Negative Evidence, and the Acquisition of Verb Argument Constructions

ERIC Educational Resources Information Center

Perfors, Amy; Tenenbaum, Joshua B.; Wonnacott, Elizabeth

2010-01-01

We present a hierarchical Bayesian framework for modeling the acquisition of verb argument constructions. It embodies a domain-general approach to learning higher-level knowledge in the form of inductive constraints (or overhypotheses), and has been used to explain other aspects of language development such as the shape bias in learning object…

Analyzing thresholds and efficiency with hierarchical Bayesian logistic regression.

PubMed

Houpt, Joseph W; Bittner, Jennifer L

2018-07-01

Ideal observer analysis is a fundamental tool used widely in vision science for analyzing the efficiency with which a cognitive or perceptual system uses available information. The performance of an ideal observer provides a formal measure of the amount of information in a given experiment. The ratio of human to ideal performance is then used to compute efficiency, a construct that can be directly compared across experimental conditions while controlling for the differences due to the stimuli and/or task specific demands. In previous research using ideal observer analysis, the effects of varying experimental conditions on efficiency have been tested using ANOVAs and pairwise comparisons. In this work, we present a model that combines Bayesian estimates of psychometric functions with hierarchical logistic regression for inference about both unadjusted human performance metrics and efficiencies. Our approach improves upon the existing methods by constraining the statistical analysis using a standard model connecting stimulus intensity to human observer accuracy and by accounting for variability in the estimates of human and ideal observer performance scores. This allows for both individual and group level inferences. Copyright © 2018 Elsevier Ltd. All rights reserved.

A Bayesian generative model for learning semantic hierarchies

PubMed Central

Mittelman, Roni; Sun, Min; Kuipers, Benjamin; Savarese, Silvio

2014-01-01

Building fine-grained visual recognition systems that are capable of recognizing tens of thousands of categories, has received much attention in recent years. The well known semantic hierarchical structure of categories and concepts, has been shown to provide a key prior which allows for optimal predictions. The hierarchical organization of various domains and concepts has been subject to extensive research, and led to the development of the WordNet domains hierarchy (Fellbaum, 1998), which was also used to organize the images in the ImageNet (Deng et al., 2009) dataset, in which the category count approaches the human capacity. Still, for the human visual system, the form of the hierarchy must be discovered with minimal use of supervision or innate knowledge. In this work, we propose a new Bayesian generative model for learning such domain hierarchies, based on semantic input. Our model is motivated by the super-subordinate organization of domain labels and concepts that characterizes WordNet, and accounts for several important challenges: maintaining context information when progressing deeper into the hierarchy, learning a coherent semantic concept for each node, and modeling uncertainty in the perception process. PMID:24904452

A Bayesian Approach to Model Selection in Hierarchical Mixtures-of-Experts Architectures.

PubMed

Tanner, Martin A.; Peng, Fengchun; Jacobs, Robert A.

1997-03-01

There does not exist a statistical model that shows good performance on all tasks. Consequently, the model selection problem is unavoidable; investigators must decide which model is best at summarizing the data for each task of interest. This article presents an approach to the model selection problem in hierarchical mixtures-of-experts architectures. These architectures combine aspects of generalized linear models with those of finite mixture models in order to perform tasks via a recursive "divide-and-conquer" strategy. Markov chain Monte Carlo methodology is used to estimate the distribution of the architectures' parameters. One part of our approach to model selection attempts to estimate the worth of each component of an architecture so that relatively unused components can be pruned from the architecture's structure. A second part of this approach uses a Bayesian hypothesis testing procedure in order to differentiate inputs that carry useful information from nuisance inputs. Simulation results suggest that the approach presented here adheres to the dictum of Occam's razor; simple architectures that are adequate for summarizing the data are favored over more complex structures. Copyright 1997 Elsevier Science Ltd. All Rights Reserved.

Bayesian Poisson hierarchical models for crash data analysis: Investigating the impact of model choice on site-specific predictions.

PubMed

Khazraee, S Hadi; Johnson, Valen; Lord, Dominique

2018-08-01

The Poisson-gamma (PG) and Poisson-lognormal (PLN) regression models are among the most popular means for motor vehicle crash data analysis. Both models belong to the Poisson-hierarchical family of models. While numerous studies have compared the overall performance of alternative Bayesian Poisson-hierarchical models, little research has addressed the impact of model choice on the expected crash frequency prediction at individual sites. This paper sought to examine whether there are any trends among candidate models predictions e.g., that an alternative model's prediction for sites with certain conditions tends to be higher (or lower) than that from another model. In addition to the PG and PLN models, this research formulated a new member of the Poisson-hierarchical family of models: the Poisson-inverse gamma (PIGam). Three field datasets (from Texas, Michigan and Indiana) covering a wide range of over-dispersion characteristics were selected for analysis. This study demonstrated that the model choice can be critical when the calibrated models are used for prediction at new sites, especially when the data are highly over-dispersed. For all three datasets, the PIGam model would predict higher expected crash frequencies than would the PLN and PG models, in order, indicating a clear link between the models predictions and the shape of their mixing distributions (i.e., gamma, lognormal, and inverse gamma, respectively). The thicker tail of the PIGam and PLN models (in order) may provide an advantage when the data are highly over-dispersed. The analysis results also illustrated a major deficiency of the Deviance Information Criterion (DIC) in comparing the goodness-of-fit of hierarchical models; models with drastically different set of coefficients (and thus predictions for new sites) may yield similar DIC values, because the DIC only accounts for the parameters in the lowest (observation) level of the hierarchy and ignores the higher levels (regression coefficients). Copyright © 2018. Published by Elsevier Ltd.

A Bayesian, generalized frailty model for comet assays.

PubMed

Ghebretinsae, Aklilu Habteab; Faes, Christel; Molenberghs, Geert; De Boeck, Marlies; Geys, Helena

2013-05-01

This paper proposes a flexible modeling approach for so-called comet assay data regularly encountered in preclinical research. While such data consist of non-Gaussian outcomes in a multilevel hierarchical structure, traditional analyses typically completely or partly ignore this hierarchical nature by summarizing measurements within a cluster. Non-Gaussian outcomes are often modeled using exponential family models. This is true not only for binary and count data, but also for, example, time-to-event outcomes. Two important reasons for extending this family are for (1) the possible occurrence of overdispersion, meaning that the variability in the data may not be adequately described by the models, which often exhibit a prescribed mean-variance link, and (2) the accommodation of a hierarchical structure in the data, owing to clustering in the data. The first issue is dealt with through so-called overdispersion models. Clustering is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. In the case of time-to-event data, one encounters, for example, the gamma frailty model (Duchateau and Janssen, 2007 ). While both of these issues may occur simultaneously, models combining both are uncommon. Molenberghs et al. ( 2010 ) proposed a broad class of generalized linear models accommodating overdispersion and clustering through two separate sets of random effects. Here, we use this method to model data from a comet assay with a three-level hierarchical structure. Although a conjugate gamma random effect is used for the overdispersion random effect, both gamma and normal random effects are considered for the hierarchical random effect. Apart from model formulation, we place emphasis on Bayesian estimation. Our proposed method has an upper hand over the traditional analysis in that it (1) uses the appropriate distribution stipulated in the literature; (2) deals with the complete hierarchical nature; and (3) uses all information instead of summary measures. The fit of the model to the comet assay is compared against the background of more conventional model fits. Results indicate the toxicity of 1,2-dimethylhydrazine dihydrochloride at different dose levels (low, medium, and high).

Linking bovine tuberculosis on cattle farms to white-tailed deer and environmental variables using Bayesian hierarchical analysis

USGS Publications Warehouse

Walter, W. David; Smith, Rick; Vanderklok, Mike; VerCauterren, Kurt C.

2014-01-01

Bovine tuberculosis is a bacterial disease caused by Mycobacterium bovis in livestock and wildlife with hosts that include Eurasian badgers (Meles meles), brushtail possum (Trichosurus vulpecula), and white-tailed deer (Odocoileus virginianus). Risk-assessment efforts in Michigan have been initiated on farms to minimize interactions of cattle with wildlife hosts but research onM. bovis on cattle farms has not investigated the spatial context of disease epidemiology. To incorporate spatially explicit data, initial likelihood of infection probabilities for cattle farms tested for M. bovis, prevalence of M. bovis in white-tailed deer, deer density, and environmental variables for each farm were modeled in a Bayesian hierarchical framework. We used geo-referenced locations of 762 cattle farms that have been tested for M. bovis, white-tailed deer prevalence, and several environmental variables that may lead to long-term survival and viability of M. bovis on farms and surrounding habitats (i.e., soil type, habitat type). Bayesian hierarchical analyses identified deer prevalence and proportion of sandy soil within our sampling grid as the most supported model. Analysis of cattle farms tested for M. bovisidentified that for every 1% increase in sandy soil resulted in an increase in odds of infection by 4%. Our analysis revealed that the influence of prevalence of M. bovis in white-tailed deer was still a concern even after considerable efforts to prevent cattle interactions with white-tailed deer through on-farm mitigation and reduction in the deer population. Cattle farms test positive for M. bovis annually in our study area suggesting that the potential for an environmental source either on farms or in the surrounding landscape may contributing to new or re-infections with M. bovis. Our research provides an initial assessment of potential environmental factors that could be incorporated into additional modeling efforts as more knowledge of deer herd factors and cattle farm prevalence is documented.

Hierarchical Bayesian modeling of heterogeneous variances in average daily weight gain of commercial feedlot cattle.

PubMed

Cernicchiaro, N; Renter, D G; Xiang, S; White, B J; Bello, N M

2013-06-01

Variability in ADG of feedlot cattle can affect profits, thus making overall returns more unstable. Hence, knowledge of the factors that contribute to heterogeneity of variances in animal performance can help feedlot managers evaluate risks and minimize profit volatility when making managerial and economic decisions in commercial feedlots. The objectives of the present study were to evaluate heteroskedasticity, defined as heterogeneity of variances, in ADG of cohorts of commercial feedlot cattle, and to identify cattle demographic factors at feedlot arrival as potential sources of variance heterogeneity, accounting for cohort- and feedlot-level information in the data structure. An operational dataset compiled from 24,050 cohorts from 25 U. S. commercial feedlots in 2005 and 2006 was used for this study. Inference was based on a hierarchical Bayesian model implemented with Markov chain Monte Carlo, whereby cohorts were modeled at the residual level and feedlot-year clusters were modeled as random effects. Forward model selection based on deviance information criteria was used to screen potentially important explanatory variables for heteroskedasticity at cohort- and feedlot-year levels. The Bayesian modeling framework was preferred as it naturally accommodates the inherently hierarchical structure of feedlot data whereby cohorts are nested within feedlot-year clusters. Evidence for heterogeneity of variance components of ADG was substantial and primarily concentrated at the cohort level. Feedlot-year specific effects were, by far, the greatest contributors to ADG heteroskedasticity among cohorts, with an estimated ∼12-fold change in dispersion between most and least extreme feedlot-year clusters. In addition, identifiable demographic factors associated with greater heterogeneity of cohort-level variance included smaller cohort sizes, fewer days on feed, and greater arrival BW, as well as feedlot arrival during summer months. These results support that heterogeneity of variances in ADG is prevalent in feedlot performance and indicate potential sources of heteroskedasticity. Further investigation of factors associated with heteroskedasticity in feedlot performance is warranted to increase consistency and uniformity in commercial beef cattle production and subsequent profitability.

SPATIO-TEMPORAL MODELING OF AGRICULTURAL YIELD DATA WITH AN APPLICATION TO PRICING CROP INSURANCE CONTRACTS

PubMed Central

Ozaki, Vitor A.; Ghosh, Sujit K.; Goodwin, Barry K.; Shirota, Ricardo

2009-01-01

This article presents a statistical model of agricultural yield data based on a set of hierarchical Bayesian models that allows joint modeling of temporal and spatial autocorrelation. This method captures a comprehensive range of the various uncertainties involved in predicting crop insurance premium rates as opposed to the more traditional ad hoc, two-stage methods that are typically based on independent estimation and prediction. A panel data set of county-average yield data was analyzed for 290 counties in the State of Paraná (Brazil) for the period of 1990 through 2002. Posterior predictive criteria are used to evaluate different model specifications. This article provides substantial improvements in the statistical and actuarial methods often applied to the calculation of insurance premium rates. These improvements are especially relevant to situations where data are limited. PMID:19890450

Improving the Accuracy of Planet Occurrence Rates from Kepler Using Approximate Bayesian Computation

NASA Astrophysics Data System (ADS)

Hsu, Danley C.; Ford, Eric B.; Ragozzine, Darin; Morehead, Robert C.

2018-05-01

We present a new framework to characterize the occurrence rates of planet candidates identified by Kepler based on hierarchical Bayesian modeling, approximate Bayesian computing (ABC), and sequential importance sampling. For this study, we adopt a simple 2D grid in planet radius and orbital period as our model and apply our algorithm to estimate occurrence rates for Q1–Q16 planet candidates orbiting solar-type stars. We arrive at significantly increased planet occurrence rates for small planet candidates (R p < 1.25 R ⊕) at larger orbital periods (P > 80 day) compared to the rates estimated by the more common inverse detection efficiency method (IDEM). Our improved methodology estimates that the occurrence rate density of small planet candidates in the habitable zone of solar-type stars is {1.6}-0.5+1.2 per factor of 2 in planet radius and orbital period. Additionally, we observe a local minimum in the occurrence rate for strong planet candidates marginalized over orbital period between 1.5 and 2 R ⊕ that is consistent with previous studies. For future improvements, the forward modeling approach of ABC is ideally suited to incorporating multiple populations, such as planets, astrophysical false positives, and pipeline false alarms, to provide accurate planet occurrence rates and uncertainties. Furthermore, ABC provides a practical statistical framework for answering complex questions (e.g., frequency of different planetary architectures) and providing sound uncertainties, even in the face of complex selection effects, observational biases, and follow-up strategies. In summary, ABC offers a powerful tool for accurately characterizing a wide variety of astrophysical populations.

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

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

Brewer, Brendon J.; Foreman-Mackey, Daniel; Hogg, David W., E-mail: bj.brewer@auckland.ac.nz

We present and implement a probabilistic (Bayesian) method for producing catalogs from images of stellar fields. The method is capable of inferring the number of sources N in the image and can also handle the challenges introduced by noise, overlapping sources, and an unknown point-spread function. The luminosity function of the stars can also be inferred, even when the precise luminosity of each star is uncertain, via the use of a hierarchical Bayesian model. The computational feasibility of the method is demonstrated on two simulated images with different numbers of stars. We find that our method successfully recovers the inputmore » parameter values along with principled uncertainties even when the field is crowded. We also compare our results with those obtained from the SExtractor software. While the two approaches largely agree about the fluxes of the bright stars, the Bayesian approach provides more accurate inferences about the faint stars and the number of stars, particularly in the crowded case.« less

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.

A small-area ecologic study of myocardial infarction, neighborhood deprivation, and sex: a Bayesian modeling approach.

PubMed

Deguen, Séverine; Lalloue, Benoît; Bard, Denis; Havard, Sabrina; Arveiler, Dominique; Zmirou-Navier, Denis

2010-07-01

Socioeconomic inequalities in the risk of coronary heart disease (CHD) are well documented for men and women. CHD incidence is greater for men but its association with socioeconomic status is usually found to be stronger among women. We explored the sex-specific association between neighborhood deprivation level and the risk of myocardial infarction (MI) at a small-area scale. We studied 1193 myocardial infarction events in people aged 35-74 years in the Strasbourg metropolitan area, France (2000-2003). We used a deprivation index to assess the neighborhood deprivation level. To take into account spatial dependence and the variability of MI rates due to the small number of events, we used a hierarchical Bayesian modeling approach. We fitted hierarchical Bayesian models to estimate sex-specific relative and absolute MI risks across deprivation categories. We tested departure from additive joint effects of deprivation and sex. The risk of MI increased with the deprivation level for both sexes, but was higher for men for all deprivation classes. Relative rates increased along the deprivation scale more steadily for women and followed a different pattern: linear for men and nonlinear for women. Our data provide evidence of effect modification, with departure from an additive joint effect of deprivation and sex. We document sex differences in the socioeconomic gradient of MI risk in Strasbourg. Women appear more susceptible at levels of extreme deprivation; this result is not a chance finding, given the large difference in event rates between men and women.

Hierarchical Bayesian inference of the initial mass function in composite stellar populations

NASA Astrophysics Data System (ADS)

Dries, M.; Trager, S. C.; Koopmans, L. V. E.; Popping, G.; Somerville, R. S.

2018-03-01

The initial mass function (IMF) is a key ingredient in many studies of galaxy formation and evolution. Although the IMF is often assumed to be universal, there is continuing evidence that it is not universal. Spectroscopic studies that derive the IMF of the unresolved stellar populations of a galaxy often assume that this spectrum can be described by a single stellar population (SSP). To alleviate these limitations, in this paper we have developed a unique hierarchical Bayesian framework for modelling composite stellar populations (CSPs). Within this framework, we use a parametrized IMF prior to regulate a direct inference of the IMF. We use this new framework to determine the number of SSPs that is required to fit a set of realistic CSP mock spectra. The CSP mock spectra that we use are based on semi-analytic models and have an IMF that varies as a function of stellar velocity dispersion of the galaxy. Our results suggest that using a single SSP biases the determination of the IMF slope to a higher value than the true slope, although the trend with stellar velocity dispersion is overall recovered. If we include more SSPs in the fit, the Bayesian evidence increases significantly and the inferred IMF slopes of our mock spectra converge, within the errors, to their true values. Most of the bias is already removed by using two SSPs instead of one. We show that we can reconstruct the variable IMF of our mock spectra for signal-to-noise ratios exceeding ˜75.

A Bayesian Ensemble Approach for Epidemiological Projections

PubMed Central

Lindström, Tom; Tildesley, Michael; Webb, Colleen

2015-01-01

Mathematical models are powerful tools for epidemiology and can be used to compare control actions. However, different models and model parameterizations may provide different prediction of outcomes. In other fields of research, ensemble modeling has been used to combine multiple projections. We explore the possibility of applying such methods to epidemiology by adapting Bayesian techniques developed for climate forecasting. We exemplify the implementation with single model ensembles based on different parameterizations of the Warwick model run for the 2001 United Kingdom foot and mouth disease outbreak and compare the efficacy of different control actions. This allows us to investigate the effect that discrepancy among projections based on different modeling assumptions has on the ensemble prediction. A sensitivity analysis showed that the choice of prior can have a pronounced effect on the posterior estimates of quantities of interest, in particular for ensembles with large discrepancy among projections. However, by using a hierarchical extension of the method we show that prior sensitivity can be circumvented. We further extend the method to include a priori beliefs about different modeling assumptions and demonstrate that the effect of this can have different consequences depending on the discrepancy among projections. We propose that the method is a promising analytical tool for ensemble modeling of disease outbreaks. PMID:25927892

Do marginalized neighbourhoods have less healthy retail food environments? An analysis using Bayesian spatial latent factor and hurdle models.

PubMed

Luan, Hui; Minaker, Leia M; Law, Jane

2016-08-22

Findings of whether marginalized neighbourhoods have less healthy retail food environments (RFE) are mixed across countries, in part because inconsistent approaches have been used to characterize RFE 'healthfulness' and marginalization, and researchers have used non-spatial statistical methods to respond to this ultimately spatial issue. This study uses in-store features to categorize healthy and less healthy food outlets. Bayesian spatial hierarchical models are applied to explore the association between marginalization dimensions and RFE healthfulness (i.e., relative healthy food access that modelled via a probability distribution) at various geographical scales. Marginalization dimensions are derived from a spatial latent factor model. Zero-inflation occurring at the walkable-distance scale is accounted for with a spatial hurdle model. Neighbourhoods with higher residential instability, material deprivation, and population density are more likely to have access to healthy food outlets within a walkable distance from a binary 'have' or 'not have' access perspective. At the walkable distance scale however, materially deprived neighbourhoods are found to have less healthy RFE (lower relative healthy food access). Food intervention programs should be developed for striking the balance between healthy and less healthy food access in the study region as well as improving opportunities for residents to buy and consume foods consistent with dietary recommendations.

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

Model selection and model averaging in phylogenetics: advantages of akaike information criterion and bayesian approaches over likelihood ratio tests.

PubMed

Posada, David; Buckley, Thomas R

2004-10-01

Model selection is a topic of special relevance in molecular phylogenetics that affects many, if not all, stages of phylogenetic inference. Here we discuss some fundamental concepts and techniques of model selection in the context of phylogenetics. We start by reviewing different aspects of the selection of substitution models in phylogenetics from a theoretical, philosophical and practical point of view, and summarize this comparison in table format. We argue that the most commonly implemented model selection approach, the hierarchical likelihood ratio test, is not the optimal strategy for model selection in phylogenetics, and that approaches like the Akaike Information Criterion (AIC) and Bayesian methods offer important advantages. In particular, the latter two methods are able to simultaneously compare multiple nested or nonnested models, assess model selection uncertainty, and allow for the estimation of phylogenies and model parameters using all available models (model-averaged inference or multimodel inference). We also describe how the relative importance of the different parameters included in substitution models can be depicted. To illustrate some of these points, we have applied AIC-based model averaging to 37 mitochondrial DNA sequences from the subgenus Ohomopterus(genus Carabus) ground beetles described by Sota and Vogler (2001).

Does History Repeat Itself? Wavelets and the Phylodynamics of Influenza A

PubMed Central

Tom, Jennifer A.; Sinsheimer, Janet S.; Suchard, Marc A.

2012-01-01

Unprecedented global surveillance of viruses will result in massive sequence data sets that require new statistical methods. These data sets press the limits of Bayesian phylogenetics as the high-dimensional parameters that comprise a phylogenetic tree increase the already sizable computational burden of these techniques. This burden often results in partitioning the data set, for example, by gene, and inferring the evolutionary dynamics of each partition independently, a compromise that results in stratified analyses that depend only on data within a given partition. However, parameter estimates inferred from these stratified models are likely strongly correlated, considering they rely on data from a single data set. To overcome this shortfall, we exploit the existing Monte Carlo realizations from stratified Bayesian analyses to efficiently estimate a nonparametric hierarchical wavelet-based model and learn about the time-varying parameters of effective population size that reflect levels of genetic diversity across all partitions simultaneously. Our methods are applied to complete genome influenza A sequences that span 13 years. We find that broad peaks and trends, as opposed to seasonal spikes, in the effective population size history distinguish individual segments from the complete genome. We also address hypotheses regarding intersegment dynamics within a formal statistical framework that accounts for correlation between segment-specific parameters. PMID:22160768

Bayesian Estimation of Circumplex Models Subject to Prior Theory Constraints and Scale-Usage Bias

ERIC Educational Resources Information Center

Lenk, Peter; Wedel, Michel; Bockenholt, Ulf

2006-01-01

This paper presents a hierarchical Bayes circumplex model for ordinal ratings data. The circumplex model was proposed to represent the circular ordering of items in psychological testing by imposing inequalities on the correlations of the items. We provide a specification of the circumplex, propose identifying constraints and conjugate priors for…

Analyzing the Factorial Structure of the Classroom Assessment Scoring System-Secondary Using a Bayesian Hierarchical Multivariate Ordinal Model

ERIC Educational Resources Information Center

Yuan, Kun; McCaffrey, Daniel F.; Savitsky, Terrance D.

2013-01-01

Standardized teaching observation protocols have become increasingly popular in evaluating teaching in recent years. One of such protocols that has gained substantial interest from researchers and practitioners is the Classroom Assessment Scoring System-Secondary (CLASSS). According to the developer, CLASS-S has three domains of teacher-student…

Hierarchical models and bayesian analysis of bird survey information

Treesearch

John R. Sauer; William A. Link; J. Andrew Royle

2005-01-01

Summary of bird survey information is a critical component of conservation activities, but often our summaries rely on statistical methods that do not accommodate the limitations of the information. Prioritization of species requires ranking and analysis of species by magnitude of population trend, but often magnitude of trend is a misleading measure of actual decline...

A Bayesian Hierarchical Selection Model for Academic Growth with Missing Data

ERIC Educational Resources Information Center

Allen, Jeff

2017-01-01

Using a sample of schools testing annually in grades 9-11 with a vertically linked series of assessments, a latent growth curve model is used to model test scores with student intercepts and slopes nested within school. Missed assessments can occur because of student mobility, student dropout, absenteeism, and other reasons. Missing data…

Accounting for imperfect detection in Hill numbers for biodiversity studies

USGS Publications Warehouse

Broms, Kristin M.; Hooten, Mevin B.; Fitzpatrick, Ryan M.

2015-01-01

The occupancy-based Hill number estimators are always at their asymptotic values (i.e. as if an infinite number of samples have been taken for the study region), therefore making it easy to compare biodiversity between different assemblages. In addition, the Hill numbers are computed as derived quantities within a Bayesian hierarchical model, allowing for straightforward inference.

Making the Most of What We Have: A Practical Application of Multidimensional Item Response Theory in Test Scoring

ERIC Educational Resources Information Center

de la Torre, Jimmy; Patz, Richard J.

2005-01-01

This article proposes a practical method that capitalizes on the availability of information from multiple tests measuring correlated abilities given in a single test administration. By simultaneously estimating different abilities with the use of a hierarchical Bayesian framework, more precise estimates for each ability dimension are obtained.…

Discriminative Bayesian Dictionary Learning for Classification.

PubMed

Akhtar, Naveed; Shafait, Faisal; Mian, Ajmal

2016-12-01

We propose a Bayesian approach to learn discriminative dictionaries for sparse representation of data. The proposed approach infers probability distributions over the atoms of a discriminative dictionary using a finite approximation of Beta Process. It also computes sets of Bernoulli distributions that associate class labels to the learned dictionary atoms. This association signifies the selection probabilities of the dictionary atoms in the expansion of class-specific data. Furthermore, the non-parametric character of the proposed approach allows it to infer the correct size of the dictionary. We exploit the aforementioned Bernoulli distributions in separately learning a linear classifier. The classifier uses the same hierarchical Bayesian model as the dictionary, which we present along the analytical inference solution for Gibbs sampling. For classification, a test instance is first sparsely encoded over the learned dictionary and the codes are fed to the classifier. We performed experiments for face and action recognition; and object and scene-category classification using five public datasets and compared the results with state-of-the-art discriminative sparse representation approaches. Experiments show that the proposed Bayesian approach consistently outperforms the existing approaches.

Cortical Hierarchies Perform Bayesian Causal Inference in Multisensory Perception

PubMed Central

Rohe, Tim; Noppeney, Uta

2015-01-01

To form a veridical percept of the environment, the brain needs to integrate sensory signals from a common source but segregate those from independent sources. Thus, perception inherently relies on solving the “causal inference problem.” Behaviorally, humans solve this problem optimally as predicted by Bayesian Causal Inference; yet, the underlying neural mechanisms are unexplored. Combining psychophysics, Bayesian modeling, functional magnetic resonance imaging (fMRI), and multivariate decoding in an audiovisual spatial localization task, we demonstrate that Bayesian Causal Inference is performed by a hierarchy of multisensory processes in the human brain. At the bottom of the hierarchy, in auditory and visual areas, location is represented on the basis that the two signals are generated by independent sources (= segregation). At the next stage, in posterior intraparietal sulcus, location is estimated under the assumption that the two signals are from a common source (= forced fusion). Only at the top of the hierarchy, in anterior intraparietal sulcus, the uncertainty about the causal structure of the world is taken into account and sensory signals are combined as predicted by Bayesian Causal Inference. Characterizing the computational operations of signal interactions reveals the hierarchical nature of multisensory perception in human neocortex. It unravels how the brain accomplishes Bayesian Causal Inference, a statistical computation fundamental for perception and cognition. Our results demonstrate how the brain combines information in the face of uncertainty about the underlying causal structure of the world. PMID:25710328

Inferring the Growth of Massive Galaxies Using Bayesian Spectral Synthesis Modeling

NASA Astrophysics Data System (ADS)

Stillman, Coley Michael; Poremba, Megan R.; Moustakas, John

2018-01-01

The most massive galaxies in the universe are typically found at the centers of massive galaxy clusters. Studying these galaxies can provide valuable insight into the hierarchical growth of massive dark matter halos. One of the key challenges of measuring the stellar mass growth of massive galaxies is converting the measured light profiles into stellar mass. We use Prospector, a state-of-the-art Bayesian spectral synthesis modeling code, to infer the total stellar masses of a pilot sample of massive central galaxies selected from the Sloan Digital Sky Survey. We compare our stellar mass estimates to previous measurements, and present some of the quantitative diagnostics provided by Prospector.

Program SPACECAP: software for estimating animal density using spatially explicit capture-recapture models

USGS Publications Warehouse

Gopalaswamy, Arjun M.; Royle, J. Andrew; Hines, James E.; Singh, Pallavi; Jathanna, Devcharan; Kumar, N. Samba; Karanth, K. Ullas

2012-01-01

1. The advent of spatially explicit capture-recapture models is changing the way ecologists analyse capture-recapture data. However, the advantages offered by these new models are not fully exploited because they can be difficult to implement. 2. To address this need, we developed a user-friendly software package, created within the R programming environment, called SPACECAP. This package implements Bayesian spatially explicit hierarchical models to analyse spatial capture-recapture data. 3. Given that a large number of field biologists prefer software with graphical user interfaces for analysing their data, SPACECAP is particularly useful as a tool to increase the adoption of Bayesian spatially explicit capture-recapture methods in practice.

Bayesian naturalness, simplicity, and testability applied to the B ‑ L MSSM GUT

NASA Astrophysics Data System (ADS)

Fundira, Panashe; Purves, Austin

2018-04-01

Recent years have seen increased use of Bayesian model comparison to quantify notions such as naturalness, simplicity, and testability, especially in the area of supersymmetric model building. After demonstrating that Bayesian model comparison can resolve a paradox that has been raised in the literature concerning the naturalness of the proton mass, we apply Bayesian model comparison to GUTs, an area to which it has not been applied before. We find that the GUTs are substantially favored over the nonunifying puzzle model. Of the GUTs we consider, the B ‑ L MSSM GUT is the most favored, but the MSSM GUT is almost equally favored.

Nutritional habits, lifestyle, and genetic predisposition in cardiovascular and metabolic traits in Turkish population.

PubMed

Karaca, Sefayet; Erge, Sema; Cesuroglu, Tomris; Polimanti, Renato

2016-06-01

Cardiovascular and metabolic traits (CMT) are influenced by complex interactive processes including diet, lifestyle, and genetic predisposition. The present study investigated the interactions of these risk factors in relation to CMTs in the Turkish population. We applied bootstrap agglomerative hierarchical clustering and Bayesian network learning algorithms to identify the causative relationships among genes involved in different biological mechanisms (i.e., lipid metabolism, hormone metabolism, cellular detoxification, aging, and energy metabolism), lifestyle (i.e., physical activity, smoking behavior, and metropolitan residency), anthropometric traits (i.e., body mass index, body fat ratio, and waist-to-hip ratio), and dietary habits (i.e., daily intakes of macro- and micronutrients) in relation to CMTs (i.e., health conditions and blood parameters). We identified significant correlations between dietary habits (soybean and vitamin B12 intakes) and different cardiometabolic diseases that were confirmed by the Bayesian network-learning algorithm. Genetic factors contributed to these disease risks also through the pleiotropy of some genetic variants (i.e., F5 rs6025 and MTR rs180508). However, we also observed that certain genetic associations are indirect since they are due to the causative relationships among the CMTs (e.g., APOC3 rs5128 is associated with low-density lipoproteins cholesterol and, by extension, total cholesterol). Our study applied a novel approach to integrate various sources of information and dissect the complex interactive processes related to CMTs. Our data indicated that complex causative networks are present: causative relationships exist among CMTs and are affected by genetic factors (with pleiotropic and non-pleiotropic effects) and dietary habits. Copyright © 2016 Elsevier Inc. All rights reserved.

A hierarchical model for estimating density in camera-trap studies

USGS Publications Warehouse

Royle, J. Andrew; Nichols, James D.; Karanth, K.Ullas; Gopalaswamy, Arjun M.

2009-01-01

Estimating animal density using capture–recapture data from arrays of detection devices such as camera traps has been problematic due to the movement of individuals and heterogeneity in capture probability among them induced by differential exposure to trapping.We develop a spatial capture–recapture model for estimating density from camera-trapping data which contains explicit models for the spatial point process governing the distribution of individuals and their exposure to and detection by traps.We adopt a Bayesian approach to analysis of the hierarchical model using the technique of data augmentation.The model is applied to photographic capture–recapture data on tigers Panthera tigris in Nagarahole reserve, India. Using this model, we estimate the density of tigers to be 14·3 animals per 100 km2 during 2004.Synthesis and applications. Our modelling framework largely overcomes several weaknesses in conventional approaches to the estimation of animal density from trap arrays. It effectively deals with key problems such as individual heterogeneity in capture probabilities, movement of traps, presence of potential ‘holes’ in the array and ad hoc estimation of sample area. The formulation, thus, greatly enhances flexibility in the conduct of field surveys as well as in the analysis of data, from studies that may involve physical, photographic or DNA-based ‘captures’ of individual animals.

TYPE Ia SUPERNOVA COLORS AND EJECTA VELOCITIES: HIERARCHICAL BAYESIAN REGRESSION WITH NON-GAUSSIAN DISTRIBUTIONS

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

Mandel, Kaisey S.; Kirshner, Robert P.; Foley, Ryan J., E-mail: kmandel@cfa.harvard.edu

2014-12-20

We investigate the statistical dependence of the peak intrinsic colors of Type Ia supernovae (SNe Ia) on their expansion velocities at maximum light, measured from the Si II λ6355 spectral feature. We construct a new hierarchical Bayesian regression model, accounting for the random effects of intrinsic scatter, measurement error, and reddening by host galaxy dust, and implement a Gibbs sampler and deviance information criteria to estimate the correlation. The method is applied to the apparent colors from BVRI light curves and Si II velocity data for 79 nearby SNe Ia. The apparent color distributions of high-velocity (HV) and normal velocitymore » (NV) supernovae exhibit significant discrepancies for B – V and B – R, but not other colors. Hence, they are likely due to intrinsic color differences originating in the B band, rather than dust reddening. The mean intrinsic B – V and B – R color differences between HV and NV groups are 0.06 ± 0.02 and 0.09 ± 0.02 mag, respectively. A linear model finds significant slopes of –0.021 ± 0.006 and –0.030 ± 0.009 mag (10{sup 3} km s{sup –1}){sup –1} for intrinsic B – V and B – R colors versus velocity, respectively. Because the ejecta velocity distribution is skewed toward high velocities, these effects imply non-Gaussian intrinsic color distributions with skewness up to +0.3. Accounting for the intrinsic-color-velocity correlation results in corrections to A{sub V} extinction estimates as large as –0.12 mag for HV SNe Ia and +0.06 mag for NV events. Velocity measurements from SN Ia spectra have the potential to diminish systematic errors from the confounding of intrinsic colors and dust reddening affecting supernova distances.« less

A Gentle Introduction to Bayesian Analysis: Applications to Developmental Research

ERIC Educational Resources Information Center

van de Schoot, Rens; Kaplan, David; Denissen, Jaap; Asendorpf, Jens B.; Neyer, Franz J.; van Aken, Marcel A. G.

2014-01-01

Bayesian statistical methods are becoming ever more popular in applied and fundamental research. In this study a gentle introduction to Bayesian analysis is provided. It is shown under what circumstances it is attractive to use Bayesian estimation, and how to interpret properly the results. First, the ingredients underlying Bayesian methods are…

Bayesian Hierarchical Air-Sea Interaction Modeling: Application to the Labrador Sea

NASA Technical Reports Server (NTRS)

Niiler, Pearn P.

2002-01-01

The objectives are to: 1) Organize data from 26 MINIMET drifters in the Labrador Sea, including sensor calibration and error checking of ARGOS transmissions. 2) Produce wind direction, barometer, and sea surface temperature time series. In addition, provide data from historical file of 150 SHARP drifters in the Labrador Sea. 3) Work with data interpretation and data-modeling assimilation issues.

Abrupt Strategy Change Underlies Gradual Performance Change: Bayesian Hierarchical Models of Component and Aggregate Strategy Use

ERIC Educational Resources Information Center

Wynton, Sarah K. A.; Anglim, Jeromy

2017-01-01

While researchers have often sought to understand the learning curve in terms of multiple component processes, few studies have measured and mathematically modeled these processes on a complex task. In particular, there remains a need to reconcile how abrupt changes in strategy use can co-occur with gradual changes in task completion time. Thus,…

ScreenBEAM: a novel meta-analysis algorithm for functional genomics screens via Bayesian hierarchical modeling | Office of Cancer Genomics

Cancer.gov

Functional genomics (FG) screens, using RNAi or CRISPR technology, have become a standard tool for systematic, genome-wide loss-of-function studies for therapeutic target discovery. As in many large-scale assays, however, off-target effects, variable reagents' potency and experimental noise must be accounted for appropriately control for false positives.

Mapping pre-European settlement vegetation at fine resolutions using a hierarchical Bayesian model and GIS

Treesearch

Hong S. He; Daniel C. Dey; Xiuli Fan; Mevin B. Hooten; John M. Kabrick; Christopher K. Wikle; Zhaofei. Fan

2007-01-01

In the Midwestern United States, the GeneralLandOffice (GLO) survey records provide the only reasonably accurate data source of forest composition and tree species distribution at the time of pre-European settlement (circa late 1800 to early 1850). However, GLO data have two fundamental limitations: coarse spatial resolutions (the square mile section and half mile...

Temporal-Spatial Ambient Concentrator Estimator (T-SpACE): Hierarchical Bayesian Model Software Used to Estimate Ambient Concentrations of NAAQS Air Pollutants in Support of Health Studies

EPA Science Inventory

To fulfill its mission to protect human health and the environment, EPA has established National Ambient Air Quality Standards (NAAQS) on six selected air pollutants known as criteria pollutants: ozone (O3); carbon monoxide (CO); lead (Pb); nitrogen dioxide (NO2); sulfur dioxide ...

Assessing the impact of fine particulate matter (PM2.5) on respiratory-cardiovascular chronic diseases in the New York City Metropolitan area using Hierarchical Bayesian Model estimates

EPA Science Inventory

An enhanced research paradigm is presented to address the spatial and temporal gaps in fine particulate matter (PM2.5) measurements and generate realistic and representative concentration fields for use in epidemiological studies of human exposure to ambient air particulate conce...

Hierarchical Bayesian inference on genetic and non-genetic components of partial efficiencies determining feed efficiency in dairy cattle

USDA-ARS?s Scientific Manuscript database

Dairy cattle feed efficiency (FE) can be defined as the ability to convert DMI into milk energy (MILKE) and maintenance or metabolic body weight (MBW). In other words, DMI is conditional on MILKE and MBW (DMI|MILKE,MBW). These partial regressions or partial efficiencies (PE) of DMI on MILKE and MBW ...

Fully Bayesian Estimation of Data from Single Case Designs

ERIC Educational Resources Information Center

Rindskopf, David

2013-01-01

Single case designs (SCDs) generally consist of a small number of short time series in two or more phases. The analysis of SCDs statistically fits in the framework of a multilevel model, or hierarchical model. The usual analysis does not take into account the uncertainty in the estimation of the random effects. This not only has an effect on the…

Improving phylogenetic analyses by incorporating additional information from genetic sequence databases.

PubMed

Liang, Li-Jung; Weiss, Robert E; Redelings, Benjamin; Suchard, Marc A

2009-10-01

Statistical analyses of phylogenetic data culminate in uncertain estimates of underlying model parameters. Lack of additional data hinders the ability to reduce this uncertainty, as the original phylogenetic dataset is often complete, containing the entire gene or genome information available for the given set of taxa. Informative priors in a Bayesian analysis can reduce posterior uncertainty; however, publicly available phylogenetic software specifies vague priors for model parameters by default. We build objective and informative priors using hierarchical random effect models that combine additional datasets whose parameters are not of direct interest but are similar to the analysis of interest. We propose principled statistical methods that permit more precise parameter estimates in phylogenetic analyses by creating informative priors for parameters of interest. Using additional sequence datasets from our lab or public databases, we construct a fully Bayesian semiparametric hierarchical model to combine datasets. A dynamic iteratively reweighted Markov chain Monte Carlo algorithm conveniently recycles posterior samples from the individual analyses. We demonstrate the value of our approach by examining the insertion-deletion (indel) process in the enolase gene across the Tree of Life using the phylogenetic software BALI-PHY; we incorporate prior information about indels from 82 curated alignments downloaded from the BAliBASE database.

Dual Sticky Hierarchical Dirichlet Process Hidden Markov Model and Its Application to Natural Language Description of Motions.

PubMed

Hu, Weiming; Tian, Guodong; Kang, Yongxin; Yuan, Chunfeng; Maybank, Stephen

2017-09-25

In this paper, a new nonparametric Bayesian model called the dual sticky hierarchical Dirichlet process hidden Markov model (HDP-HMM) is proposed for mining activities from a collection of time series data such as trajectories. All the time series data are clustered. Each cluster of time series data, corresponding to a motion pattern, is modeled by an HMM. Our model postulates a set of HMMs that share a common set of states (topics in an analogy with topic models for document processing), but have unique transition distributions. For the application to motion trajectory modeling, topics correspond to motion activities. The learnt topics are clustered into atomic activities which are assigned predicates. We propose a Bayesian inference method to decompose a given trajectory into a sequence of atomic activities. On combining the learnt sources and sinks, semantic motion regions, and the learnt sequence of atomic activities, the action represented by the trajectory can be described in natural language in as automatic a way as possible. The effectiveness of our dual sticky HDP-HMM is validated on several trajectory datasets. The effectiveness of the natural language descriptions for motions is demonstrated on the vehicle trajectories extracted from a traffic scene.

Estimating the Term Structure With a Semiparametric Bayesian Hierarchical Model: An Application to Corporate Bonds.

PubMed

Cruz-Marcelo, Alejandro; Ensor, Katherine B; Rosner, Gary L

2011-06-01

The term structure of interest rates is used to price defaultable bonds and credit derivatives, as well as to infer the quality of bonds for risk management purposes. We introduce a model that jointly estimates term structures by means of a Bayesian hierarchical model with a prior probability model based on Dirichlet process mixtures. The modeling methodology borrows strength across term structures for purposes of estimation. The main advantage of our framework is its ability to produce reliable estimators at the company level even when there are only a few bonds per company. After describing the proposed model, we discuss an empirical application in which the term structure of 197 individual companies is estimated. The sample of 197 consists of 143 companies with only one or two bonds. In-sample and out-of-sample tests are used to quantify the improvement in accuracy that results from approximating the term structure of corporate bonds with estimators by company rather than by credit rating, the latter being a popular choice in the financial literature. A complete description of a Markov chain Monte Carlo (MCMC) scheme for the proposed model is available as Supplementary Material.

Estimating the Term Structure With a Semiparametric Bayesian Hierarchical Model: An Application to Corporate Bonds1

PubMed Central

Cruz-Marcelo, Alejandro; Ensor, Katherine B.; Rosner, Gary L.

2011-01-01

The term structure of interest rates is used to price defaultable bonds and credit derivatives, as well as to infer the quality of bonds for risk management purposes. We introduce a model that jointly estimates term structures by means of a Bayesian hierarchical model with a prior probability model based on Dirichlet process mixtures. The modeling methodology borrows strength across term structures for purposes of estimation. The main advantage of our framework is its ability to produce reliable estimators at the company level even when there are only a few bonds per company. After describing the proposed model, we discuss an empirical application in which the term structure of 197 individual companies is estimated. The sample of 197 consists of 143 companies with only one or two bonds. In-sample and out-of-sample tests are used to quantify the improvement in accuracy that results from approximating the term structure of corporate bonds with estimators by company rather than by credit rating, the latter being a popular choice in the financial literature. A complete description of a Markov chain Monte Carlo (MCMC) scheme for the proposed model is available as Supplementary Material. PMID:21765566

Using time-varying asymptotic length and body condition of top piscivores to indicate ecosystem regime shift in the main basin of Lake Huron: a Bayesian hierarchical modeling approach

USGS Publications Warehouse

He, Ji X.; Bence, James R.; Roseman, Edward F.; Fielder, David G.; Ebener, Mark P.

2015-01-01

We evaluated the ecosystem regime shift in the main basin of Lake Huron that was indicated by the 2003 collapse of alewives, and dramatic declines in Chinook salmon abundance thereafter. We found that the period of 1995-2002 should be considered as the early phase of the final regime shift. We developed two Bayesian hierarchical models to describe time-varying growth based on the von Bertalanffy growth function and the length-mass relationship. We used asymptotic length as an index of growth potential, and predicted body mass at a given length as an index of body condition. Modeling fits to length and body mass at age of lake trout, Chinook salmon, and walleye were excellent. Based on posterior distributions, we evaluated the shifts in among-year geometric means of the growth potential and body condition. For a given top piscivore, one of the two indices responded to the regime shift much earlier than the 2003 collapse of alewives, the other corresponded to the 2003 changes, and which index provided the early signal differed among the three top piscivores.

Relative age and birthplace effect in Japanese professional sports: a quantitative evaluation using a Bayesian hierarchical Poisson model.

PubMed

Ishigami, Hideaki

2016-01-01

Relative age effect (RAE) in sports has been well documented. Recent studies investigate the effect of birthplace in addition to the RAE. The first objective of this study was to show the magnitude of the RAE in two major professional sports in Japan, baseball and soccer. Second, we examined the birthplace effect and compared its magnitude with that of the RAE. The effect sizes were estimated using a Bayesian hierarchical Poisson model with the number of players as dependent variable. The RAEs were 9.0% and 7.7% per month for soccer and baseball, respectively. These estimates imply that children born in the first month of a school year have about three times greater chance of becoming a professional player than those born in the last month of the year. Over half of the difference in likelihoods of becoming a professional player between birthplaces was accounted for by weather conditions, with the likelihood decreasing by 1% per snow day. An effect of population size was not detected in the data. By investigating different samples, we demonstrated that using quarterly data leads to underestimation and that the age range of sampled athletes should be set carefully.

Hierarchical Spatial Concept Formation Based on Multimodal Information for Human Support Robots.

PubMed

Hagiwara, Yoshinobu; Inoue, Masakazu; Kobayashi, Hiroyoshi; Taniguchi, Tadahiro

2018-01-01

In this paper, we propose a hierarchical spatial concept formation method based on the Bayesian generative model with multimodal information e.g., vision, position and word information. Since humans have the ability to select an appropriate level of abstraction according to the situation and describe their position linguistically, e.g., "I am in my home" and "I am in front of the table," a hierarchical structure of spatial concepts is necessary in order for human support robots to communicate smoothly with users. The proposed method enables a robot to form hierarchical spatial concepts by categorizing multimodal information using hierarchical multimodal latent Dirichlet allocation (hMLDA). Object recognition results using convolutional neural network (CNN), hierarchical k-means clustering result of self-position estimated by Monte Carlo localization (MCL), and a set of location names are used, respectively, as features in vision, position, and word information. Experiments in forming hierarchical spatial concepts and evaluating how the proposed method can predict unobserved location names and position categories are performed using a robot in the real world. Results verify that, relative to comparable baseline methods, the proposed method enables a robot to predict location names and position categories closer to predictions made by humans. As an application example of the proposed method in a home environment, a demonstration in which a human support robot moves to an instructed place based on human speech instructions is achieved based on the formed hierarchical spatial concept.

Hierarchical Spatial Concept Formation Based on Multimodal Information for Human Support Robots

PubMed Central

Hagiwara, Yoshinobu; Inoue, Masakazu; Kobayashi, Hiroyoshi; Taniguchi, Tadahiro

2018-01-01

In this paper, we propose a hierarchical spatial concept formation method based on the Bayesian generative model with multimodal information e.g., vision, position and word information. Since humans have the ability to select an appropriate level of abstraction according to the situation and describe their position linguistically, e.g., “I am in my home” and “I am in front of the table,” a hierarchical structure of spatial concepts is necessary in order for human support robots to communicate smoothly with users. The proposed method enables a robot to form hierarchical spatial concepts by categorizing multimodal information using hierarchical multimodal latent Dirichlet allocation (hMLDA). Object recognition results using convolutional neural network (CNN), hierarchical k-means clustering result of self-position estimated by Monte Carlo localization (MCL), and a set of location names are used, respectively, as features in vision, position, and word information. Experiments in forming hierarchical spatial concepts and evaluating how the proposed method can predict unobserved location names and position categories are performed using a robot in the real world. Results verify that, relative to comparable baseline methods, the proposed method enables a robot to predict location names and position categories closer to predictions made by humans. As an application example of the proposed method in a home environment, a demonstration in which a human support robot moves to an instructed place based on human speech instructions is achieved based on the formed hierarchical spatial concept. PMID:29593521

Bayesian Local Contamination Models for Multivariate Outliers

PubMed Central

Page, Garritt L.; Dunson, David B.

2013-01-01

In studies where data are generated from multiple locations or sources it is common for there to exist observations that are quite unlike the majority. Motivated by the application of establishing a reference value in an inter-laboratory setting when outlying labs are present, we propose a local contamination model that is able to accommodate unusual multivariate realizations in a flexible way. The proposed method models the process level of a hierarchical model using a mixture with a parametric component and a possibly nonparametric contamination. Much of the flexibility in the methodology is achieved by allowing varying random subsets of the elements in the lab-specific mean vectors to be allocated to the contamination component. Computational methods are developed and the methodology is compared to three other possible approaches using a simulation study. We apply the proposed method to a NIST/NOAA sponsored inter-laboratory study which motivated the methodological development. PMID:24363465

Bayesian Spatiotemporal Pattern and Eco-climatological Drivers of Striped Skunk Rabies in the North Central Plains

PubMed Central

Raghavan, Ram K.; Hanlon, Cathleen A.; Goodin, Douglas G.; Anderson, Gary A.

2016-01-01

Striped skunks are one of the most important terrestrial reservoirs of rabies virus in North America, and yet the prevalence of rabies among this host is only passively monitored and the disease among this host remains largely unmanaged. Oral vaccination campaigns have not efficiently targeted striped skunks, while periodic spillovers of striped skunk variant viruses to other animals, including some domestic animals, are routinely recorded. In this study we evaluated the spatial and spatio-temporal patterns of infection status among striped skunk cases submitted for rabies testing in the North Central Plains of US in a Bayesian hierarchical framework, and also evaluated potential eco-climatological drivers of such patterns. Two Bayesian hierarchical models were fitted to point-referenced striped skunk rabies cases [n = 656 (negative), and n = 310 (positive)] received at a leading rabies diagnostic facility between the years 2007–2013. The first model included only spatial and temporal terms and a second covariate model included additional covariates representing eco-climatic conditions within a 4km2 home-range area for striped skunks. The better performing covariate model indicated the presence of significant spatial and temporal trends in the dataset and identified higher amounts of land covered by low-intensity developed areas [Odds ratio (OR) = 3.41; 95% Bayesian Credible Intervals (CrI) = 2.08, 3.85], higher level of patch fragmentation (OR = 1.70; 95% CrI = 1.25, 2.89), and diurnal temperature range (OR = 0.54; 95% CrI = 0.27, 0.91) to be important drivers of striped skunk rabies incidence in the study area. Model validation statistics indicated satisfactory performance for both models; however, the covariate model fared better. The findings of this study are important in the context of rabies management among striped skunks in North America, and the relevance of physical and climatological factors as risk factors for skunk to human rabies transmission and the space-time patterns of striped skunk rabies are discussed. PMID:27127994

Bayesian Hierarchical Modeling for Big Data Fusion in Soil Hydrology

NASA Astrophysics Data System (ADS)

Mohanty, B.; Kathuria, D.; Katzfuss, M.

2016-12-01

Soil moisture datasets from remote sensing (RS) platforms (such as SMOS and SMAP) and reanalysis products from land surface models are typically available on a coarse spatial granularity of several square km. Ground based sensors on the other hand provide observations on a finer spatial scale (meter scale or less) but are sparsely available. Soil moisture is affected by high variability due to complex interactions between geologic, topographic, vegetation and atmospheric variables. Hydrologic processes usually occur at a scale of 1 km or less and therefore spatially ubiquitous and temporally periodic soil moisture products at this scale are required to aid local decision makers in agriculture, weather prediction and reservoir operations. Past literature has largely focused on downscaling RS soil moisture for a small extent of a field or a watershed and hence the applicability of such products has been limited. The present study employs a spatial Bayesian Hierarchical Model (BHM) to derive soil moisture products at a spatial scale of 1 km for the state of Oklahoma by fusing point scale Mesonet data and coarse scale RS data for soil moisture and its auxiliary covariates such as precipitation, topography, soil texture and vegetation. It is seen that the BHM model handles change of support problems easily while performing accurate uncertainty quantification arising from measurement errors and imperfect retrieval algorithms. The computational challenge arising due to the large number of measurements is tackled by utilizing basis function approaches and likelihood approximations. The BHM model can be considered as a complex Bayesian extension of traditional geostatistical prediction methods (such as Kriging) for large datasets in the presence of uncertainties.

Clustering and Bayesian hierarchical modeling for the definition of informative prior distributions in hydrogeology

NASA Astrophysics Data System (ADS)

Cucchi, K.; Kawa, N.; Hesse, F.; Rubin, Y.

2017-12-01

In order to reduce uncertainty in the prediction of subsurface flow and transport processes, practitioners should use all data available. However, classic inverse modeling frameworks typically only make use of information contained in in-situ field measurements to provide estimates of hydrogeological parameters. Such hydrogeological information about an aquifer is difficult and costly to acquire. In this data-scarce context, the transfer of ex-situ information coming from previously investigated sites can be critical for improving predictions by better constraining the estimation procedure. Bayesian inverse modeling provides a coherent framework to represent such ex-situ information by virtue of the prior distribution and combine them with in-situ information from the target site. In this study, we present an innovative data-driven approach for defining such informative priors for hydrogeological parameters at the target site. Our approach consists in two steps, both relying on statistical and machine learning methods. The first step is data selection; it consists in selecting sites similar to the target site. We use clustering methods for selecting similar sites based on observable hydrogeological features. The second step is data assimilation; it consists in assimilating data from the selected similar sites into the informative prior. We use a Bayesian hierarchical model to account for inter-site variability and to allow for the assimilation of multiple types of site-specific data. We present the application and validation of the presented methods on an established database of hydrogeological parameters. Data and methods are implemented in the form of an open-source R-package and therefore facilitate easy use by other practitioners.

Abrupt strategy change underlies gradual performance change: Bayesian hierarchical models of component and aggregate strategy use.

PubMed

Wynton, Sarah K A; Anglim, Jeromy

2017-10-01

While researchers have often sought to understand the learning curve in terms of multiple component processes, few studies have measured and mathematically modeled these processes on a complex task. In particular, there remains a need to reconcile how abrupt changes in strategy use can co-occur with gradual changes in task completion time. Thus, the current study aimed to assess the degree to which strategy change was abrupt or gradual, and whether strategy aggregation could partially explain gradual performance change. It also aimed to show how Bayesian methods could be used to model the effect of practice on strategy use. To achieve these aims, 162 participants completed 15 blocks of practice on a complex computer-based task-the Wynton-Anglim booking (WAB) task. The task allowed for multiple component strategies (i.e., memory retrieval, information reduction, and insight) that could also be aggregated to a global measure of strategy use. Bayesian hierarchical models were used to compare abrupt and gradual functions of component and aggregate strategy use. Task completion time was well-modeled by a power function, and global strategy use explained substantial variance in performance. Change in component strategy use tended to be abrupt, whereas change in global strategy use was gradual and well-modeled by a power function. Thus, differential timing of component strategy shifts leads to gradual changes in overall strategy efficiency, and this provides one reason for why smooth learning curves can co-occur with abrupt changes in strategy use. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

A Bayesian Semiparametric Approach for Incorporating Longitudinal Information on Exposure History for Inference in Case-Control Studies

PubMed Central

Bhadra, Dhiman; Daniels, Michael J.; Kim, Sungduk; Ghosh, Malay; Mukherjee, Bhramar

2014-01-01

In a typical case-control study, exposure information is collected at a single time-point for the cases and controls. However, case-control studies are often embedded in existing cohort studies containing a wealth of longitudinal exposure history on the participants. Recent medical studies have indicated that incorporating past exposure history, or a constructed summary measure of cumulative exposure derived from the past exposure history, when available, may lead to more precise and clinically meaningful estimates of the disease risk. In this paper, we propose a flexible Bayesian semiparametric approach to model the longitudinal exposure profiles of the cases and controls and then use measures of cumulative exposure based on a weighted integral of this trajectory in the final disease risk model. The estimation is done via a joint likelihood. In the construction of the cumulative exposure summary, we introduce an influence function, a smooth function of time to characterize the association pattern of the exposure profile on the disease status with different time windows potentially having differential influence/weights. This enables us to analyze how the present disease status of a subject is influenced by his/her past exposure history conditional on the current ones. The joint likelihood formulation allows us to properly account for uncertainties associated with both stages of the estimation process in an integrated manner. Analysis is carried out in a hierarchical Bayesian framework using Reversible jump Markov chain Monte Carlo (RJMCMC) algorithms. The proposed methodology is motivated by, and applied to a case-control study of prostate cancer where longitudinal biomarker information is available for the cases and controls. PMID:22313248

Bayesian inference of T Tauri star properties using multi-wavelength survey photometry

NASA Astrophysics Data System (ADS)

Barentsen, Geert; Vink, J. S.; Drew, J. E.; Sale, S. E.

2013-03-01

There are many pertinent open issues in the area of star and planet formation. Large statistical samples of young stars across star-forming regions are needed to trigger a breakthrough in our understanding, but most optical studies are based on a wide variety of spectrographs and analysis methods, which introduces large biases. Here we show how graphical Bayesian networks can be employed to construct a hierarchical probabilistic model which allows pre-main-sequence ages, masses, accretion rates and extinctions to be estimated using two widely available photometric survey data bases (Isaac Newton Telescope Photometric Hα Survey r'/Hα/i' and Two Micron All Sky Survey J-band magnitudes). Because our approach does not rely on spectroscopy, it can easily be applied to ho-mogeneously study the large number of clusters for which Gaia will yield membership lists. We explain how the analysis is carried out using the Markov chain Monte Carlo method and provide PYTHON source code. We then demonstrate its use on 587 known low-mass members of the star-forming region NGC 2264 (Cone Nebula), arriving at a median age of 3.0 Myr, an accretion fraction of 20 ± 2 per cent and a median accretion rate of 10-8.4 M⊙ yr-1. The Bayesian analysis formulated in this work delivers results which are in agreement with spectroscopic studies already in the literature, but achieves this with great efficiency by depending only on photometry. It is a significant step forward from previous photometric studies because the probabilistic approach ensures that nuisance parameters, such as extinction and distance, are fully included in the analysis with a clear picture on any degeneracies.

Identifying food deserts and swamps based on relative healthy food access: a spatio-temporal Bayesian approach.

PubMed

Luan, Hui; Law, Jane; Quick, Matthew

2015-12-30

Obesity and other adverse health outcomes are influenced by individual- and neighbourhood-scale risk factors, including the food environment. At the small-area scale, past research has analysed spatial patterns of food environments for one time period, overlooking how food environments change over time. Further, past research has infrequently analysed relative healthy food access (RHFA), a measure that is more representative of food purchasing and consumption behaviours than absolute outlet density. This research applies a Bayesian hierarchical model to analyse the spatio-temporal patterns of RHFA in the Region of Waterloo, Canada, from 2011 to 2014 at the small-area level. RHFA is calculated as the proportion of healthy food outlets (healthy outlets/healthy + unhealthy outlets) within 4-km from each small-area. This model measures spatial autocorrelation of RHFA, temporal trend of RHFA for the study region, and spatio-temporal trends of RHFA for small-areas. For the study region, a significant decreasing trend in RHFA is observed (-0.024), suggesting that food swamps have become more prevalent during the study period. For small-areas, significant decreasing temporal trends in RHFA were observed for all small-areas. Specific small-areas located in south Waterloo, north Kitchener, and southeast Cambridge exhibited the steepest decreasing spatio-temporal trends and are classified as spatio-temporal food swamps. This research demonstrates a Bayesian spatio-temporal modelling approach to analyse RHFA at the small-area scale. Results suggest that food swamps are more prevalent than food deserts in the Region of Waterloo. Analysing spatio-temporal trends of RHFA improves understanding of local food environment, highlighting specific small-areas where policies should be targeted to increase RHFA and reduce risk factors of adverse health outcomes such as obesity.

On the Adequacy of Bayesian Evaluations of Categorization Models: Reply to Vanpaemel and Lee (2012)

ERIC Educational Resources Information Center

Wills, Andy J.; Pothos, Emmanuel M.

2012-01-01

Vanpaemel and Lee (2012) argued, and we agree, that the comparison of formal models can be facilitated by Bayesian methods. However, Bayesian methods neither precede nor supplant our proposals (Wills & Pothos, 2012), as Bayesian methods can be applied both to our proposals and to their polar opposites. Furthermore, the use of Bayesian methods to…

In Silico Syndrome Prediction for Coronary Artery Disease in Traditional Chinese Medicine

PubMed Central

Lu, Peng; Chen, Jianxin; Zhao, Huihui; Gao, Yibo; Luo, Liangtao; Zuo, Xiaohan; Shi, Qi; Yang, Yiping; Yi, Jianqiang; Wang, Wei

2012-01-01

Coronary artery disease (CAD) is the leading causes of deaths in the world. The differentiation of syndrome (ZHENG) is the criterion of diagnosis and therapeutic in TCM. Therefore, syndrome prediction in silico can be improving the performance of treatment. In this paper, we present a Bayesian network framework to construct a high-confidence syndrome predictor based on the optimum subset, that is, collected by Support Vector Machine (SVM) feature selection. Syndrome of CAD can be divided into asthenia and sthenia syndromes. According to the hierarchical characteristics of syndrome, we firstly label every case three types of syndrome (asthenia, sthenia, or both) to solve several syndromes with some patients. On basis of the three syndromes' classes, we design SVM feature selection to achieve the optimum symptom subset and compare this subset with Markov blanket feature select using ROC. Using this subset, the six predictors of CAD's syndrome are constructed by the Bayesian network technique. We also design Naïve Bayes, C4.5 Logistic, Radial basis function (RBF) network compared with Bayesian network. In a conclusion, the Bayesian network method based on the optimum symptoms shows a practical method to predict six syndromes of CAD in TCM. PMID:22567030

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

Differences in Mortality among Heroin, Cocaine, and Methamphetamine Users: A Hierarchical Bayesian Approach

PubMed Central

Liang, Li-Jung; Huang, David; Brecht, Mary-Lynn; Hser, Yih-ing

2010-01-01

Studies examining differences in mortality among long-term drug users have been limited. In this paper, we introduce a Bayesian framework that jointly models survival data using a Weibull proportional hazard model with frailty, and substance and alcohol data using mixed-effects models, to examine differences in mortality among heroin, cocaine, and methamphetamine users from five long-term follow-up studies. The traditional approach to analyzing combined survival data from numerous studies assumes that the studies are homogeneous, thus the estimates may be biased due to unobserved heterogeneity among studies. Our approach allows us to structurally combine the data from different studies while accounting for correlation among subjects within each study. Markov chain Monte Carlo facilitates the implementation of Bayesian analyses. Despite the complexity of the model, our approach is relatively straightforward to implement using WinBUGS. We demonstrate our joint modeling approach to the combined data and discuss the results from both approaches. PMID:21052518

Online Dectection and Modeling of Safety Boundaries for Aerospace Application Using Bayesian Statistics

NASA Technical Reports Server (NTRS)

He, Yuning

2015-01-01

The behavior of complex aerospace systems is governed by numerous parameters. For safety analysis it is important to understand how the system behaves with respect to these parameter values. In particular, understanding the boundaries between safe and unsafe regions is of major importance. In this paper, we describe a hierarchical Bayesian statistical modeling approach for the online detection and characterization of such boundaries. Our method for classification with active learning uses a particle filter-based model and a boundary-aware metric for best performance. From a library of candidate shapes incorporated with domain expert knowledge, the location and parameters of the boundaries are estimated using advanced Bayesian modeling techniques. The results of our boundary analysis are then provided in a form understandable by the domain expert. We illustrate our approach using a simulation model of a NASA neuro-adaptive flight control system, as well as a system for the detection of separation violations in the terminal airspace.

Using Bayesian hierarchical models to better understand nitrate sources and sinks in agricultural watersheds.

PubMed

Xia, Yongqiu; Weller, Donald E; Williams, Meghan N; Jordan, Thomas E; Yan, Xiaoyuan

2016-11-15

Export coefficient models (ECMs) are often used to predict nutrient sources and sinks in watersheds because ECMs can flexibly incorporate processes and have minimal data requirements. However, ECMs do not quantify uncertainties in model structure, parameters, or predictions; nor do they account for spatial and temporal variability in land characteristics, weather, and management practices. We applied Bayesian hierarchical methods to address these problems in ECMs used to predict nitrate concentration in streams. We compared four model formulations, a basic ECM and three models with additional terms to represent competing hypotheses about the sources of error in ECMs and about spatial and temporal variability of coefficients: an ADditive Error Model (ADEM), a SpatioTemporal Parameter Model (STPM), and a Dynamic Parameter Model (DPM). The DPM incorporates a first-order random walk to represent spatial correlation among parameters and a dynamic linear model to accommodate temporal correlation. We tested the modeling approach in a proof of concept using watershed characteristics and nitrate export measurements from watersheds in the Coastal Plain physiographic province of the Chesapeake Bay drainage. Among the four models, the DPM was the best--it had the lowest mean error, explained the most variability (R 2  = 0.99), had the narrowest prediction intervals, and provided the most effective tradeoff between fit complexity (its deviance information criterion, DIC, was 45.6 units lower than any other model, indicating overwhelming support for the DPM). The superiority of the DPM supports its underlying hypothesis that the main source of error in ECMs is their failure to account for parameter variability rather than structural error. Analysis of the fitted DPM coefficients for cropland export and instream retention revealed some of the factors controlling nitrate concentration: cropland nitrate exports were positively related to stream flow and watershed average slope, while instream nitrate retention was positively correlated with nitrate concentration. By quantifying spatial and temporal variability in sources and sinks, the DPM provides new information to better target management actions to the most effective times and places. Given the wide use of ECMs as research and management tools, our approach can be broadly applied in other watersheds and to other materials. Copyright © 2016 Elsevier Ltd. All rights reserved.

Bayesian analysis of non-linear differential equation models with application to a gut microbial ecosystem.

PubMed

Lawson, Daniel J; Holtrop, Grietje; Flint, Harry

2011-07-01

Process models specified by non-linear dynamic differential equations contain many parameters, which often must be inferred from a limited amount of data. We discuss a hierarchical Bayesian approach combining data from multiple related experiments in a meaningful way, which permits more powerful inference than treating each experiment as independent. The approach is illustrated with a simulation study and example data from experiments replicating the aspects of the human gut microbial ecosystem. A predictive model is obtained that contains prediction uncertainty caused by uncertainty in the parameters, and we extend the model to capture situations of interest that cannot easily be studied experimentally. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Detecting a Change in School Performance: A Bayesian Analysis for a Multilevel Join Point Problem. CSE Technical Report 542.

ERIC Educational Resources Information Center

Thum, Yeow Meng; Bhattacharya, Suman Kumar

To better describe individual behavior within a system, this paper uses a sample of longitudinal test scores from a large urban school system to consider hierarchical Bayes estimation of a multilevel linear regression model in which each individual regression slope of test score on time switches at some unknown point in time, "kj."…

Capturing the Cumulative Effects of School Reform: An 11-Year Study of the Impacts of America's Choice on Student Achievement

ERIC Educational Resources Information Center

May, Henry; Supovitz, Jonathan A.

2006-01-01

This article presents the results of an 11-year longitudinal study of the impact of America's Choice comprehensive school reform (CSR) design on student learning gains in Rochester, New York. A quasi-experimental interrupted time-series approach using Bayesian hierarchical growth curve analysis with crossed random effects is used to compare the…

Topics in Bayesian Hierarchical Modeling and its Monte Carlo Computations

NASA Astrophysics Data System (ADS)

Tak, Hyung Suk

The first chapter addresses a Beta-Binomial-Logit model that is a Beta-Binomial conjugate hierarchical model with covariate information incorporated via a logistic regression. Various researchers in the literature have unknowingly used improper posterior distributions or have given incorrect statements about posterior propriety because checking posterior propriety can be challenging due to the complicated functional form of a Beta-Binomial-Logit model. We derive data-dependent necessary and sufficient conditions for posterior propriety within a class of hyper-prior distributions that encompass those used in previous studies. Frequency coverage properties of several hyper-prior distributions are also investigated to see when and whether Bayesian interval estimates of random effects meet their nominal confidence levels. The second chapter deals with a time delay estimation problem in astrophysics. When the gravitational field of an intervening galaxy between a quasar and the Earth is strong enough to split light into two or more images, the time delay is defined as the difference between their travel times. The time delay can be used to constrain cosmological parameters and can be inferred from the time series of brightness data of each image. To estimate the time delay, we construct a Gaussian hierarchical model based on a state-space representation for irregularly observed time series generated by a latent continuous-time Ornstein-Uhlenbeck process. Our Bayesian approach jointly infers model parameters via a Gibbs sampler. We also introduce a profile likelihood of the time delay as an approximation of its marginal posterior distribution. The last chapter specifies a repelling-attracting Metropolis algorithm, a new Markov chain Monte Carlo method to explore multi-modal distributions in a simple and fast manner. This algorithm is essentially a Metropolis-Hastings algorithm with a proposal that consists of a downhill move in density that aims to make local modes repelling, followed by an uphill move in density that aims to make local modes attracting. The downhill move is achieved via a reciprocal Metropolis ratio so that the algorithm prefers downward movement. The uphill move does the opposite using the standard Metropolis ratio which prefers upward movement. This down-up movement in density increases the probability of a proposed move to a different mode.

Testing comparative phylogeographic models of marine vicariance and dispersal using a hierarchical Bayesian approach

PubMed Central

2008-01-01

Background Marine allopatric speciation is an enigma because pelagic larval dispersal can potentially connect disjunct populations thereby preventing reproductive and morphological divergence. Here we present a new hierarchical approximate Bayesian computation model (HABC) that tests two hypotheses of marine allopatric speciation: 1.) "soft vicariance", where a speciation involves fragmentation of a large widespread ancestral species range that was previously connected by long distance gene flow; and 2.) peripatric colonization, where speciations in peripheral archipelagos emerge from sweepstakes colonizations from central source regions. The HABC approach analyzes all the phylogeographic datasets at once in order to make across taxon-pair inferences about biogeographic processes while explicitly allowing for uncertainty in the demographic differences within each taxon-pair. Our method uses comparative phylogeographic data that consists of single locus mtDNA sequences from multiple co-distributed taxa containing pairs of central and peripheral populations. We use the method on two comparative phylogeographic data sets consisting of cowrie gastropod endemics co-distributed in the Hawaiian (11 taxon-pairs) and Marquesan archipelagos (7 taxon-pairs). Results Given the Marquesan data, we find strong evidence of simultaneous colonization across all seven cowrie gastropod endemics co-distributed in the Marquesas. In contrast, the lower sample sizes in the Hawaiian data lead to greater uncertainty associated with the Hawaiian estimates. Although, the hyper-parameter estimates point to soft vicariance in a subset of the 11 Hawaiian taxon-pairs, the hyper-prior and hyper-posterior are too similar to make a definitive conclusion. Both results are not inconsistent with what is known about the geologic history of the archipelagos. Simulations verify that our method can successfully distinguish these two histories across a wide range of conditions given sufficient sampling. Conclusion Although soft vicariance and colonization are likely to produce similar genetic patterns when a single taxon-pair is used, our hierarchical Bayesian model can potentially detect if either history is a dominant process across co-distributed taxon-pairs. As comparative phylogeographic datasets grow to include > 100 co-distributed taxon-pairs, the HABC approach will be well suited to dissect temporal patterns in community assembly and evolution, thereby providing a bridge linking comparative phylogeography with community ecology. PMID:19038027

Integrative Bayesian variable selection with gene-based informative priors for genome-wide association studies.

PubMed

Zhang, Xiaoshuai; Xue, Fuzhong; Liu, Hong; Zhu, Dianwen; Peng, Bin; Wiemels, Joseph L; Yang, Xiaowei

2014-12-10

Genome-wide Association Studies (GWAS) are typically designed to identify phenotype-associated single nucleotide polymorphisms (SNPs) individually using univariate analysis methods. Though providing valuable insights into genetic risks of common diseases, the genetic variants identified by GWAS generally account for only a small proportion of the total heritability for complex diseases. To solve this "missing heritability" problem, we implemented a strategy called integrative Bayesian Variable Selection (iBVS), which is based on a hierarchical model that incorporates an informative prior by considering the gene interrelationship as a network. It was applied here to both simulated and real data sets. Simulation studies indicated that the iBVS method was advantageous in its performance with highest AUC in both variable selection and outcome prediction, when compared to Stepwise and LASSO based strategies. In an analysis of a leprosy case-control study, iBVS selected 94 SNPs as predictors, while LASSO selected 100 SNPs. The Stepwise regression yielded a more parsimonious model with only 3 SNPs. The prediction results demonstrated that the iBVS method had comparable performance with that of LASSO, but better than Stepwise strategies. The proposed iBVS strategy is a novel and valid method for Genome-wide Association Studies, with the additional advantage in that it produces more interpretable posterior probabilities for each variable unlike LASSO and other penalized regression methods.

Coupled Land-Atmosphere Dynamics Govern Long Duration Floods: A Pilot Study in Missouri River Basin Using a Bayesian Hierarchical Model

NASA Astrophysics Data System (ADS)

Najibi, N.; Lu, M.; Devineni, N.

2017-12-01

Long duration floods cause substantial damages and prolonged interruptions to water resource facilities and critical infrastructure. We present a novel generalized statistical and physical based model for flood duration with a deeper understanding of dynamically coupled nexus of the land surface wetness, effective atmospheric circulation and moisture transport/release. We applied the model on large reservoirs in the Missouri River Basin. The results indicate that the flood duration is not only a function of available moisture in the air, but also the antecedent condition of the blocking system of atmospheric pressure, resulting in enhanced moisture convergence, as well as the effectiveness of moisture condensation process leading to release. Quantifying these dynamics with a two-layer climate informed Bayesian multilevel model, we explain more than 80% variations in flood duration. The model considers the complex interaction between moisture transport, synoptic-to-large-scale atmospheric circulation pattern, and the antecedent wetness condition in the basin. Our findings suggest that synergy between a large low-pressure blocking system and a higher rate of divergent wind often triggers a long duration flood, and the prerequisite for moisture supply to trigger such event is moderate, which is more associated with magnitude than duration. In turn, this condition causes an extremely long duration flood if the surface wetness rate advancing to the flood event was already increased.

Can Bayesian Theories of Autism Spectrum Disorder Help Improve Clinical Practice?

PubMed

Haker, Helene; Schneebeli, Maya; Stephan, Klaas Enno

2016-01-01

Diagnosis and individualized treatment of autism spectrum disorder (ASD) represent major problems for contemporary psychiatry. Tackling these problems requires guidance by a pathophysiological theory. In this paper, we consider recent theories that re-conceptualize ASD from a "Bayesian brain" perspective, which posit that the core abnormality of ASD resides in perceptual aberrations due to a disbalance in the precision of prediction errors (sensory noise) relative to the precision of predictions (prior beliefs). This results in percepts that are dominated by sensory inputs and less guided by top-down regularization and shifts the perceptual focus to detailed aspects of the environment with difficulties in extracting meaning. While these Bayesian theories have inspired ongoing empirical studies, their clinical implications have not yet been carved out. Here, we consider how this Bayesian perspective on disease mechanisms in ASD might contribute to improving clinical care for affected individuals. Specifically, we describe a computational strategy, based on generative (e.g., hierarchical Bayesian) models of behavioral and functional neuroimaging data, for establishing diagnostic tests. These tests could provide estimates of specific cognitive processes underlying ASD and delineate pathophysiological mechanisms with concrete treatment targets. Written with a clinical audience in mind, this article outlines how the development of computational diagnostics applicable to behavioral and functional neuroimaging data in routine clinical practice could not only fundamentally alter our concept of ASD but eventually also transform the clinical management of this disorder.

Can Bayesian Theories of Autism Spectrum Disorder Help Improve Clinical Practice?

PubMed Central

Haker, Helene; Schneebeli, Maya; Stephan, Klaas Enno

2016-01-01

Diagnosis and individualized treatment of autism spectrum disorder (ASD) represent major problems for contemporary psychiatry. Tackling these problems requires guidance by a pathophysiological theory. In this paper, we consider recent theories that re-conceptualize ASD from a “Bayesian brain” perspective, which posit that the core abnormality of ASD resides in perceptual aberrations due to a disbalance in the precision of prediction errors (sensory noise) relative to the precision of predictions (prior beliefs). This results in percepts that are dominated by sensory inputs and less guided by top-down regularization and shifts the perceptual focus to detailed aspects of the environment with difficulties in extracting meaning. While these Bayesian theories have inspired ongoing empirical studies, their clinical implications have not yet been carved out. Here, we consider how this Bayesian perspective on disease mechanisms in ASD might contribute to improving clinical care for affected individuals. Specifically, we describe a computational strategy, based on generative (e.g., hierarchical Bayesian) models of behavioral and functional neuroimaging data, for establishing diagnostic tests. These tests could provide estimates of specific cognitive processes underlying ASD and delineate pathophysiological mechanisms with concrete treatment targets. Written with a clinical audience in mind, this article outlines how the development of computational diagnostics applicable to behavioral and functional neuroimaging data in routine clinical practice could not only fundamentally alter our concept of ASD but eventually also transform the clinical management of this disorder. PMID:27378955

Defining Probability in Sex Offender Risk Assessment.

PubMed

Elwood, Richard W

2016-12-01

There is ongoing debate and confusion over using actuarial scales to predict individuals' risk of sexual recidivism. Much of the debate comes from not distinguishing Frequentist from Bayesian definitions of probability. Much of the confusion comes from applying Frequentist probability to individuals' risk. By definition, only Bayesian probability can be applied to the single case. The Bayesian concept of probability resolves most of the confusion and much of the debate in sex offender risk assessment. Although Bayesian probability is well accepted in risk assessment generally, it has not been widely used to assess the risk of sex offenders. I review the two concepts of probability and show how the Bayesian view alone provides a coherent scheme to conceptualize individuals' risk of sexual recidivism.

Applying Bayesian statistics to the study of psychological trauma: A suggestion for future research.

PubMed

Yalch, Matthew M

2016-03-01

Several contemporary researchers have noted the virtues of Bayesian methods of data analysis. Although debates continue about whether conventional or Bayesian statistics is the "better" approach for researchers in general, there are reasons why Bayesian methods may be well suited to the study of psychological trauma in particular. This article describes how Bayesian statistics offers practical solutions to the problems of data non-normality, small sample size, and missing data common in research on psychological trauma. After a discussion of these problems and the effects they have on trauma research, this article explains the basic philosophical and statistical foundations of Bayesian statistics and how it provides solutions to these problems using an applied example. Results of the literature review and the accompanying example indicates the utility of Bayesian statistics in addressing problems common in trauma research. Bayesian statistics provides a set of methodological tools and a broader philosophical framework that is useful for trauma researchers. Methodological resources are also provided so that interested readers can learn more. (c) 2016 APA, all rights reserved).

Construction of monitoring model and algorithm design on passenger security during shipping based on improved Bayesian network.

PubMed

Wang, Jiali; Zhang, Qingnian; Ji, Wenfeng

2014-01-01

A large number of data is needed by the computation of the objective Bayesian network, but the data is hard to get in actual computation. The calculation method of Bayesian network was improved in this paper, and the fuzzy-precise Bayesian network was obtained. Then, the fuzzy-precise Bayesian network was used to reason Bayesian network model when the data is limited. The security of passengers during shipping is affected by various factors, and it is hard to predict and control. The index system that has the impact on the passenger safety during shipping was established on basis of the multifield coupling theory in this paper. Meanwhile, the fuzzy-precise Bayesian network was applied to monitor the security of passengers in the shipping process. The model was applied to monitor the passenger safety during shipping of a shipping company in Hainan, and the effectiveness of this model was examined. This research work provides guidance for guaranteeing security of passengers during shipping.

Construction of Monitoring Model and Algorithm Design on Passenger Security during Shipping Based on Improved Bayesian Network

PubMed Central

Wang, Jiali; Zhang, Qingnian; Ji, Wenfeng

2014-01-01

A large number of data is needed by the computation of the objective Bayesian network, but the data is hard to get in actual computation. The calculation method of Bayesian network was improved in this paper, and the fuzzy-precise Bayesian network was obtained. Then, the fuzzy-precise Bayesian network was used to reason Bayesian network model when the data is limited. The security of passengers during shipping is affected by various factors, and it is hard to predict and control. The index system that has the impact on the passenger safety during shipping was established on basis of the multifield coupling theory in this paper. Meanwhile, the fuzzy-precise Bayesian network was applied to monitor the security of passengers in the shipping process. The model was applied to monitor the passenger safety during shipping of a shipping company in Hainan, and the effectiveness of this model was examined. This research work provides guidance for guaranteeing security of passengers during shipping. PMID:25254227

Identification of transmissivity fields using a Bayesian strategy and perturbative approach

NASA Astrophysics Data System (ADS)

Zanini, Andrea; Tanda, Maria Giovanna; Woodbury, Allan D.

2017-10-01

The paper deals with the crucial problem of the groundwater parameter estimation that is the basis for efficient modeling and reclamation activities. A hierarchical Bayesian approach is developed: it uses the Akaike's Bayesian Information Criteria in order to estimate the hyperparameters (related to the covariance model chosen) and to quantify the unknown noise variance. The transmissivity identification proceeds in two steps: the first, called empirical Bayesian interpolation, uses Y* (Y = lnT) observations to interpolate Y values on a specified grid; the second, called empirical Bayesian update, improve the previous Y estimate through the addition of hydraulic head observations. The relationship between the head and the lnT has been linearized through a perturbative solution of the flow equation. In order to test the proposed approach, synthetic aquifers from literature have been considered. The aquifers in question contain a variety of boundary conditions (both Dirichelet and Neuman type) and scales of heterogeneities (σY2 = 1.0 and σY2 = 5.3). The estimated transmissivity fields were compared to the true one. The joint use of Y* and head measurements improves the estimation of Y considering both degrees of heterogeneity. Even if the variance of the strong transmissivity field can be considered high for the application of the perturbative approach, the results show the same order of approximation of the non-linear methods proposed in literature. The procedure allows to compute the posterior probability distribution of the target quantities and to quantify the uncertainty in the model prediction. Bayesian updating has advantages related both to the Monte-Carlo (MC) and non-MC approaches. In fact, as the MC methods, Bayesian updating allows computing the direct posterior probability distribution of the target quantities and as non-MC methods it has computational times in the order of seconds.

A Comparison of Full and Empirical Bayes Techniques for Inferring Sea Level Changes from Tide Gauge Records

NASA Astrophysics Data System (ADS)

Piecuch, C. G.; Huybers, P. J.; Tingley, M.

2016-12-01

Sea level observations from coastal tide gauges are some of the longest instrumental records of the ocean. However, these data can be noisy, biased, and gappy, featuring missing values, and reflecting land motion and local effects. Coping with these issues in a formal manner is a challenging task. Some studies use Bayesian approaches to estimate sea level from tide gauge records, making inference probabilistically. Such methods are typically empirically Bayesian in nature: model parameters are treated as known and assigned point values. But, in reality, parameters are not perfectly known. Empirical Bayes methods thus neglect a potentially important source of uncertainty, and so may overestimate the precision (i.e., underestimate the uncertainty) of sea level estimates. We consider whether empirical Bayes methods underestimate uncertainty in sea level from tide gauge data, comparing to a full Bayes method that treats parameters as unknowns to be solved for along with the sea level field. We develop a hierarchical algorithm that we apply to tide gauge data on the North American northeast coast over 1893-2015. The algorithm is run in full Bayes mode, solving for the sea level process and parameters, and in empirical mode, solving only for the process using fixed parameter values. Error bars on sea level from the empirical method are smaller than from the full Bayes method, and the relative discrepancies increase with time; the 95% credible interval on sea level values from the empirical Bayes method in 1910 and 2010 is 23% and 56% narrower, respectively, than from the full Bayes approach. To evaluate the representativeness of the credible intervals, empirical Bayes and full Bayes methods are applied to corrupted data of a known surrogate field. Using rank histograms to evaluate the solutions, we find that the full Bayes method produces generally reliable error bars, whereas the empirical Bayes method gives too-narrow error bars, such that the 90% credible interval only encompasses 70% of true process values. Results demonstrate that parameter uncertainty is an important source of process uncertainty, and advocate for the fully Bayesian treatment of tide gauge records in ocean circulation and climate studies.

Mechanisms of Hierarchical Reinforcement Learning in Corticostriatal Circuits 1: Computational Analysis

PubMed Central

Badre, David

2012-01-01

Growing evidence suggests that the prefrontal cortex (PFC) is organized hierarchically, with more anterior regions having increasingly abstract representations. How does this organization support hierarchical cognitive control and the rapid discovery of abstract action rules? We present computational models at different levels of description. A neural circuit model simulates interacting corticostriatal circuits organized hierarchically. In each circuit, the basal ganglia gate frontal actions, with some striatal units gating the inputs to PFC and others gating the outputs to influence response selection. Learning at all of these levels is accomplished via dopaminergic reward prediction error signals in each corticostriatal circuit. This functionality allows the system to exhibit conditional if–then hypothesis testing and to learn rapidly in environments with hierarchical structure. We also develop a hybrid Bayesian-reinforcement learning mixture of experts (MoE) model, which can estimate the most likely hypothesis state of individual participants based on their observed sequence of choices and rewards. This model yields accurate probabilistic estimates about which hypotheses are attended by manipulating attentional states in the generative neural model and recovering them with the MoE model. This 2-pronged modeling approach leads to multiple quantitative predictions that are tested with functional magnetic resonance imaging in the companion paper. PMID:21693490

Bayesian dynamic modeling of time series of dengue disease case counts.

PubMed

Martínez-Bello, Daniel Adyro; López-Quílez, Antonio; Torres-Prieto, Alexander

2017-07-01

The aim of this study is to model the association between weekly time series of dengue case counts and meteorological variables, in a high-incidence city of Colombia, applying Bayesian hierarchical dynamic generalized linear models over the period January 2008 to August 2015. Additionally, we evaluate the model's short-term performance for predicting dengue cases. The methodology shows dynamic Poisson log link models including constant or time-varying coefficients for the meteorological variables. Calendar effects were modeled using constant or first- or second-order random walk time-varying coefficients. The meteorological variables were modeled using constant coefficients and first-order random walk time-varying coefficients. We applied Markov Chain Monte Carlo simulations for parameter estimation, and deviance information criterion statistic (DIC) for model selection. We assessed the short-term predictive performance of the selected final model, at several time points within the study period using the mean absolute percentage error. The results showed the best model including first-order random walk time-varying coefficients for calendar trend and first-order random walk time-varying coefficients for the meteorological variables. Besides the computational challenges, interpreting the results implies a complete analysis of the time series of dengue with respect to the parameter estimates of the meteorological effects. We found small values of the mean absolute percentage errors at one or two weeks out-of-sample predictions for most prediction points, associated with low volatility periods in the dengue counts. We discuss the advantages and limitations of the dynamic Poisson models for studying the association between time series of dengue disease and meteorological variables. The key conclusion of the study is that dynamic Poisson models account for the dynamic nature of the variables involved in the modeling of time series of dengue disease, producing useful models for decision-making in public health.

FRIT characterized hierarchical kernel memory arrangement for multiband palmprint recognition

NASA Astrophysics Data System (ADS)

Kisku, Dakshina R.; Gupta, Phalguni; Sing, Jamuna K.

2015-10-01

In this paper, we present a hierarchical kernel associative memory (H-KAM) based computational model with Finite Ridgelet Transform (FRIT) representation for multispectral palmprint recognition. To characterize a multispectral palmprint image, the Finite Ridgelet Transform is used to achieve a very compact and distinctive representation of linear singularities while it also captures the singularities along lines and edges. The proposed system makes use of Finite Ridgelet Transform to represent multispectral palmprint image and it is then modeled by Kernel Associative Memories. Finally, the recognition scheme is thoroughly tested with a benchmarking multispectral palmprint database CASIA. For recognition purpose a Bayesian classifier is used. The experimental results exhibit robustness of the proposed system under different wavelengths of palm image.

Improving the Calibration of the SN Ia Anchor Datasets with a Bayesian Hierarchal Model

NASA Astrophysics Data System (ADS)

Currie, Miles; Rubin, David

2018-01-01

Inter-survey calibration remains one of the largest systematic uncertainties in SN Ia cosmology today. Ideally, each survey would measure their system throughputs and observe well characterized spectrophotometric standard stars, but many important surveys have not done so. For these surveys, we calibrate using tertiary survey stars tied to SDSS and Pan-STARRS. We improve on previous efforts by taking the spatially variable response of each telescope/camera into account, and using improved color transformations in the surveys’ natural instrumental photometric system. We use a global hierarchical model of the data, automatically providing a covariance matrix of magnitude offsets and bandpass shifts which reduces the systematic uncertainty in inter-survey calibration, thereby providing better cosmological constraints.

Hierarchical modeling of population stability and species group attributes from survey data

USGS Publications Warehouse

Sauer, J.R.; Link, W.A.

2002-01-01

Many ecological studies require analysis of collections of estimates. For example, population change is routinely estimated for many species from surveys such as the North American Breeding Bird Survey (BBS), and the species are grouped and used in comparative analyses. We developed a hierarchical model for estimation of group attributes from a collection of estimates of population trend. The model uses information from predefined groups of species to provide a context and to supplement data for individual species; summaries of group attributes are improved by statistical methods that simultaneously analyze collections of trend estimates. The model is Bayesian; trends are treated as random variables rather than fixed parameters. We use Markov Chain Monte Carlo (MCMC) methods to fit the model. Standard assessments of population stability cannot distinguish magnitude of trend and statistical significance of trend estimates, but the hierarchical model allows us to legitimately describe the probability that a trend is within given bounds. Thus we define population stability in terms of the probability that the magnitude of population change for a species is less than or equal to a predefined threshold. We applied the model to estimates of trend for 399 species from the BBS to estimate the proportion of species with increasing populations and to identify species with unstable populations. Analyses are presented for the collection of all species and for 12 species groups commonly used in BBS summaries. Overall, we estimated that 49% of species in the BBS have positive trends and 33 species have unstable populations. However, the proportion of species with increasing trends differs among habitat groups, with grassland birds having only 19% of species with positive trend estimates and wetland birds having 68% of species with positive trend estimates.

Bayesian Hierarchical Models to Augment the Mediterranean Forecast System

DTIC Science & Technology

2006-09-30

med.bhm.html LONG-TERM GOALS Eighteen months into the project, the long-term goals and objectives remain as stated in the progress report last...in the representation of the background error Report Documentation Page Form ApprovedOMB No. 0704-0188 Public reporting burden for the collection of...Information Operations and Reports , 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any

Efficient Matrix Models for Relational Learning

DTIC Science & Technology

2009-10-01

74 4.5.3 Comparison to pLSI- pHITS . . . . . . . . . . . . . . . . . . . . 76 5 Hierarchical Bayesian Collective...Behaviour of Newton vs. Stochastic Newton on a three-factor model. 4.5.3 Comparison to pLSI- pHITS Caveat: Collective Matrix Factorization makes no guarantees...leads to better results; and another where a co-clustering model, pLSI- pHITS , has the advantage. pLSI- pHITS [24] is a relational clustering technique

A Bayesian Hierarchical Model for Large-Scale Educational Surveys: An Application to the National Assessment of Educational Progress. Research Report. ETS RR-04-38

ERIC Educational Resources Information Center

Johnson, Matthew S.; Jenkins, Frank

2005-01-01

Large-scale educational assessments such as the National Assessment of Educational Progress (NAEP) sample examinees to whom an exam will be administered. In most situations the sampling design is not a simple random sample and must be accounted for in the estimating model. After reviewing the current operational estimation procedure for NAEP, this…

Semiparametric regression during 2003–2007*

PubMed Central

Ruppert, David; Wand, M.P.; Carroll, Raymond J.

2010-01-01

Semiparametric regression is a fusion between parametric regression and nonparametric regression that integrates low-rank penalized splines, mixed model and hierarchical Bayesian methodology – thus allowing more streamlined handling of longitudinal and spatial correlation. We review progress in the field over the five-year period between 2003 and 2007. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application. PMID:20305800

Experiments in Error Propagation within Hierarchal Combat Models

DTIC Science & Technology

2015-09-01

Bayesian Information Criterion CNO Chief of Naval Operations DOE Design of Experiments DOD Department of Defense MANA Map Aware Non-uniform Automata ...ground up” approach. First, it develops a mission-level model for one on one submarine combat in Map Aware Non-uniform Automata (MANA) simulation, an... Automata (MANA), an agent based simulation that can model the different postures of submarines. It feeds the results from MANA into stochastic

Soldier Quality of Life Assessment

DTIC Science & Technology

2016-09-01

ABSTRACT This report documents survey research and modeling of Soldier quality of life (QoL) on contingency base camps by the U.S. Army Natick...Science and Technology Objective Demonstration, was to develop a way to quantify QoL for camps housing fewer than 1000 personnel. A discrete choice survey ... Survey results were analyzed using hierarchical Bayesian logistic regression to develop a quantitative model for estimating QoL based on base camp

The drift diffusion model as the choice rule in reinforcement learning.

PubMed

Pedersen, Mads Lund; Frank, Michael J; Biele, Guido

2017-08-01

Current reinforcement-learning models often assume simplified decision processes that do not fully reflect the dynamic complexities of choice processes. Conversely, sequential-sampling models of decision making account for both choice accuracy and response time, but assume that decisions are based on static decision values. To combine these two computational models of decision making and learning, we implemented reinforcement-learning models in which the drift diffusion model describes the choice process, thereby capturing both within- and across-trial dynamics. To exemplify the utility of this approach, we quantitatively fit data from a common reinforcement-learning paradigm using hierarchical Bayesian parameter estimation, and compared model variants to determine whether they could capture the effects of stimulant medication in adult patients with attention-deficit hyperactivity disorder (ADHD). The model with the best relative fit provided a good description of the learning process, choices, and response times. A parameter recovery experiment showed that the hierarchical Bayesian modeling approach enabled accurate estimation of the model parameters. The model approach described here, using simultaneous estimation of reinforcement-learning and drift diffusion model parameters, shows promise for revealing new insights into the cognitive and neural mechanisms of learning and decision making, as well as the alteration of such processes in clinical groups.

Hierarchical modeling of bycatch rates of sea turtles in the western North Atlantic

USGS Publications Warehouse

Gardner, B.; Sullivan, P.J.; Epperly, S.; Morreale, S.J.

2008-01-01

Previous studies indicate that the locations of the endangered loggerhead Caretta caretta and critically endangered leatherback Dermochelys coriacea sea turtles are influenced by water temperatures, and that incidental catch rates in the pelagic longline fishery vary by region. We present a Bayesian hierarchical model to examine the effects of environmental variables, including water temperature, on the number of sea turtles captured in the US pelagic longline fishery in the western North Atlantic. The modeling structure is highly flexible, utilizes a Bayesian model selection technique, and is fully implemented in the software program WinBUGS. The number of sea turtles captured is modeled as a zero-inflated Poisson distribution and the model incorporates fixed effects to examine region-specific differences in the parameter estimates. Results indicate that water temperature, region, bottom depth, and target species are all significant predictors of the number of loggerhead sea turtles captured. For leatherback sea turtles, the model with only target species had the most posterior model weight, though a re-parameterization of the model indicates that temperature influences the zero-inflation parameter. The relationship between the number of sea turtles captured and the variables of interest all varied by region. This suggests that management decisions aimed at reducing sea turtle bycatch may be more effective if they are spatially explicit. ?? Inter-Research 2008.

The drift diffusion model as the choice rule in reinforcement learning

PubMed Central

Frank, Michael J.

2017-01-01

Current reinforcement-learning models often assume simplified decision processes that do not fully reflect the dynamic complexities of choice processes. Conversely, sequential-sampling models of decision making account for both choice accuracy and response time, but assume that decisions are based on static decision values. To combine these two computational models of decision making and learning, we implemented reinforcement-learning models in which the drift diffusion model describes the choice process, thereby capturing both within- and across-trial dynamics. To exemplify the utility of this approach, we quantitatively fit data from a common reinforcement-learning paradigm using hierarchical Bayesian parameter estimation, and compared model variants to determine whether they could capture the effects of stimulant medication in adult patients with attention-deficit hyper-activity disorder (ADHD). The model with the best relative fit provided a good description of the learning process, choices, and response times. A parameter recovery experiment showed that the hierarchical Bayesian modeling approach enabled accurate estimation of the model parameters. The model approach described here, using simultaneous estimation of reinforcement-learning and drift diffusion model parameters, shows promise for revealing new insights into the cognitive and neural mechanisms of learning and decision making, as well as the alteration of such processes in clinical groups. PMID:27966103

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.

Using hierarchical Bayesian multi-species mixture models to estimate tandem hoop-net based habitat associations and detection probabilities of fishes in reservoirs

USGS Publications Warehouse

Stewart, David R.; Long, James M.

2015-01-01

Species distribution models are useful tools to evaluate habitat relationships of fishes. We used hierarchical Bayesian multispecies mixture models to evaluate the relationships of both detection and abundance with habitat of reservoir fishes caught using tandem hoop nets. A total of 7,212 fish from 12 species were captured, and the majority of the catch was composed of Channel Catfish Ictalurus punctatus (46%), Bluegill Lepomis macrochirus(25%), and White Crappie Pomoxis annularis (14%). Detection estimates ranged from 8% to 69%, and modeling results suggested that fishes were primarily influenced by reservoir size and context, water clarity and temperature, and land-use types. Species were differentially abundant within and among habitat types, and some fishes were found to be more abundant in turbid, less impacted (e.g., by urbanization and agriculture) reservoirs with longer shoreline lengths; whereas, other species were found more often in clear, nutrient-rich impoundments that had generally shorter shoreline length and were surrounded by a higher percentage of agricultural land. Our results demonstrated that habitat and reservoir characteristics may differentially benefit species and assemblage structure. This study provides a useful framework for evaluating capture efficiency for not only hoop nets but other gear types used to sample fishes in reservoirs.

Applying Bayesian hierarchical models to examine motorcycle crashes at signalized intersections.

PubMed

Haque, Md Mazharul; Chin, Hoong Chor; Huang, Helai

2010-01-01

Motorcycles are overrepresented in road traffic crashes and particularly vulnerable at signalized intersections. The objective of this study is to identify causal factors affecting the motorcycle crashes at both four-legged and T signalized intersections. Treating the data in time-series cross-section panels, this study explores different Hierarchical Poisson models and found that the model allowing autoregressive lag-1 dependence specification in the error term is the most suitable. Results show that the number of lanes at the four-legged signalized intersections significantly increases motorcycle crashes largely because of the higher exposure resulting from higher motorcycle accumulation at the stop line. Furthermore, the presence of a wide median and an uncontrolled left-turn lane at major roadways of four-legged intersections exacerbate this potential hazard. For T signalized intersections, the presence of exclusive right-turn lane at both major and minor roadways and an uncontrolled left-turn lane at major roadways increases motorcycle crashes. Motorcycle crashes increase on high-speed roadways because they are more vulnerable and less likely to react in time during conflicts. The presence of red light cameras reduces motorcycle crashes significantly for both four-legged and T intersections. With the red light camera, motorcycles are less exposed to conflicts because it is observed that they are more disciplined in queuing at the stop line and less likely to jump start at the start of green.

Estimation of hyper-parameters for a hierarchical model of combined cortical and extra-brain current sources in the MEG inverse problem.

PubMed

Morishige, Ken-ichi; Yoshioka, Taku; Kawawaki, Dai; Hiroe, Nobuo; Sato, Masa-aki; Kawato, Mitsuo

2014-11-01

One of the major obstacles in estimating cortical currents from MEG signals is the disturbance caused by magnetic artifacts derived from extra-cortical current sources such as heartbeats and eye movements. To remove the effect of such extra-brain sources, we improved the hybrid hierarchical variational Bayesian method (hyVBED) proposed by Fujiwara et al. (NeuroImage, 2009). hyVBED simultaneously estimates cortical and extra-brain source currents by placing dipoles on cortical surfaces as well as extra-brain sources. This method requires EOG data for an EOG forward model that describes the relationship between eye dipoles and electric potentials. In contrast, our improved approach requires no EOG and less a priori knowledge about the current variance of extra-brain sources. We propose a new method, "extra-dipole," that optimally selects hyper-parameter values regarding current variances of the cortical surface and extra-brain source dipoles. With the selected parameter values, the cortical and extra-brain dipole currents were accurately estimated from the simulated MEG data. The performance of this method was demonstrated to be better than conventional approaches, such as principal component analysis and independent component analysis, which use only statistical properties of MEG signals. Furthermore, we applied our proposed method to measured MEG data during covert pursuit of a smoothly moving target and confirmed its effectiveness. Copyright © 2014 Elsevier Inc. All rights reserved.

A semiparametric Bayesian proportional hazards model for interval censored data with frailty effects.

PubMed

Henschel, Volkmar; Engel, Jutta; Hölzel, Dieter; Mansmann, Ulrich

2009-02-10

Multivariate analysis of interval censored event data based on classical likelihood methods is notoriously cumbersome. Likelihood inference for models which additionally include random effects are not available at all. Developed algorithms bear problems for practical users like: matrix inversion, slow convergence, no assessment of statistical uncertainty. MCMC procedures combined with imputation are used to implement hierarchical models for interval censored data within a Bayesian framework. Two examples from clinical practice demonstrate the handling of clustered interval censored event times as well as multilayer random effects for inter-institutional quality assessment. The software developed is called survBayes and is freely available at CRAN. The proposed software supports the solution of complex analyses in many fields of clinical epidemiology as well as health services research.

Estimation of selection intensity under overdominance by Bayesian methods.

PubMed

Buzbas, Erkan Ozge; Joyce, Paul; Abdo, Zaid

2009-01-01

A balanced pattern in the allele frequencies of polymorphic loci is a potential sign of selection, particularly of overdominance. Although this type of selection is of some interest in population genetics, there exists no likelihood based approaches specifically tailored to make inference on selection intensity. To fill this gap, we present Bayesian methods to estimate selection intensity under k-allele models with overdominance. Our model allows for an arbitrary number of loci and alleles within a locus. The neutral and selected variability within each locus are modeled with corresponding k-allele models. To estimate the posterior distribution of the mean selection intensity in a multilocus region, a hierarchical setup between loci is used. The methods are demonstrated with data at the Human Leukocyte Antigen loci from world-wide populations.

A hierarchical model for regional analysis of population change using Christmas Bird Count data, with application to the American Black Duck

USGS Publications Warehouse

Link, W.A.; Sauer, J.R.; Niven, D.K.

2006-01-01

Analysis of Christmas Bird Count (CBC) data is complicated by the need to account for variation in effort on counts and to provide summaries over large geographic regions. We describe a hierarchical model for analysis of population change using CBC data that addresses these needs. The effect of effort is modeled parametrically, with parameter values varying among strata as identically distributed random effects. Year and site effects are modeled hierarchically, accommodating large regional variation in number of samples and precision of estimates. The resulting model is complex, but a Bayesian analysis can be conducted using Markov chain Monte Carlo techniques. We analyze CBC data for American Black Ducks (Anas rubripes), a species of considerable management interest that has historically been monitored using winter surveys. Over the interval 1966-2003, Black Duck populations showed distinct regional patterns of population change. The patterns shown by CBC data are similar to those shown by the Midwinter Waterfowl Inventory for the United States.

Efficient fuzzy Bayesian inference algorithms for incorporating expert knowledge in parameter estimation

NASA Astrophysics Data System (ADS)

Rajabi, Mohammad Mahdi; Ataie-Ashtiani, Behzad

2016-05-01

Bayesian inference has traditionally been conceived as the proper framework for the formal incorporation of expert knowledge in parameter estimation of groundwater models. However, conventional Bayesian inference is incapable of taking into account the imprecision essentially embedded in expert provided information. In order to solve this problem, a number of extensions to conventional Bayesian inference have been introduced in recent years. One of these extensions is 'fuzzy Bayesian inference' which is the result of integrating fuzzy techniques into Bayesian statistics. Fuzzy Bayesian inference has a number of desirable features which makes it an attractive approach for incorporating expert knowledge in the parameter estimation process of groundwater models: (1) it is well adapted to the nature of expert provided information, (2) it allows to distinguishably model both uncertainty and imprecision, and (3) it presents a framework for fusing expert provided information regarding the various inputs of the Bayesian inference algorithm. However an important obstacle in employing fuzzy Bayesian inference in groundwater numerical modeling applications is the computational burden, as the required number of numerical model simulations often becomes extremely exhaustive and often computationally infeasible. In this paper, a novel approach of accelerating the fuzzy Bayesian inference algorithm is proposed which is based on using approximate posterior distributions derived from surrogate modeling, as a screening tool in the computations. The proposed approach is first applied to a synthetic test case of seawater intrusion (SWI) in a coastal aquifer. It is shown that for this synthetic test case, the proposed approach decreases the number of required numerical simulations by an order of magnitude. Then the proposed approach is applied to a real-world test case involving three-dimensional numerical modeling of SWI in Kish Island, located in the Persian Gulf. An expert elicitation methodology is developed and applied to the real-world test case in order to provide a road map for the use of fuzzy Bayesian inference in groundwater modeling applications.

Hierarchical models and Bayesian analysis of bird survey information

USGS Publications Warehouse

Sauer, J.R.; Link, W.A.; Royle, J. Andrew; Ralph, C. John; Rich, Terrell D.

2005-01-01

Summary of bird survey information is a critical component of conservation activities, but often our summaries rely on statistical methods that do not accommodate the limitations of the information. Prioritization of species requires ranking and analysis of species by magnitude of population trend, but often magnitude of trend is a misleading measure of actual decline when trend is poorly estimated. Aggregation of population information among regions is also complicated by varying quality of estimates among regions. Hierarchical models provide a reasonable means of accommodating concerns about aggregation and ranking of quantities of varying precision. In these models the need to consider multiple scales is accommodated by placing distributional assumptions on collections of parameters. For collections of species trends, this allows probability statements to be made about the collections of species-specific parameters, rather than about the estimates. We define and illustrate hierarchical models for two commonly encountered situations in bird conservation: (1) Estimating attributes of collections of species estimates, including ranking of trends, estimating number of species with increasing populations, and assessing population stability with regard to predefined trend magnitudes; and (2) estimation of regional population change, aggregating information from bird surveys over strata. User-friendly computer software makes hierarchical models readily accessible to scientists.

The Population Consequences of Disturbance Model Application to North Atlantic Right Whales (Eubalaena glacialis)

DTIC Science & Technology

2012-09-30

marine mammal to its population status. Recent developments in the PCAD working group have led to modified analyses (now defined as PCOD – Population...variability, and the spatial characteristics of human activities into the PCOD model. Report Documentation Page Form ApprovedOMB No. 0704-0188 Public...consequences of disturbance ( PCOD ) (Thomas et al. 2011). OBJECTIVES The objectives for this study are to: 1) develop a Hierarchical Bayesian Model

Bayesian Hierarchical Models to Augment the Mediterranean Forecast System

DTIC Science & Technology

2010-09-30

In part 2 (Bonazzi et al., 2010), the impact of the ensemble forecast methodology based on MFS-Wind-BHM perturbations is documented. Forecast...absence of dt data stage inputs, the forecast impact of MFS-Error-BHM is neutral. Experiments are underway now to introduce dt back into the MFS-Error...BHM and quantify forecast impacts at MFS. MFS-SuperEnsemble-BHM We have assembled all needed datasets and completed algorithmic development

Systemic antibiotics in the treatment of aggressive periodontitis. A systematic review and a Bayesian Network meta-analysis.

PubMed

Rabelo, Cleverton Correa; Feres, Magda; Gonçalves, Cristiane; Figueiredo, Luciene C; Faveri, Marcelo; Tu, Yu-Kang; Chambrone, Leandro

2015-07-01

The aim of this study was to assess the effect of systemic antibiotic therapy on the treatment of aggressive periodontitis (AgP). This study was conducted and reported in accordance with the PRISMA statement. The MEDLINE, EMBASE and CENTRAL databases were searched up to June 2014 for randomized clinical trials comparing the treatment of subjects with AgP with either scaling and root planing (SRP) alone or associated with systemic antibiotics. Bayesian network meta-analysis was prepared using the Bayesian random-effects hierarchical models and the outcomes reported at 6-month post-treatment. Out of 350 papers identified, 14 studies were eligible. Greater gain in clinical attachment (CA) (mean difference [MD]: 1.08 mm; p < 0.0001) and reduction in probing depth (PD) (MD: 1.05 mm; p < 0.00001) were observed for SRP + metronidazole (Mtz), and for SRP + Mtz + amoxicillin (Amx) (MD: 0.45 mm, MD: 0.53 mm, respectively; p < 0.00001) than SRP alone/placebo. Bayesian network meta-analysis showed additional benefits in CA gain and PD reduction when SRP was associated with systemic antibiotics. SRP plus systemic antibiotics led to an additional clinical effect compared with SRP alone in the treatment of AgP. Of the antibiotic protocols available for inclusion into the Bayesian network meta-analysis, Mtz and Mtz/Amx provided to the most beneficial outcomes. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Kernel-imbedded Gaussian processes for disease classification using microarray gene expression data

PubMed Central

Zhao, Xin; Cheung, Leo Wang-Kit

2007-01-01

Background Designing appropriate machine learning methods for identifying genes that have a significant discriminating power for disease outcomes has become more and more important for our understanding of diseases at genomic level. Although many machine learning methods have been developed and applied to the area of microarray gene expression data analysis, the majority of them are based on linear models, which however are not necessarily appropriate for the underlying connection between the target disease and its associated explanatory genes. Linear model based methods usually also bring in false positive significant features more easily. Furthermore, linear model based algorithms often involve calculating the inverse of a matrix that is possibly singular when the number of potentially important genes is relatively large. This leads to problems of numerical instability. To overcome these limitations, a few non-linear methods have recently been introduced to the area. Many of the existing non-linear methods have a couple of critical problems, the model selection problem and the model parameter tuning problem, that remain unsolved or even untouched. In general, a unified framework that allows model parameters of both linear and non-linear models to be easily tuned is always preferred in real-world applications. Kernel-induced learning methods form a class of approaches that show promising potentials to achieve this goal. Results A hierarchical statistical model named kernel-imbedded Gaussian process (KIGP) is developed under a unified Bayesian framework for binary disease classification problems using microarray gene expression data. In particular, based on a probit regression setting, an adaptive algorithm with a cascading structure is designed to find the appropriate kernel, to discover the potentially significant genes, and to make the optimal class prediction accordingly. A Gibbs sampler is built as the core of the algorithm to make Bayesian inferences. Simulation studies showed that, even without any knowledge of the underlying generative model, the KIGP performed very close to the theoretical Bayesian bound not only in the case with a linear Bayesian classifier but also in the case with a very non-linear Bayesian classifier. This sheds light on its broader usability to microarray data analysis problems, especially to those that linear methods work awkwardly. The KIGP was also applied to four published microarray datasets, and the results showed that the KIGP performed better than or at least as well as any of the referred state-of-the-art methods did in all of these cases. Conclusion Mathematically built on the kernel-induced feature space concept under a Bayesian framework, the KIGP method presented in this paper provides a unified machine learning approach to explore both the linear and the possibly non-linear underlying relationship between the target features of a given binary disease classification problem and the related explanatory gene expression data. More importantly, it incorporates the model parameter tuning into the framework. The model selection problem is addressed in the form of selecting a proper kernel type. The KIGP method also gives Bayesian probabilistic predictions for disease classification. These properties and features are beneficial to most real-world applications. The algorithm is naturally robust in numerical computation. The simulation studies and the published data studies demonstrated that the proposed KIGP performs satisfactorily and consistently. PMID:17328811

Bayesian Statistics for Biological Data: Pedigree Analysis

ERIC Educational Resources Information Center

Stanfield, William D.; Carlton, Matthew A.

2004-01-01

The use of Bayes' formula is applied to the biological problem of pedigree analysis to show that the Bayes' formula and non-Bayesian or "classical" methods of probability calculation give different answers. First year college students of biology can be introduced to the Bayesian statistics.

Prediction in Health Domain Using Bayesian Networks Optimization Based on Induction Learning Techniques

NASA Astrophysics Data System (ADS)

Felgaer, Pablo; Britos, Paola; García-Martínez, Ramón

A Bayesian network is a directed acyclic graph in which each node represents a variable and each arc a probabilistic dependency; they are used to provide: a compact form to represent the knowledge and flexible methods of reasoning. Obtaining it from data is a learning process that is divided in two steps: structural learning and parametric learning. In this paper we define an automatic learning method that optimizes the Bayesian networks applied to classification, using a hybrid method of learning that combines the advantages of the induction techniques of the decision trees (TDIDT-C4.5) with those of the Bayesian networks. The resulting method is applied to prediction in health domain.

On weak lensing shape noise

NASA Astrophysics Data System (ADS)

Niemi, Sami-Matias; Kitching, Thomas D.; Cropper, Mark

2015-12-01

One of the most powerful techniques to study the dark sector of the Universe is weak gravitational lensing. In practice, to infer the reduced shear, weak lensing measures galaxy shapes, which are the consequence of both the intrinsic ellipticity of the sources and of the integrated gravitational lensing effect along the line of sight. Hence, a very large number of galaxies is required in order to average over their individual properties and to isolate the weak lensing cosmic shear signal. If this `shape noise' can be reduced, significant advances in the power of a weak lensing surveys can be expected. This paper describes a general method for extracting the probability distributions of parameters from catalogues of data using Voronoi cells, which has several applications, and has synergies with Bayesian hierarchical modelling approaches. This allows us to construct a probability distribution for the variance of the intrinsic ellipticity as a function of galaxy property using only photometric data, allowing a reduction of shape noise. As a proof of concept the method is applied to the CFHTLenS survey data. We use this approach to investigate trends of galaxy properties in the data and apply this to the case of weak lensing power spectra.

BAYESIAN ESTIMATION OF THERMONUCLEAR REACTION RATES

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

Iliadis, C.; Anderson, K. S.; Coc, A.

The problem of estimating non-resonant astrophysical S -factors and thermonuclear reaction rates, based on measured nuclear cross sections, is of major interest for nuclear energy generation, neutrino physics, and element synthesis. Many different methods have been applied to this problem in the past, almost all of them based on traditional statistics. Bayesian methods, on the other hand, are now in widespread use in the physical sciences. In astronomy, for example, Bayesian statistics is applied to the observation of extrasolar planets, gravitational waves, and Type Ia supernovae. However, nuclear physics, in particular, has been slow to adopt Bayesian methods. We presentmore » astrophysical S -factors and reaction rates based on Bayesian statistics. We develop a framework that incorporates robust parameter estimation, systematic effects, and non-Gaussian uncertainties in a consistent manner. The method is applied to the reactions d(p, γ ){sup 3}He, {sup 3}He({sup 3}He,2p){sup 4}He, and {sup 3}He( α , γ ){sup 7}Be, important for deuterium burning, solar neutrinos, and Big Bang nucleosynthesis.« less

Assessing the Dynamic Effects of Climate on Individual Tree Growth Across Time and Space

NASA Astrophysics Data System (ADS)

Itter, M.; Finley, A. O.; D'Amato, A. W.; Foster, J. R.; Bradford, J. B.

2015-12-01

The relationship between climate variability and an ecosystem process, such as forest growth, is frequently not fixed over time, but changes due to complex interactions between unobserved ecological factors and the process of interest. Climate data and forecasts are frequently spatially and temporally misaligned with ecological observations making inference regarding the effects of climate on ecosystem processes particularly challenging. Here we develop a Bayesian dynamic hierarchical model for annual tree growth increment that allows the effects of climate to evolve over time, applies climate data at a spatial-temporal scale consistent with observations, and controls for individual-level variability commonly encountered in ecological datasets. The model is applied to individual tree data from northern Minnesota using a modified Thornthwaite-type water balance model to transform PRISM temperature and precipitation estimates to physiologically relevant values of actual and potential evapotranspiration (AET, PET), and climatic water deficit. Model results indicate that mean tree growth is most sensitive to AET during the growing season and PET and minimum temperature in the spring prior to growth. The effects of these variables on tree growth, however, are not stationary with significant effects observed in only a subset of years during the 111-year study period. Importantly, significant effects of climate do not result from anomalous climate observations, but follow from large growth deviations unexplained by tree age and size, and time since forest disturbance. Results differ markedly from alternative models that assume the effects of climate are stationary over time or apply climate estimates at the individual scale. Forecasts of future tree growth as a function of climate follow directly from the dynamic hierarchical model allowing for assessment of forest change. Current work is focused on extending the model framework to include regional climate and ecosystem effects for application to a larger tree growth dataset spanning a latitudinal gradient within the US from Maine to Florida.

Ritual human sacrifice promoted and sustained the evolution of stratified societies.

PubMed

Watts, Joseph; Sheehan, Oliver; Atkinson, Quentin D; Bulbulia, Joseph; Gray, Russell D

2016-04-14

Evidence for human sacrifice is found throughout the archaeological record of early civilizations, the ethnographic records of indigenous world cultures, and the texts of the most prolific contemporary religions. According to the social control hypothesis, human sacrifice legitimizes political authority and social class systems, functioning to stabilize such social stratification. Support for the social control hypothesis is largely limited to historical anecdotes of human sacrifice, where the causal claims have not been subject to rigorous quantitative cross-cultural tests. Here we test the social control hypothesis by applying Bayesian phylogenetic methods to a geographically and socially diverse sample of 93 traditional Austronesian cultures. We find strong support for models in which human sacrifice stabilizes social stratification once stratification has arisen, and promotes a shift to strictly inherited class systems. Whilst evolutionary theories of religion have focused on the functionality of prosocial and moral beliefs, our results reveal a darker link between religion and the evolution of modern hierarchical societies.

Prior Design for Dependent Dirichlet Processes: An Application to Marathon Modeling

PubMed Central

F. Pradier, Melanie; J. R. Ruiz, Francisco; Perez-Cruz, Fernando

2016-01-01

This paper presents a novel application of Bayesian nonparametrics (BNP) for marathon data modeling. We make use of two well-known BNP priors, the single-p dependent Dirichlet process and the hierarchical Dirichlet process, in order to address two different problems. First, we study the impact of age, gender and environment on the runners’ performance. We derive a fair grading method that allows direct comparison of runners regardless of their age and gender. Unlike current grading systems, our approach is based not only on top world records, but on the performances of all runners. The presented methodology for comparison of densities can be adopted in many other applications straightforwardly, providing an interesting perspective to build dependent Dirichlet processes. Second, we analyze the running patterns of the marathoners in time, obtaining information that can be valuable for training purposes. We also show that these running patterns can be used to predict finishing time given intermediate interval measurements. We apply our models to New York City, Boston and London marathons. PMID:26821155

Reconstructing plate-motion changes in the presence of finite-rotations noise.

PubMed

Iaffaldano, Giampiero; Bodin, Thomas; Sambridge, Malcolm

2012-01-01

Understanding lithospheric plate motions is of paramount importance to geodynamicists. Much effort is going into kinematic reconstructions featuring progressively finer temporal resolution. However, the challenge of precisely identifying ocean-floor magnetic lineations, and uncertainties in geomagnetic reversal timescales result in substantial finite-rotations noise. Unless some type of temporal smoothing is applied, the scenario arising at the native temporal resolution is puzzling, as plate motions vary erratically and significantly over short periods (<1 Myr). This undermines our ability to make geodynamic inferences, as the rates at which forces need to be built upon plates to explain these kinematics far exceed the most optimistic estimates. Here we show that the largest kinematic changes reconstructed across the Atlantic, Indian and South Pacific ridges arise from data noise. We overcome this limitation using a trans-dimensional hierarchical Bayesian framework. We find that plate-motion changes occur on timescales no shorter than a few million years, yielding simpler kinematic patterns and more plausible dynamics.

A statistical approach to rank multiple priorities in environmental epidemiology: an example from high-risk areas in Sardinia, Italy.

PubMed

Catelan, Dolores; Biggeri, Annibale

2008-11-01

In environmental epidemiology, long lists of relative risk estimates from exposed populations are compared to a reference to scrutinize the dataset for extremes. Here, inference on disease profiles for given areas, or for fixed disease population signatures, are of interest and summaries can be obtained averaging over areas or diseases. We have developed a multivariate hierarchical Bayesian approach to estimate posterior rank distributions and we show how to produce league tables of ranks with credibility intervals useful to address the above mentioned inferential problems. Applying the procedure to a real dataset from the report "Environment and Health in Sardinia (Italy)" we selected 18 areas characterized by high environmental pressure for industrial, mining or military activities investigated for 29 causes of deaths among male residents. Ranking diseases highlighted the increased burdens of neoplastic (cancerous), and non-neoplastic respiratory diseases in the heavily polluted area of Portoscuso. The averaged ranks by disease over areas showed lung cancer among the three highest positions.

Effect of Clustering Algorithm on Establishing Markov State Model for Molecular Dynamics Simulations.

PubMed

Li, Yan; Dong, Zigang

2016-06-27

Recently, the Markov state model has been applied for kinetic analysis of molecular dynamics simulations. However, discretization of the conformational space remains a primary challenge in model building, and it is not clear how the space decomposition by distinct clustering strategies exerts influence on the model output. In this work, different clustering algorithms are employed to partition the conformational space sampled in opening and closing of fatty acid binding protein 4 as well as inactivation and activation of the epidermal growth factor receptor. Various classifications are achieved, and Markov models are set up accordingly. On the basis of the models, the total net flux and transition rate are calculated between two distinct states. Our results indicate that geometric and kinetic clustering perform equally well. The construction and outcome of Markov models are heavily dependent on the data traits. Compared to other methods, a combination of Bayesian and hierarchical clustering is feasible in identification of metastable states.

The Bayesian Revolution Approaches Psychological Development

ERIC Educational Resources Information Center

Shultz, Thomas R.

2007-01-01

This commentary reviews five articles that apply Bayesian ideas to psychological development, some with psychology experiments, some with computational modeling, and some with both experiments and modeling. The reviewed work extends the current Bayesian revolution into tasks often studied in children, such as causal learning and word learning, and…

A Gentle Introduction to Bayesian Analysis: Applications to Developmental Research

PubMed Central

van de Schoot, Rens; Kaplan, David; Denissen, Jaap; Asendorpf, Jens B; Neyer, Franz J; van Aken, Marcel AG

2014-01-01

Bayesian statistical methods are becoming ever more popular in applied and fundamental research. In this study a gentle introduction to Bayesian analysis is provided. It is shown under what circumstances it is attractive to use Bayesian estimation, and how to interpret properly the results. First, the ingredients underlying Bayesian methods are introduced using a simplified example. Thereafter, the advantages and pitfalls of the specification of prior knowledge are discussed. To illustrate Bayesian methods explained in this study, in a second example a series of studies that examine the theoretical framework of dynamic interactionism are considered. In the Discussion the advantages and disadvantages of using Bayesian statistics are reviewed, and guidelines on how to report on Bayesian statistics are provided. PMID:24116396

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.

Estimating age from recapture data: integrating incremental growth measures with ancillary data to infer age-at-length

USGS Publications Warehouse

Eaton, Mitchell J.; Link, William A.

2011-01-01

Estimating the age of individuals in wild populations can be of fundamental importance for answering ecological questions, modeling population demographics, and managing exploited or threatened species. Significant effort has been devoted to determining age through the use of growth annuli, secondary physical characteristics related to age, and growth models. Many species, however, either do not exhibit physical characteristics useful for independent age validation or are too rare to justify sacrificing a large number of individuals to establish the relationship between size and age. Length-at-age models are well represented in the fisheries and other wildlife management literature. Many of these models overlook variation in growth rates of individuals and consider growth parameters as population parameters. More recent models have taken advantage of hierarchical structuring of parameters and Bayesian inference methods to allow for variation among individuals as functions of environmental covariates or individual-specific random effects. Here, we describe hierarchical models in which growth curves vary as individual-specific stochastic processes, and we show how these models can be fit using capture–recapture data for animals of unknown age along with data for animals of known age. We combine these independent data sources in a Bayesian analysis, distinguishing natural variation (among and within individuals) from measurement error. We illustrate using data for African dwarf crocodiles, comparing von Bertalanffy and logistic growth models. The analysis provides the means of predicting crocodile age, given a single measurement of head length. The von Bertalanffy was much better supported than the logistic growth model and predicted that dwarf crocodiles grow from 19.4 cm total length at birth to 32.9 cm in the first year and 45.3 cm by the end of their second year. Based on the minimum size of females observed with hatchlings, reproductive maturity was estimated to be at nine years. These size benchmarks are believed to represent thresholds for important demographic parameters; improved estimates of age, therefore, will increase the precision of population projection models. The modeling approach that we present can be applied to other species and offers significant advantages when multiple sources of data are available and traditional aging techniques are not practical.

A Model-Based Approach to Infer Shifts in Regional Fire Regimes Over Time Using Sediment Charcoal Records

NASA Astrophysics Data System (ADS)

Itter, M.; Finley, A. O.; Hooten, M.; Higuera, P. E.; Marlon, J. R.; McLachlan, J. S.; Kelly, R.

2016-12-01

Sediment charcoal records are used in paleoecological analyses to identify individual local fire events and to estimate fire frequency and regional biomass burned at centennial to millenial time scales. Methods to identify local fire events based on sediment charcoal records have been well developed over the past 30 years, however, an integrated statistical framework for fire identification is still lacking. We build upon existing paleoecological methods to develop a hierarchical Bayesian point process model for local fire identification and estimation of fire return intervals. The model is unique in that it combines sediment charcoal records from multiple lakes across a region in a spatially-explicit fashion leading to estimation of a joint, regional fire return interval in addition to lake-specific local fire frequencies. Further, the model estimates a joint regional charcoal deposition rate free from the effects of local fires that can be used as a measure of regional biomass burned over time. Finally, the hierarchical Bayesian approach allows for tractable error propagation such that estimates of fire return intervals reflect the full range of uncertainty in sediment charcoal records. Specific sources of uncertainty addressed include sediment age models, the separation of local versus regional charcoal sources, and generation of a composite charcoal record The model is applied to sediment charcoal records from a dense network of lakes in the Yukon Flats region of Alaska. The multivariate joint modeling approach results in improved estimates of regional charcoal deposition with reduced uncertainty in the identification of individual fire events and local fire return intervals compared to individual lake approaches. Modeled individual-lake fire return intervals range from 100 to 500 years with a regional interval of roughly 200 years. Regional charcoal deposition to the network of lakes is correlated up to 50 kilometers. Finally, the joint regional charcoal deposition rate exhibits changes over time coincident with major climatic and vegetation shifts over the past 10,000 years. Ongoing work will use the regional charcoal deposition rate to estimate changes in biomass burned as a function of climate variability and regional vegetation pattern.

Estimating National-scale Emissions using Dense Monitoring Networks

NASA Astrophysics Data System (ADS)

Ganesan, A.; Manning, A.; Grant, A.; Young, D.; Oram, D.; Sturges, W. T.; Moncrieff, J. B.; O'Doherty, S.

2014-12-01

The UK's DECC (Deriving Emissions linked to Climate Change) network consists of four greenhouse gas measurement stations that are situated to constrain emissions from the UK and Northwest Europe. These four stations are located in Mace Head (West Coast of Ireland), and on telecommunication towers at Ridge Hill (Western England), Tacolneston (Eastern England) and Angus (Eastern Scotland). With the exception of Angus, which currently only measures carbon dioxide (CO2) and methane (CH4), the remaining sites are additionally equipped to monitor nitrous oxide (N2O). We present an analysis of the network's CH4 and N2O observations from 2011-2013 and compare derived top-down regional emissions with bottom-up inventories, including a recently produced high-resolution inventory (UK National Atmospheric Emissions Inventory). As countries are moving toward national-level emissions estimation, we also address some of the considerations that need to be made when designing these national networks. One of the novel aspects of this work is that we use a hierarchical Bayesian inversion framework. This methodology, which has newly been applied to greenhouse gas emissions estimation, is designed to estimate temporally and spatially varying model-measurement uncertainties and correlation scales, in addition to fluxes. Through this analysis, we demonstrate the importance of characterizing these covariance parameters in order to properly use data from high-density monitoring networks. This UK case study highlights the ways in which this new inverse framework can be used to address some of the limitations of traditional Bayesian inverse methods.

Analysis of Extreme Snow Water Equivalent Data in Central New Hampshire

NASA Astrophysics Data System (ADS)

Vuyovich, C.; Skahill, B. E.; Kanney, J. F.; Carr, M.

2017-12-01

Heavy snowfall and snowmelt-related events have been linked to widespread flooding and damages in many regions of the U.S. Design of critical infrastructure in these regions requires spatial estimates of extreme snow water equivalent (SWE). In this study, we develop station specific and spatially explicit estimates of extreme SWE using data from fifteen snow sampling stations maintained by the New Hampshire Department of Environmental Services. The stations are located in the Mascoma, Pemigewasset, Winnipesaukee, Ossipee, Salmon Falls, Lamprey, Sugar, and Isinglass basins in New Hampshire. The average record length for the fifteen stations is approximately fifty-nine years. The spatial analysis of extreme SWE involves application of two Bayesian Hierarchical Modeling methods, one that assumes conditional independence, and another which uses the Smith max-stable process model to account for spatial dependence. We also apply additional max-stable process models, albeit not in a Bayesian framework, that better model the observed dependence among the extreme SWE data. The spatial process modeling leverages readily available and relevant spatially explicit covariate data. The noted additional max-stable process models also used the nonstationary winter North Atlantic Oscillation index, which has been observed to influence snowy weather along the east coast of the United States. We find that, for this data set, SWE return level estimates are consistently higher when derived using methods which account for the observed spatial dependence among the extreme data. This is particularly significant for design scenarios of relevance for critical infrastructure evaluation.

Bayesian hierarchical piecewise regression models: a tool to detect trajectory divergence between groups in long-term observational studies.

PubMed

Buscot, Marie-Jeanne; Wotherspoon, Simon S; Magnussen, Costan G; Juonala, Markus; Sabin, Matthew A; Burgner, David P; Lehtimäki, Terho; Viikari, Jorma S A; Hutri-Kähönen, Nina; Raitakari, Olli T; Thomson, Russell J

2017-06-06

Bayesian hierarchical piecewise regression (BHPR) modeling has not been previously formulated to detect and characterise the mechanism of trajectory divergence between groups of participants that have longitudinal responses with distinct developmental phases. These models are useful when participants in a prospective cohort study are grouped according to a distal dichotomous health outcome. Indeed, a refined understanding of how deleterious risk factor profiles develop across the life-course may help inform early-life interventions. Previous techniques to determine between-group differences in risk factors at each age may result in biased estimate of the age at divergence. We demonstrate the use of Bayesian hierarchical piecewise regression (BHPR) to generate a point estimate and credible interval for the age at which trajectories diverge between groups for continuous outcome measures that exhibit non-linear within-person response profiles over time. We illustrate our approach by modeling the divergence in childhood-to-adulthood body mass index (BMI) trajectories between two groups of adults with/without type 2 diabetes mellitus (T2DM) in the Cardiovascular Risk in Young Finns Study (YFS). Using the proposed BHPR approach, we estimated the BMI profiles of participants with T2DM diverged from healthy participants at age 16 years for males (95% credible interval (CI):13.5-18 years) and 21 years for females (95% CI: 19.5-23 years). These data suggest that a critical window for weight management intervention in preventing T2DM might exist before the age when BMI growth rate is naturally expected to decrease. Simulation showed that when using pairwise comparison of least-square means from categorical mixed models, smaller sample sizes tended to conclude a later age of divergence. In contrast, the point estimate of the divergence time is not biased by sample size when using the proposed BHPR method. BHPR is a powerful analytic tool to model long-term non-linear longitudinal outcomes, enabling the identification of the age at which risk factor trajectories diverge between groups of participants. The method is suitable for the analysis of unbalanced longitudinal data, with only a limited number of repeated measures per participants and where the time-related outcome is typically marked by transitional changes or by distinct phases of change over time.

A Robust Deconvolution Method based on Transdimensional Hierarchical Bayesian Inference

NASA Astrophysics Data System (ADS)

Kolb, J.; Lekic, V.

2012-12-01

Analysis of P-S and S-P conversions allows us to map receiver side crustal and lithospheric structure. This analysis often involves deconvolution of the parent wave field from the scattered wave field as a means of suppressing source-side complexity. A variety of deconvolution techniques exist including damped spectral division, Wiener filtering, iterative time-domain deconvolution, and the multitaper method. All of these techniques require estimates of noise characteristics as input parameters. We present a deconvolution method based on transdimensional Hierarchical Bayesian inference in which both noise magnitude and noise correlation are used as parameters in calculating the likelihood probability distribution. Because the noise for P-S and S-P conversion analysis in terms of receiver functions is a combination of both background noise - which is relatively easy to characterize - and signal-generated noise - which is much more difficult to quantify - we treat measurement errors as an known quantity, characterized by a probability density function whose mean and variance are model parameters. This transdimensional Hierarchical Bayesian approach has been successfully used previously in the inversion of receiver functions in terms of shear and compressional wave speeds of an unknown number of layers [1]. In our method we used a Markov chain Monte Carlo (MCMC) algorithm to find the receiver function that best fits the data while accurately assessing the noise parameters. In order to parameterize the receiver function we model the receiver function as an unknown number of Gaussians of unknown amplitude and width. The algorithm takes multiple steps before calculating the acceptance probability of a new model, in order to avoid getting trapped in local misfit minima. Using both observed and synthetic data, we show that the MCMC deconvolution method can accurately obtain a receiver function as well as an estimate of the noise parameters given the parent and daughter components. Furthermore, we demonstrate that this new approach is far less susceptible to generating spurious features even at high noise levels. Finally, the method yields not only the most-likely receiver function, but also quantifies its full uncertainty. [1] Bodin, T., M. Sambridge, H. Tkalčić, P. Arroucau, K. Gallagher, and N. Rawlinson (2012), Transdimensional inversion of receiver functions and surface wave dispersion, J. Geophys. Res., 117, B02301

Bayesian Exploratory Factor Analysis

PubMed Central

Conti, Gabriella; Frühwirth-Schnatter, Sylvia; Heckman, James J.; Piatek, Rémi

2014-01-01

This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor, and the corresponding factor loadings. Classical identification criteria are applied and integrated into our Bayesian procedure to generate models that are stable and clearly interpretable. A Monte Carlo study confirms the validity of the approach. The method is used to produce interpretable low dimensional aggregates from a high dimensional set of psychological measurements. PMID:25431517

Advances in Parameter and Uncertainty Quantification Using Bayesian Hierarchical Techniques with a Spatially Referenced Watershed Model (Invited)

NASA Astrophysics Data System (ADS)

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

2013-12-01

Estimating water and material stores and fluxes in watershed studies is frequently complicated by uncertainties in quantifying hydrological and biogeochemical effects of factors such as land use, soils, and climate. Although these process-related effects are commonly measured and modeled in separate catchments, researchers are especially challenged by their complexity across catchments and diverse environmental settings, leading to a poor understanding of how model parameters and prediction uncertainties vary spatially. To address these concerns, we illustrate the use of Bayesian hierarchical modeling techniques with a dynamic version of the spatially referenced watershed model SPARROW (SPAtially Referenced Regression On Watershed attributes). The dynamic SPARROW model is designed to predict streamflow and other water cycle components (e.g., evapotranspiration, soil and groundwater storage) for monthly varying hydrological regimes, using mechanistic functions, mass conservation constraints, and statistically estimated parameters. In this application, the model domain includes nearly 30,000 NHD (National Hydrologic Data) stream reaches and their associated catchments in the Susquehanna River Basin. We report the results of our comparisons of alternative models of varying complexity, including models with different explanatory variables as well as hierarchical models that account for spatial and temporal variability in model parameters and variance (error) components. The model errors are evaluated for changes with season and catchment size and correlations in time and space. The hierarchical models consist of a two-tiered structure in which climate forcing parameters are modeled as random variables, conditioned on watershed properties. Quantification of spatial and temporal variations in the hydrological parameters and model uncertainties in this approach leads to more efficient (lower variance) and less biased model predictions throughout the river network. Moreover, predictions of water-balance components are reported according to probabilistic metrics (e.g., percentiles, prediction intervals) that include both parameter and model uncertainties. These improvements in predictions of streamflow dynamics can inform the development of more accurate predictions of spatial and temporal variations in biogeochemical stores and fluxes (e.g., nutrients and carbon) in watersheds.

Calibrating the sqHIMMELI v1.0 wetland methane emission model with hierarchical modeling and adaptive MCMC

NASA Astrophysics Data System (ADS)

Susiluoto, Jouni; Raivonen, Maarit; Backman, Leif; Laine, Marko; Makela, Jarmo; Peltola, Olli; Vesala, Timo; Aalto, Tuula

2018-03-01

Estimating methane (CH4) emissions from natural wetlands is complex, and the estimates contain large uncertainties. The models used for the task are typically heavily parameterized and the parameter values are not well known. In this study, we perform a Bayesian model calibration for a new wetland CH4 emission model to improve the quality of the predictions and to understand the limitations of such models.The detailed process model that we analyze contains descriptions for CH4 production from anaerobic respiration, CH4 oxidation, and gas transportation by diffusion, ebullition, and the aerenchyma cells of vascular plants. The processes are controlled by several tunable parameters. We use a hierarchical statistical model to describe the parameters and obtain the posterior distributions of the parameters and uncertainties in the processes with adaptive Markov chain Monte Carlo (MCMC), importance resampling, and time series analysis techniques. For the estimation, the analysis utilizes measurement data from the Siikaneva flux measurement site in southern Finland. The uncertainties related to the parameters and the modeled processes are described quantitatively. At the process level, the flux measurement data are able to constrain the CH4 production processes, methane oxidation, and the different gas transport processes. The posterior covariance structures explain how the parameters and the processes are related. Additionally, the flux and flux component uncertainties are analyzed both at the annual and daily levels. The parameter posterior densities obtained provide information regarding importance of the different processes, which is also useful for development of wetland methane emission models other than the square root HelsinkI Model of MEthane buiLd-up and emIssion for peatlands (sqHIMMELI). The hierarchical modeling allows us to assess the effects of some of the parameters on an annual basis. The results of the calibration and the cross validation suggest that the early spring net primary production could be used to predict parameters affecting the annual methane production. Even though the calibration is specific to the Siikaneva site, the hierarchical modeling approach is well suited for larger-scale studies and the results of the estimation pave way for a regional or global-scale Bayesian calibration of wetland emission models.

Analysis of dengue fever risk using geostatistics model in bone regency

NASA Astrophysics Data System (ADS)

Amran, Stang, Mallongi, Anwar

2017-03-01

This research aim is to analysis of dengue fever risk based on Geostatistics model in Bone Regency. Risk levels of dengue fever are denoted by parameter of Binomial distribution. Effect of temperature, rainfalls, elevation, and larvae abundance are investigated through Geostatistics model. Bayesian hierarchical method is used in estimation process. Using dengue fever data in eleven locations this research shows that temperature and rainfall have significant effect of dengue fever risk in Bone regency.

A hybrid Bayesian hierarchical model combining cohort and case-control studies for meta-analysis of diagnostic tests: Accounting for partial verification bias.

PubMed

Ma, Xiaoye; Chen, Yong; Cole, Stephen R; Chu, Haitao

2016-12-01

To account for between-study heterogeneity in meta-analysis of diagnostic accuracy studies, bivariate random effects models have been recommended to jointly model the sensitivities and specificities. As study design and population vary, the definition of disease status or severity could differ across studies. Consequently, sensitivity and specificity may be correlated with disease prevalence. To account for this dependence, a trivariate random effects model had been proposed. However, the proposed approach can only include cohort studies with information estimating study-specific disease prevalence. In addition, some diagnostic accuracy studies only select a subset of samples to be verified by the reference test. It is known that ignoring unverified subjects may lead to partial verification bias in the estimation of prevalence, sensitivities, and specificities in a single study. However, the impact of this bias on a meta-analysis has not been investigated. In this paper, we propose a novel hybrid Bayesian hierarchical model combining cohort and case-control studies and correcting partial verification bias at the same time. We investigate the performance of the proposed methods through a set of simulation studies. Two case studies on assessing the diagnostic accuracy of gadolinium-enhanced magnetic resonance imaging in detecting lymph node metastases and of adrenal fluorine-18 fluorodeoxyglucose positron emission tomography in characterizing adrenal masses are presented. © The Author(s) 2014.

A Hybrid Bayesian Hierarchical Model Combining Cohort and Case-control Studies for Meta-analysis of Diagnostic Tests: Accounting for Partial Verification Bias

PubMed Central

Ma, Xiaoye; Chen, Yong; Cole, Stephen R.; Chu, Haitao

2014-01-01

To account for between-study heterogeneity in meta-analysis of diagnostic accuracy studies, bivariate random effects models have been recommended to jointly model the sensitivities and specificities. As study design and population vary, the definition of disease status or severity could differ across studies. Consequently, sensitivity and specificity may be correlated with disease prevalence. To account for this dependence, a trivariate random effects model had been proposed. However, the proposed approach can only include cohort studies with information estimating study-specific disease prevalence. In addition, some diagnostic accuracy studies only select a subset of samples to be verified by the reference test. It is known that ignoring unverified subjects may lead to partial verification bias in the estimation of prevalence, sensitivities and specificities in a single study. However, the impact of this bias on a meta-analysis has not been investigated. In this paper, we propose a novel hybrid Bayesian hierarchical model combining cohort and case-control studies and correcting partial verification bias at the same time. We investigate the performance of the proposed methods through a set of simulation studies. Two case studies on assessing the diagnostic accuracy of gadolinium-enhanced magnetic resonance imaging in detecting lymph node metastases and of adrenal fluorine-18 fluorodeoxyglucose positron emission tomography in characterizing adrenal masses are presented. PMID:24862512

Bayesian Hierarchical Random Effects Models in Forensic Science.

PubMed

Aitken, Colin G G

2018-01-01

Statistical modeling of the evaluation of evidence with the use of the likelihood ratio has a long history. It dates from the Dreyfus case at the end of the nineteenth century through the work at Bletchley Park in the Second World War to the present day. The development received a significant boost in 1977 with a seminal work by Dennis Lindley which introduced a Bayesian hierarchical random effects model for the evaluation of evidence with an example of refractive index measurements on fragments of glass. Many models have been developed since then. The methods have now been sufficiently well-developed and have become so widespread that it is timely to try and provide a software package to assist in their implementation. With that in mind, a project (SAILR: Software for the Analysis and Implementation of Likelihood Ratios) was funded by the European Network of Forensic Science Institutes through their Monopoly programme to develop a software package for use by forensic scientists world-wide that would assist in the statistical analysis and implementation of the approach based on likelihood ratios. It is the purpose of this document to provide a short review of a small part of this history. The review also provides a background, or landscape, for the development of some of the models within the SAILR package and references to SAILR as made as appropriate.

A species-level phylogeny of all extant and late Quaternary extinct mammals using a novel heuristic-hierarchical Bayesian approach.

PubMed

Faurby, Søren; Svenning, Jens-Christian

2015-03-01

Across large clades, two problems are generally encountered in the estimation of species-level phylogenies: (a) the number of taxa involved is generally so high that computation-intensive approaches cannot readily be utilized and (b) even for clades that have received intense study (e.g., mammals), attention has been centered on relatively few selected species, and most taxa must therefore be positioned on the basis of very limited genetic data. Here, we describe a new heuristic-hierarchical Bayesian approach and use it to construct a species-level phylogeny for all extant and late Quaternary extinct mammals. In this approach, species with large quantities of genetic data are placed nearly freely in the mammalian phylogeny according to these data, whereas the placement of species with lower quantities of data is performed with steadily stricter restrictions for decreasing data quantities. The advantages of the proposed method include (a) an improved ability to incorporate phylogenetic uncertainty in downstream analyses based on the resulting phylogeny, (b) a reduced potential for long-branch attraction or other types of errors that place low-data taxa far from their true position, while maintaining minimal restrictions for better-studied taxa, and (c) likely improved placement of low-data taxa due to the use of closer outgroups. Copyright © 2014 Elsevier Inc. All rights reserved.

Merging information from multi-model flood projections in a hierarchical Bayesian framework

NASA Astrophysics Data System (ADS)

Le Vine, Nataliya

2016-04-01

Multi-model ensembles are becoming widely accepted for flood frequency change analysis. The use of multiple models results in large uncertainty around estimates of flood magnitudes, due to both uncertainty in model selection and natural variability of river flow. The challenge is therefore to extract the most meaningful signal from the multi-model predictions, accounting for both model quality and uncertainties in individual model estimates. The study demonstrates the potential of a recently proposed hierarchical Bayesian approach to combine information from multiple models. The approach facilitates explicit treatment of shared multi-model discrepancy as well as the probabilistic nature of the flood estimates, by treating the available models as a sample from a hypothetical complete (but unobserved) set of models. The advantages of the approach are: 1) to insure an adequate 'baseline' conditions with which to compare future changes; 2) to reduce flood estimate uncertainty; 3) to maximize use of statistical information in circumstances where multiple weak predictions individually lack power, but collectively provide meaningful information; 4) to adjust multi-model consistency criteria when model biases are large; and 5) to explicitly consider the influence of the (model performance) stationarity assumption. Moreover, the analysis indicates that reducing shared model discrepancy is the key to further reduction of uncertainty in the flood frequency analysis. The findings are of value regarding how conclusions about changing exposure to flooding are drawn, and to flood frequency change attribution studies.

A Bayesian hierarchical model with novel prior specifications for estimating HIV testing rates

PubMed Central

An, Qian; Kang, Jian; Song, Ruiguang; Hall, H. Irene

2016-01-01

Human immunodeficiency virus (HIV) infection is a severe infectious disease actively spreading globally, and acquired immunodeficiency syndrome (AIDS) is an advanced stage of HIV infection. The HIV testing rate, that is, the probability that an AIDS-free HIV infected person seeks a test for HIV during a particular time interval, given no previous positive test has been obtained prior to the start of the time, is an important parameter for public health. In this paper, we propose a Bayesian hierarchical model with two levels of hierarchy to estimate the HIV testing rate using annual AIDS and AIDS-free HIV diagnoses data. At level one, we model the latent number of HIV infections for each year using a Poisson distribution with the intensity parameter representing the HIV incidence rate. At level two, the annual numbers of AIDS and AIDS-free HIV diagnosed cases and all undiagnosed cases stratified by the HIV infections at different years are modeled using a multinomial distribution with parameters including the HIV testing rate. We propose a new class of priors for the HIV incidence rate and HIV testing rate taking into account the temporal dependence of these parameters to improve the estimation accuracy. We develop an efficient posterior computation algorithm based on the adaptive rejection metropolis sampling technique. We demonstrate our model using simulation studies and the analysis of the national HIV surveillance data in the USA. PMID:26567891

Constraint of soil moisture on CO2 efflux from tundra lichen, moss, and tussock in Council, Alaska using a hierarchical Bayesian model

NASA Astrophysics Data System (ADS)

Kim, Y.; Nishina, K.; Chae, N.; Park, S.; Yoon, Y.; Lee, B.

2014-04-01

The tundra ecosystem is quite vulnerable to drastic climate change in the Arctic, and the quantification of carbon dynamics is of significant importance in response to thawing permafrost, changes in the snow-covered period and snow and shrub community extent, and the decline of sea ice in the Arctic. Here, CO2 efflux measurements using a manual chamber system within a 40 m × 40 m (5 m interval; 81 total points) plot were conducted in dominant tundra vegetation on the Seward Peninsula of Alaska, during the growing seasons of 2011 and 2012, for the assessment of the driving parameters of CO2 efflux. We applied a hierarchical Bayesian (HB) model - which is a function of soil temperature, soil moisture, vegetation type and thaw depth - to quantify the effect of environmental parameters on CO2 efflux, and to estimate growing season CO2 emission. Our results showed that average CO2 efflux in 2011 is 1.4-fold higher than in 2012, resulting from the distinct difference in soil moisture between the two years. Tussock-dominated CO2 efflux is 1.4 to 2.3 times higher than those measured in lichen and moss communities, reflecting tussock as a significant CO2 source in the Arctic, with wide area distribution on a circumpolar scale. CO2 efflux followed soil temperature nearly exponentially from both the observed data and the posterior medians of the HB model. This reveals soil temperature as the most important parameter in regulating CO2 efflux, rather than soil moisture and thaw depth. Obvious changes in soil moisture during the growing seasons of 2011 and 2012 resulted in an explicit difference in CO2 efflux - 742 and 539 g CO2 m-2 period-1 in 2011 and 2012, respectively, suggesting that the 2012 CO2 emission rate was constrained by 27% (95% credible interval: 17-36%) compared to 2011, due to higher soil moisture from severe rain. Estimated growing season CO2 emission rate ranged from 0.86 Mg CO2 period-1 in 2012 to 1.2 Mg CO2 period-1 in 2011 within a 40 m × 40 m plot, corresponding to 86% and 80% of the annual CO2 emission rates within the Alaska western tundra ecosystem. Therefore, the HB model can be readily applied to observed CO2 efflux, as it demands only four environmental parameters and can also be effective for quantitatively assessing the driving parameters of CO2 efflux.

Bayesian estimation and use of high-throughput remote sensing indices for quantitative genetic analyses of leaf growth.

PubMed

Baker, Robert L; Leong, Wen Fung; An, Nan; Brock, Marcus T; Rubin, Matthew J; Welch, Stephen; Weinig, Cynthia

2018-02-01

We develop Bayesian function-valued trait models that mathematically isolate genetic mechanisms underlying leaf growth trajectories by factoring out genotype-specific differences in photosynthesis. Remote sensing data can be used instead of leaf-level physiological measurements. Characterizing the genetic basis of traits that vary during ontogeny and affect plant performance is a major goal in evolutionary biology and agronomy. Describing genetic programs that specifically regulate morphological traits can be complicated by genotypic differences in physiological traits. We describe the growth trajectories of leaves using novel Bayesian function-valued trait (FVT) modeling approaches in Brassica rapa recombinant inbred lines raised in heterogeneous field settings. While frequentist approaches estimate parameter values by treating each experimental replicate discretely, Bayesian models can utilize information in the global dataset, potentially leading to more robust trait estimation. We illustrate this principle by estimating growth asymptotes in the face of missing data and comparing heritabilities of growth trajectory parameters estimated by Bayesian and frequentist approaches. Using pseudo-Bayes factors, we compare the performance of an initial Bayesian logistic growth model and a model that incorporates carbon assimilation (A max ) as a cofactor, thus statistically accounting for genotypic differences in carbon resources. We further evaluate two remotely sensed spectroradiometric indices, photochemical reflectance (pri2) and MERIS Terrestrial Chlorophyll Index (mtci) as covariates in lieu of A max , because these two indices were genetically correlated with A max across years and treatments yet allow much higher throughput compared to direct leaf-level gas-exchange measurements. For leaf lengths in uncrowded settings, including A max improves model fit over the initial model. The mtci and pri2 indices also outperform direct A max measurements. Of particular importance for evolutionary biologists and plant breeders, hierarchical Bayesian models estimating FVT parameters improve heritabilities compared to frequentist approaches.

BiomeNet: A Bayesian Model for Inference of Metabolic Divergence among Microbial Communities

PubMed Central

Chipman, Hugh; Gu, Hong; Bielawski, Joseph P.

2014-01-01

Metagenomics yields enormous numbers of microbial sequences that can be assigned a metabolic function. Using such data to infer community-level metabolic divergence is hindered by the lack of a suitable statistical framework. Here, we describe a novel hierarchical Bayesian model, called BiomeNet (Bayesian inference of metabolic networks), for inferring differential prevalence of metabolic subnetworks among microbial communities. To infer the structure of community-level metabolic interactions, BiomeNet applies a mixed-membership modelling framework to enzyme abundance information. The basic idea is that the mixture components of the model (metabolic reactions, subnetworks, and networks) are shared across all groups (microbiome samples), but the mixture proportions vary from group to group. Through this framework, the model can capture nested structures within the data. BiomeNet is unique in modeling each metagenome sample as a mixture of complex metabolic systems (metabosystems). The metabosystems are composed of mixtures of tightly connected metabolic subnetworks. BiomeNet differs from other unsupervised methods by allowing researchers to discriminate groups of samples through the metabolic patterns it discovers in the data, and by providing a framework for interpreting them. We describe a collapsed Gibbs sampler for inference of the mixture weights under BiomeNet, and we use simulation to validate the inference algorithm. Application of BiomeNet to human gut metagenomes revealed a metabosystem with greater prevalence among inflammatory bowel disease (IBD) patients. Based on the discriminatory subnetworks for this metabosystem, we inferred that the community is likely to be closely associated with the human gut epithelium, resistant to dietary interventions, and interfere with human uptake of an antioxidant connected to IBD. Because this metabosystem has a greater capacity to exploit host-associated glycans, we speculate that IBD-associated communities might arise from opportunist growth of bacteria that can circumvent the host's nutrient-based mechanism for bacterial partner selection. PMID:25412107

Comparing Bayesian stable isotope mixing models: Which tools are best for sediments?

NASA Astrophysics Data System (ADS)

Morris, David; Macko, Stephen

2016-04-01

Bayesian stable isotope mixing models have received much attention as a means of coping with multiple sources and uncertainty in isotope ecology (e.g. Phillips et al., 2014), enabling the probabilistic determination of the contributions made by each food source to the total diet of the organism in question. We have applied these techniques to marine sediments for the first time. The sediments of the Chukchi Sea and Beaufort Sea offer an opportunity to utilize these models for organic geochemistry, as there are three likely sources of organic carbon; pelagic phytoplankton, sea ice algae and terrestrial material from rivers and coastal erosion, as well as considerable variation in the marine δ13C values. Bayesian mixing models using bulk δ13C and δ15N data from Shelf Basin Interaction samples allow for the probabilistic determination of the contributions made by each of the sources to the organic carbon budget, and can be compared with existing source contribution estimates based upon biomarker models (e.g. Belicka & Harvey, 2009, Faux, Belicka, & Rodger Harvey, 2011). The δ13C of this preserved material varied from -22.1 to -16.7‰ (mean -19.4±1.3‰), while δ15N varied from 4.1 to 7.6‰ (mean 5.7±1.1‰). Using the SIAR model, we found that water column productivity was the source of between 50 and 70% of the organic carbon buried in this portion of the western Arctic with the remainder mainly supplied by sea ice algal productivity (25-35%) and terrestrial inputs (15%). With many mixing models now available, this study will compare SIAR with MixSIAR and the new FRUITS model. Monte Carlo modeling of the mixing polygon will be used to validate the models, and hierarchical models will be utilised to glean more information from the data set.

Bayesian Learning and the Psychology of Rule Induction

ERIC Educational Resources Information Center

Endress, Ansgar D.

2013-01-01

In recent years, Bayesian learning models have been applied to an increasing variety of domains. While such models have been criticized on theoretical grounds, the underlying assumptions and predictions are rarely made concrete and tested experimentally. Here, I use Frank and Tenenbaum's (2011) Bayesian model of rule-learning as a case study to…

Properties of the Bayesian Knowledge Tracing Model

ERIC Educational Resources Information Center

van de Sande, Brett

2013-01-01

Bayesian Knowledge Tracing is used very widely to model student learning. It comes in two different forms: The first form is the Bayesian Knowledge Tracing "hidden Markov model" which predicts the probability of correct application of a skill as a function of the number of previous opportunities to apply that skill and the model…

Bayesian Item Selection in Constrained Adaptive Testing Using Shadow Tests

ERIC Educational Resources Information Center

Veldkamp, Bernard P.

2010-01-01

Application of Bayesian item selection criteria in computerized adaptive testing might result in improvement of bias and MSE of the ability estimates. The question remains how to apply Bayesian item selection criteria in the context of constrained adaptive testing, where large numbers of specifications have to be taken into account in the item…

Development of uncertainty-based work injury model using Bayesian structural equation modelling.

PubMed

Chatterjee, Snehamoy

2014-01-01

This paper proposed a Bayesian method-based structural equation model (SEM) of miners' work injury for an underground coal mine in India. The environmental and behavioural variables for work injury were identified and causal relationships were developed. For Bayesian modelling, prior distributions of SEM parameters are necessary to develop the model. In this paper, two approaches were adopted to obtain prior distribution for factor loading parameters and structural parameters of SEM. In the first approach, the prior distributions were considered as a fixed distribution function with specific parameter values, whereas, in the second approach, prior distributions of the parameters were generated from experts' opinions. The posterior distributions of these parameters were obtained by applying Bayesian rule. The Markov Chain Monte Carlo sampling in the form Gibbs sampling was applied for sampling from the posterior distribution. The results revealed that all coefficients of structural and measurement model parameters are statistically significant in experts' opinion-based priors, whereas, two coefficients are not statistically significant when fixed prior-based distributions are applied. The error statistics reveals that Bayesian structural model provides reasonably good fit of work injury with high coefficient of determination (0.91) and less mean squared error as compared to traditional SEM.

Prediction of community prevalence of human onchocerciasis in the Amazonian onchocerciasis focus: Bayesian approach.

PubMed Central

Carabin, Hélène; Escalona, Marisela; Marshall, Clare; Vivas-Martínez, Sarai; Botto, Carlos; Joseph, Lawrence; Basáñez, María-Gloria

2003-01-01

OBJECTIVE: To develop a Bayesian hierarchical model for human onchocerciasis with which to explore the factors that influence prevalence of microfilariae in the Amazonian focus of onchocerciasis and predict the probability of any community being at least mesoendemic (>20% prevalence of microfilariae), and thus in need of priority ivermectin treatment. METHODS: Models were developed with data from 732 individuals aged > or =15 years who lived in 29 Yanomami communities along four rivers of the south Venezuelan Orinoco basin. The models' abilities to predict prevalences of microfilariae in communities were compared. The deviance information criterion, Bayesian P-values, and residual values were used to select the best model with an approximate cross-validation procedure. FINDINGS: A three-level model that acknowledged clustering of infection within communities performed best, with host age and sex included at the individual level, a river-dependent altitude effect at the community level, and additional clustering of communities along rivers. This model correctly classified 25/29 (86%) villages with respect to their need for priority ivermectin treatment. CONCLUSION: Bayesian methods are a flexible and useful approach for public health research and control planning. Our model acknowledges the clustering of infection within communities, allows investigation of links between individual- or community-specific characteristics and infection, incorporates additional uncertainty due to missing covariate data, and informs policy decisions by predicting the probability that a new community is at least mesoendemic. PMID:12973640

Prediction of community prevalence of human onchocerciasis in the Amazonian onchocerciasis focus: Bayesian approach.

PubMed

Carabin, Hélène; Escalona, Marisela; Marshall, Clare; Vivas-Martínez, Sarai; Botto, Carlos; Joseph, Lawrence; Basáñez, María-Gloria

2003-01-01

To develop a Bayesian hierarchical model for human onchocerciasis with which to explore the factors that influence prevalence of microfilariae in the Amazonian focus of onchocerciasis and predict the probability of any community being at least mesoendemic (>20% prevalence of microfilariae), and thus in need of priority ivermectin treatment. Models were developed with data from 732 individuals aged > or =15 years who lived in 29 Yanomami communities along four rivers of the south Venezuelan Orinoco basin. The models' abilities to predict prevalences of microfilariae in communities were compared. The deviance information criterion, Bayesian P-values, and residual values were used to select the best model with an approximate cross-validation procedure. A three-level model that acknowledged clustering of infection within communities performed best, with host age and sex included at the individual level, a river-dependent altitude effect at the community level, and additional clustering of communities along rivers. This model correctly classified 25/29 (86%) villages with respect to their need for priority ivermectin treatment. Bayesian methods are a flexible and useful approach for public health research and control planning. Our model acknowledges the clustering of infection within communities, allows investigation of links between individual- or community-specific characteristics and infection, incorporates additional uncertainty due to missing covariate data, and informs policy decisions by predicting the probability that a new community is at least mesoendemic.

Evaluating impacts using a BACI design, ratios, and a Bayesian approach with a focus on restoration.

PubMed

Conner, Mary M; Saunders, W Carl; Bouwes, Nicolaas; Jordan, Chris

2015-10-01

Before-after-control-impact (BACI) designs are an effective method to evaluate natural and human-induced perturbations on ecological variables when treatment sites cannot be randomly chosen. While effect sizes of interest can be tested with frequentist methods, using Bayesian Markov chain Monte Carlo (MCMC) sampling methods, probabilities of effect sizes, such as a ≥20 % increase in density after restoration, can be directly estimated. Although BACI and Bayesian methods are used widely for assessing natural and human-induced impacts for field experiments, the application of hierarchal Bayesian modeling with MCMC sampling to BACI designs is less common. Here, we combine these approaches and extend the typical presentation of results with an easy to interpret ratio, which provides an answer to the main study question-"How much impact did a management action or natural perturbation have?" As an example of this approach, we evaluate the impact of a restoration project, which implemented beaver dam analogs, on survival and density of juvenile steelhead. Results indicated the probabilities of a ≥30 % increase were high for survival and density after the dams were installed, 0.88 and 0.99, respectively, while probabilities for a higher increase of ≥50 % were variable, 0.17 and 0.82, respectively. This approach demonstrates a useful extension of Bayesian methods that can easily be generalized to other study designs from simple (e.g., single factor ANOVA, paired t test) to more complicated block designs (e.g., crossover, split-plot). This approach is valuable for estimating the probabilities of restoration impacts or other management actions.

A Simulation Study of Methods for Selecting Subgroup-Specific Doses in Phase I Trials

PubMed Central

Morita, Satoshi; Thall, Peter F.; Takeda, Kentaro

2016-01-01

Summary Patient heterogeneity may complicate dose-finding in phase I clinical trials if the dose-toxicity curves differ between subgroups. Conducting separate trials within subgroups may lead to infeasibly small sample sizes in subgroups having low prevalence. Alternatively, it is not obvious how to conduct a single trial while accounting for heterogeneity. To address this problem, we consider a generalization of the continual reassessment method (O’Quigley, et al., 1990) based on a hierarchical Bayesian dose-toxicity model that borrows strength between subgroups under the assumption that the subgroups are exchangeable. We evaluate a design using this model that includes subgroup-specific dose selection and safety rules. A simulation study is presented that includes comparison of this method to three alternative approaches, based on non-hierarchical models, that make different types of assumptions about within-subgroup dose-toxicity curves. The simulations show that the hierarchical model-based method is recommended in settings where the dose-toxicity curves are exchangeable between subgroups. We present practical guidelines for application, and provide computer programs for trial simulation and conduct. PMID:28111916

Discriminative Hierarchical K-Means Tree for Large-Scale Image Classification.

PubMed

Chen, Shizhi; Yang, Xiaodong; Tian, Yingli

2015-09-01

A key challenge in large-scale image classification is how to achieve efficiency in terms of both computation and memory without compromising classification accuracy. The learning-based classifiers achieve the state-of-the-art accuracies, but have been criticized for the computational complexity that grows linearly with the number of classes. The nonparametric nearest neighbor (NN)-based classifiers naturally handle large numbers of categories, but incur prohibitively expensive computation and memory costs. In this brief, we present a novel classification scheme, i.e., discriminative hierarchical K-means tree (D-HKTree), which combines the advantages of both learning-based and NN-based classifiers. The complexity of the D-HKTree only grows sublinearly with the number of categories, which is much better than the recent hierarchical support vector machines-based methods. The memory requirement is the order of magnitude less than the recent Naïve Bayesian NN-based approaches. The proposed D-HKTree classification scheme is evaluated on several challenging benchmark databases and achieves the state-of-the-art accuracies, while with significantly lower computation cost and memory requirement.

Improved Model Fitting for the Empirical Green's Function Approach Using Hierarchical Models

NASA Astrophysics Data System (ADS)

Van Houtte, Chris; Denolle, Marine

2018-04-01

Stress drops calculated from source spectral studies currently show larger variability than what is implied by empirical ground motion models. One of the potential origins of the inflated variability is the simplified model-fitting techniques used in most source spectral studies. This study examines a variety of model-fitting methods and shows that the choice of method can explain some of the discrepancy. The preferred method is Bayesian hierarchical modeling, which can reduce bias, better quantify uncertainties, and allow additional effects to be resolved. Two case study earthquakes are examined, the 2016 MW7.1 Kumamoto, Japan earthquake and a MW5.3 aftershock of the 2016 MW7.8 Kaikōura earthquake. By using hierarchical models, the variation of the corner frequency, fc, and the falloff rate, n, across the focal sphere can be retrieved without overfitting the data. Other methods commonly used to calculate corner frequencies may give substantial biases. In particular, if fc was calculated for the Kumamoto earthquake using an ω-square model, the obtained fc could be twice as large as a realistic value.

Stability and structural properties of gene regulation networks with coregulation rules.

PubMed

Warrell, Jonathan; Mhlanga, Musa

2017-05-07

Coregulation of the expression of groups of genes has been extensively demonstrated empirically in bacterial and eukaryotic systems. Such coregulation can arise through the use of shared regulatory motifs, which allow the coordinated expression of modules (and module groups) of functionally related genes across the genome. Coregulation can also arise through the physical association of multi-gene complexes through chromosomal looping, which are then transcribed together. We present a general formalism for modeling coregulation rules in the framework of Random Boolean Networks (RBN), and develop specific models for transcription factor networks with modular structure (including module groups, and multi-input modules (MIM) with autoregulation) and multi-gene complexes (including hierarchical differentiation between multi-gene complex members). We develop a mean-field approach to analyse the dynamical stability of large networks incorporating coregulation, and show that autoregulated MIM and hierarchical gene-complex models can achieve greater stability than networks without coregulation whose rules have matching activation frequency. We provide further analysis of the stability of small networks of both kinds through simulations. We also characterize several general properties of the transients and attractors in the hierarchical coregulation model, and show using simulations that the steady-state distribution factorizes hierarchically as a Bayesian network in a Markov Jump Process analogue of the RBN model. Copyright © 2017. Published by Elsevier Ltd.

A hierarchical nest survival model integrating incomplete temporally varying covariates

PubMed Central

Converse, Sarah J; Royle, J Andrew; Adler, Peter H; Urbanek, Richard P; Barzen, Jeb A

2013-01-01

Nest success is a critical determinant of the dynamics of avian populations, and nest survival modeling has played a key role in advancing avian ecology and management. Beginning with the development of daily nest survival models, and proceeding through subsequent extensions, the capacity for modeling the effects of hypothesized factors on nest survival has expanded greatly. We extend nest survival models further by introducing an approach to deal with incompletely observed, temporally varying covariates using a hierarchical model. Hierarchical modeling offers a way to separate process and observational components of demographic models to obtain estimates of the parameters of primary interest, and to evaluate structural effects of ecological and management interest. We built a hierarchical model for daily nest survival to analyze nest data from reintroduced whooping cranes (Grus americana) in the Eastern Migratory Population. This reintroduction effort has been beset by poor reproduction, apparently due primarily to nest abandonment by breeding birds. We used the model to assess support for the hypothesis that nest abandonment is caused by harassment from biting insects. We obtained indices of blood-feeding insect populations based on the spatially interpolated counts of insects captured in carbon dioxide traps. However, insect trapping was not conducted daily, and so we had incomplete information on a temporally variable covariate of interest. We therefore supplemented our nest survival model with a parallel model for estimating the values of the missing insect covariates. We used Bayesian model selection to identify the best predictors of daily nest survival. Our results suggest that the black fly Simulium annulus may be negatively affecting nest survival of reintroduced whooping cranes, with decreasing nest survival as abundance of S. annulus increases. The modeling framework we have developed will be applied in the future to a larger data set to evaluate the biting-insect hypothesis and other hypotheses for nesting failure in this reintroduced population; resulting inferences will support ongoing efforts to manage this population via an adaptive management approach. Wider application of our approach offers promise for modeling the effects of other temporally varying, but imperfectly observed covariates on nest survival, including the possibility of modeling temporally varying covariates collected from incubating adults. PMID:24340185

A hierarchical nest survival model integrating incomplete temporally varying covariates

USGS Publications Warehouse

Converse, Sarah J.; Royle, J. Andrew; Adler, Peter H.; Urbanek, Richard P.; Barzan, Jeb A.

2013-01-01

Nest success is a critical determinant of the dynamics of avian populations, and nest survival modeling has played a key role in advancing avian ecology and management. Beginning with the development of daily nest survival models, and proceeding through subsequent extensions, the capacity for modeling the effects of hypothesized factors on nest survival has expanded greatly. We extend nest survival models further by introducing an approach to deal with incompletely observed, temporally varying covariates using a hierarchical model. Hierarchical modeling offers a way to separate process and observational components of demographic models to obtain estimates of the parameters of primary interest, and to evaluate structural effects of ecological and management interest. We built a hierarchical model for daily nest survival to analyze nest data from reintroduced whooping cranes (Grus americana) in the Eastern Migratory Population. This reintroduction effort has been beset by poor reproduction, apparently due primarily to nest abandonment by breeding birds. We used the model to assess support for the hypothesis that nest abandonment is caused by harassment from biting insects. We obtained indices of blood-feeding insect populations based on the spatially interpolated counts of insects captured in carbon dioxide traps. However, insect trapping was not conducted daily, and so we had incomplete information on a temporally variable covariate of interest. We therefore supplemented our nest survival model with a parallel model for estimating the values of the missing insect covariates. We used Bayesian model selection to identify the best predictors of daily nest survival. Our results suggest that the black fly Simulium annulus may be negatively affecting nest survival of reintroduced whooping cranes, with decreasing nest survival as abundance of S. annulus increases. The modeling framework we have developed will be applied in the future to a larger data set to evaluate the biting-insect hypothesis and other hypotheses for nesting failure in this reintroduced population; resulting inferences will support ongoing efforts to manage this population via an adaptive management approach. Wider application of our approach offers promise for modeling the effects of other temporally varying, but imperfectly observed covariates on nest survival, including the possibility of modeling temporally varying covariates collected from incubating adults.

Trans-dimensional inversion of microtremor array dispersion data with hierarchical autoregressive error models

NASA Astrophysics Data System (ADS)

Dettmer, Jan; Molnar, Sheri; Steininger, Gavin; Dosso, Stan E.; Cassidy, John F.

2012-02-01

This paper applies a general trans-dimensional Bayesian inference methodology and hierarchical autoregressive data-error models to the inversion of microtremor array dispersion data for shear wave velocity (vs) structure. This approach accounts for the limited knowledge of the optimal earth model parametrization (e.g. the number of layers in the vs profile) and of the data-error statistics in the resulting vs parameter uncertainty estimates. The assumed earth model parametrization influences estimates of parameter values and uncertainties due to different parametrizations leading to different ranges of data predictions. The support of the data for a particular model is often non-unique and several parametrizations may be supported. A trans-dimensional formulation accounts for this non-uniqueness by including a model-indexing parameter as an unknown so that groups of models (identified by the indexing parameter) are considered in the results. The earth model is parametrized in terms of a partition model with interfaces given over a depth-range of interest. In this work, the number of interfaces (layers) in the partition model represents the trans-dimensional model indexing. In addition, serial data-error correlations are addressed by augmenting the geophysical forward model with a hierarchical autoregressive error model that can account for a wide range of error processes with a small number of parameters. Hence, the limited knowledge about the true statistical distribution of data errors is also accounted for in the earth model parameter estimates, resulting in more realistic uncertainties and parameter values. Hierarchical autoregressive error models do not rely on point estimates of the model vector to estimate data-error statistics, and have no requirement for computing the inverse or determinant of a data-error covariance matrix. This approach is particularly useful for trans-dimensional inverse problems, as point estimates may not be representative of the state space that spans multiple subspaces of different dimensionalities. The order of the autoregressive process required to fit the data is determined here by posterior residual-sample examination and statistical tests. Inference for earth model parameters is carried out on the trans-dimensional posterior probability distribution by considering ensembles of parameter vectors. In particular, vs uncertainty estimates are obtained by marginalizing the trans-dimensional posterior distribution in terms of vs-profile marginal distributions. The methodology is applied to microtremor array dispersion data collected at two sites with significantly different geology in British Columbia, Canada. At both sites, results show excellent agreement with estimates from invasive measurements.

A Bayesian approach to landscape ecological risk assessment applied to the upper Grande Ronde watershed, Oregon

Treesearch

Kimberley K. Ayre; Wayne G. Landis

2012-01-01

We present a Bayesian network model based on the ecological risk assessment framework to evaluate potential impacts to habitats and resources resulting from wildfire, grazing, forest management activities, and insect outbreaks in a forested landscape in northeastern Oregon. The Bayesian network structure consisted of three tiers of nodes: landscape disturbances,...

Learning In networks

NASA Technical Reports Server (NTRS)

Buntine, Wray L.

1995-01-01

Intelligent systems require software incorporating probabilistic reasoning, and often times learning. Networks provide a framework and methodology for creating this kind of software. This paper introduces network models based on chain graphs with deterministic nodes. Chain graphs are defined as a hierarchical combination of Bayesian and Markov networks. To model learning, plates on chain graphs are introduced to model independent samples. The paper concludes by discussing various operations that can be performed on chain graphs with plates as a simplification process or to generate learning algorithms.

Bayesian Scalar-on-Image Regression with Application to Association Between Intracranial DTI and Cognitive Outcomes

PubMed Central

Huang, Lei; Goldsmith, Jeff; Reiss, Philip T.; Reich, Daniel S.; Crainiceanu, Ciprian M.

2013-01-01

Diffusion tensor imaging (DTI) measures water diffusion within white matter, allowing for in vivo quantification of brain pathways. These pathways often subserve specific functions, and impairment of those functions is often associated with imaging abnormalities. As a method for predicting clinical disability from DTI images, we propose a hierarchical Bayesian “scalar-on-image” regression procedure. Our procedure introduces a latent binary map that estimates the locations of predictive voxels and penalizes the magnitude of effect sizes in these voxels, thereby resolving the ill-posed nature of the problem. By inducing a spatial prior structure, the procedure yields a sparse association map that also maintains spatial continuity of predictive regions. The method is demonstrated on a simulation study and on a study of association between fractional anisotropy and cognitive disability in a cross-sectional sample of 135 multiple sclerosis patients. PMID:23792220

None of the above: A Bayesian account of the detection of novel categories.

PubMed

Navarro, Daniel J; Kemp, Charles

2017-10-01

Every time we encounter a new object, action, or event, there is some chance that we will need to assign it to a novel category. We describe and evaluate a class of probabilistic models that detect when an object belongs to a category that has not previously been encountered. The models incorporate a prior distribution that is influenced by the distribution of previous objects among categories, and we present 2 experiments that demonstrate that people are also sensitive to this distributional information. Two additional experiments confirm that distributional information is combined with similarity when both sources of information are available. We compare our approach to previous models of unsupervised categorization and to several heuristic-based models, and find that a hierarchical Bayesian approach provides the best account of our data. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

On selecting a prior for the precision parameter of Dirichlet process mixture models

USGS Publications Warehouse

Dorazio, R.M.

2009-01-01

In hierarchical mixture models the Dirichlet process is used to specify latent patterns of heterogeneity, particularly when the distribution of latent parameters is thought to be clustered (multimodal). The parameters of a Dirichlet process include a precision parameter ?? and a base probability measure G0. In problems where ?? is unknown and must be estimated, inferences about the level of clustering can be sensitive to the choice of prior assumed for ??. In this paper an approach is developed for computing a prior for the precision parameter ?? that can be used in the presence or absence of prior information about the level of clustering. This approach is illustrated in an analysis of counts of stream fishes. The results of this fully Bayesian analysis are compared with an empirical Bayes analysis of the same data and with a Bayesian analysis based on an alternative commonly used prior.

Of bugs and birds: Markov Chain Monte Carlo for hierarchical modeling in wildlife research

USGS Publications Warehouse

Link, W.A.; Cam, E.; Nichols, J.D.; Cooch, E.G.

2002-01-01

Markov chain Monte Carlo (MCMC) is a statistical innovation that allows researchers to fit far more complex models to data than is feasible using conventional methods. Despite its widespread use in a variety of scientific fields, MCMC appears to be underutilized in wildlife applications. This may be due to a misconception that MCMC requires the adoption of a subjective Bayesian analysis, or perhaps simply to its lack of familiarity among wildlife researchers. We introduce the basic ideas of MCMC and software BUGS (Bayesian inference using Gibbs sampling), stressing that a simple and satisfactory intuition for MCMC does not require extraordinary mathematical sophistication. We illustrate the use of MCMC with an analysis of the association between latent factors governing individual heterogeneity in breeding and survival rates of kittiwakes (Rissa tridactyla). We conclude with a discussion of the importance of individual heterogeneity for understanding population dynamics and designing management plans.

Revealing Neurocomputational Mechanisms of Reinforcement Learning and Decision-Making With the hBayesDM Package

PubMed Central

Ahn, Woo-Young; Haines, Nathaniel; Zhang, Lei

2017-01-01

Reinforcement learning and decision-making (RLDM) provide a quantitative framework and computational theories with which we can disentangle psychiatric conditions into the basic dimensions of neurocognitive functioning. RLDM offer a novel approach to assessing and potentially diagnosing psychiatric patients, and there is growing enthusiasm for both RLDM and computational psychiatry among clinical researchers. Such a framework can also provide insights into the brain substrates of particular RLDM processes, as exemplified by model-based analysis of data from functional magnetic resonance imaging (fMRI) or electroencephalography (EEG). However, researchers often find the approach too technical and have difficulty adopting it for their research. Thus, a critical need remains to develop a user-friendly tool for the wide dissemination of computational psychiatric methods. We introduce an R package called hBayesDM (hierarchical Bayesian modeling of Decision-Making tasks), which offers computational modeling of an array of RLDM tasks and social exchange games. The hBayesDM package offers state-of-the-art hierarchical Bayesian modeling, in which both individual and group parameters (i.e., posterior distributions) are estimated simultaneously in a mutually constraining fashion. At the same time, the package is extremely user-friendly: users can perform computational modeling, output visualization, and Bayesian model comparisons, each with a single line of coding. Users can also extract the trial-by-trial latent variables (e.g., prediction errors) required for model-based fMRI/EEG. With the hBayesDM package, we anticipate that anyone with minimal knowledge of programming can take advantage of cutting-edge computational-modeling approaches to investigate the underlying processes of and interactions between multiple decision-making (e.g., goal-directed, habitual, and Pavlovian) systems. In this way, we expect that the hBayesDM package will contribute to the dissemination of advanced modeling approaches and enable a wide range of researchers to easily perform computational psychiatric research within different populations. PMID:29601060

Extreme Rainfall Analysis using Bayesian Hierarchical Modeling in the Willamette River Basin, Oregon

NASA Astrophysics Data System (ADS)

Love, C. A.; Skahill, B. E.; AghaKouchak, A.; Karlovits, G. S.; England, J. F.; Duren, A. M.

2016-12-01

We present preliminary results of ongoing research directed at evaluating the worth of including various covariate data to support extreme rainfall analysis in the Willamette River basin using Bayesian hierarchical modeling (BHM). We also compare the BHM derived extreme rainfall estimates with their respective counterparts obtained from a traditional regional frequency analysis (RFA) using the same set of rain gage extreme rainfall data. The U.S. Army Corps of Engineers (USACE) Portland District operates thirteen dams in the 11,478 square mile Willamette River basin (WRB) located in northwestern Oregon, a major tributary of the Columbia River whose 187 miles long main stem, the Willamette River, flows northward between the Coastal and Cascade Ranges. The WRB contains approximately two-thirds of Oregon's population and 20 of the 25 most populous cities in the state. Extreme rainfall estimates are required to support risk-informed hydrologic analyses for these projects as part of the USACE Dam Safety Program. We analyze daily annual rainfall maxima data for the WRB utilizing the spatial BHM R package "spatial.gev.bma", which has been shown to be efficient in developing coherent maps of extreme rainfall by return level. Our intent is to profile for the USACE an alternate methodology to a RFA which was developed in 2008 due to the lack of an official NOAA Atlas 14 update for the state of Oregon. Unlike RFA, the advantage of a BHM-based analysis of hydrometeorological extremes is its ability to account for non-stationarity while providing robust estimates of uncertainty. BHM also allows for the inclusion of geographical and climatological factors which we show for the WRB influence regional rainfall extremes. Moreover, the Bayesian framework permits one to combine additional data types into the analysis; for example, information derived via elicitation and causal information expansion data, both being additional opportunities for future related research.

Application of hierarchical Bayesian unmixing models in river sediment source apportionment

NASA Astrophysics Data System (ADS)

Blake, Will; Smith, Hugh; Navas, Ana; Bodé, Samuel; Goddard, Rupert; Zou Kuzyk, Zou; Lennard, Amy; Lobb, David; Owens, Phil; Palazon, Leticia; Petticrew, Ellen; Gaspar, Leticia; Stock, Brian; Boeckx, Pacsal; Semmens, Brice

2016-04-01

Fingerprinting and unmixing concepts are used widely across environmental disciplines for forensic evaluation of pollutant sources. In aquatic and marine systems, this includes tracking the source of organic and inorganic pollutants in water and linking problem sediment to soil erosion and land use sources. It is, however, the particular complexity of ecological systems that has driven creation of the most sophisticated mixing models, primarily to (i) evaluate diet composition in complex ecological food webs, (ii) inform population structure and (iii) explore animal movement. In the context of the new hierarchical Bayesian unmixing model, MIXSIAR, developed to characterise intra-population niche variation in ecological systems, we evaluate the linkage between ecological 'prey' and 'consumer' concepts and river basin sediment 'source' and sediment 'mixtures' to exemplify the value of ecological modelling tools to river basin science. Recent studies have outlined advantages presented by Bayesian unmixing approaches in handling complex source and mixture datasets while dealing appropriately with uncertainty in parameter probability distributions. MixSIAR is unique in that it allows individual fixed and random effects associated with mixture hierarchy, i.e. factors that might exert an influence on model outcome for mixture groups, to be explored within the source-receptor framework. This offers new and powerful ways of interpreting river basin apportionment data. In this contribution, key components of the model are evaluated in the context of common experimental designs for sediment fingerprinting studies namely simple, nested and distributed catchment sampling programmes. Illustrative examples using geochemical and compound specific stable isotope datasets are presented and used to discuss best practice with specific attention to (1) the tracer selection process, (2) incorporation of fixed effects relating to sample timeframe and sediment type in the modelling process, (3) deriving and using informative priors in sediment fingerprinting context and (4) transparency of the process and replication of model results by other users.

BASiCS: Bayesian Analysis of Single-Cell Sequencing Data

PubMed Central

Vallejos, Catalina A.; Marioni, John C.; Richardson, Sylvia

2015-01-01

Single-cell mRNA sequencing can uncover novel cell-to-cell heterogeneity in gene expression levels in seemingly homogeneous populations of cells. However, these experiments are prone to high levels of unexplained technical noise, creating new challenges for identifying genes that show genuine heterogeneous expression within the population of cells under study. BASiCS (Bayesian Analysis of Single-Cell Sequencing data) is an integrated Bayesian hierarchical model where: (i) cell-specific normalisation constants are estimated as part of the model parameters, (ii) technical variability is quantified based on spike-in genes that are artificially introduced to each analysed cell’s lysate and (iii) the total variability of the expression counts is decomposed into technical and biological components. BASiCS also provides an intuitive detection criterion for highly (or lowly) variable genes within the population of cells under study. This is formalised by means of tail posterior probabilities associated to high (or low) biological cell-to-cell variance contributions, quantities that can be easily interpreted by users. We demonstrate our method using gene expression measurements from mouse Embryonic Stem Cells. Cross-validation and meaningful enrichment of gene ontology categories within genes classified as highly (or lowly) variable supports the efficacy of our approach. PMID:26107944

BASiCS: Bayesian Analysis of Single-Cell Sequencing Data.

PubMed

Vallejos, Catalina A; Marioni, John C; Richardson, Sylvia

2015-06-01

Single-cell mRNA sequencing can uncover novel cell-to-cell heterogeneity in gene expression levels in seemingly homogeneous populations of cells. However, these experiments are prone to high levels of unexplained technical noise, creating new challenges for identifying genes that show genuine heterogeneous expression within the population of cells under study. BASiCS (Bayesian Analysis of Single-Cell Sequencing data) is an integrated Bayesian hierarchical model where: (i) cell-specific normalisation constants are estimated as part of the model parameters, (ii) technical variability is quantified based on spike-in genes that are artificially introduced to each analysed cell's lysate and (iii) the total variability of the expression counts is decomposed into technical and biological components. BASiCS also provides an intuitive detection criterion for highly (or lowly) variable genes within the population of cells under study. This is formalised by means of tail posterior probabilities associated to high (or low) biological cell-to-cell variance contributions, quantities that can be easily interpreted by users. We demonstrate our method using gene expression measurements from mouse Embryonic Stem Cells. Cross-validation and meaningful enrichment of gene ontology categories within genes classified as highly (or lowly) variable supports the efficacy of our approach.

Bayesian flood forecasting methods: A review

NASA Astrophysics Data System (ADS)

Han, Shasha; Coulibaly, Paulin

2017-08-01

Over the past few decades, floods have been seen as one of the most common and largely distributed natural disasters in the world. If floods could be accurately forecasted in advance, then their negative impacts could be greatly minimized. It is widely recognized that quantification and reduction of uncertainty associated with the hydrologic forecast is of great importance for flood estimation and rational decision making. Bayesian forecasting system (BFS) offers an ideal theoretic framework for uncertainty quantification that can be developed for probabilistic flood forecasting via any deterministic hydrologic model. It provides suitable theoretical structure, empirically validated models and reasonable analytic-numerical computation method, and can be developed into various Bayesian forecasting approaches. This paper presents a comprehensive review on Bayesian forecasting approaches applied in flood forecasting from 1999 till now. The review starts with an overview of fundamentals of BFS and recent advances in BFS, followed with BFS application in river stage forecasting and real-time flood forecasting, then move to a critical analysis by evaluating advantages and limitations of Bayesian forecasting methods and other predictive uncertainty assessment approaches in flood forecasting, and finally discusses the future research direction in Bayesian flood forecasting. Results show that the Bayesian flood forecasting approach is an effective and advanced way for flood estimation, it considers all sources of uncertainties and produces a predictive distribution of the river stage, river discharge or runoff, thus gives more accurate and reliable flood forecasts. Some emerging Bayesian forecasting methods (e.g. ensemble Bayesian forecasting system, Bayesian multi-model combination) were shown to overcome limitations of single model or fixed model weight and effectively reduce predictive uncertainty. In recent years, various Bayesian flood forecasting approaches have been developed and widely applied, but there is still room for improvements. Future research in the context of Bayesian flood forecasting should be on assimilation of various sources of newly available information and improvement of predictive performance assessment methods.

Bayesian structural equation modeling in sport and exercise psychology.

PubMed

Stenling, Andreas; Ivarsson, Andreas; Johnson, Urban; Lindwall, Magnus

2015-08-01

Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach.

Bayesian approach for counting experiment statistics applied to a neutrino point source analysis

NASA Astrophysics Data System (ADS)

Bose, D.; Brayeur, L.; Casier, M.; de Vries, K. D.; Golup, G.; van Eijndhoven, N.

2013-12-01

In this paper we present a model independent analysis method following Bayesian statistics to analyse data from a generic counting experiment and apply it to the search for neutrinos from point sources. We discuss a test statistic defined following a Bayesian framework that will be used in the search for a signal. In case no signal is found, we derive an upper limit without the introduction of approximations. The Bayesian approach allows us to obtain the full probability density function for both the background and the signal rate. As such, we have direct access to any signal upper limit. The upper limit derivation directly compares with a frequentist approach and is robust in the case of low-counting observations. Furthermore, it allows also to account for previous upper limits obtained by other analyses via the concept of prior information without the need of the ad hoc application of trial factors. To investigate the validity of the presented Bayesian approach, we have applied this method to the public IceCube 40-string configuration data for 10 nearby blazars and we have obtained a flux upper limit, which is in agreement with the upper limits determined via a frequentist approach. Furthermore, the upper limit obtained compares well with the previously published result of IceCube, using the same data set.

Bayesian hierarchical models for regional climate reconstructions of the last glacial maximum

NASA Astrophysics Data System (ADS)

Weitzel, Nils; Hense, Andreas; Ohlwein, Christian

2017-04-01

Spatio-temporal reconstructions of past climate are important for the understanding of the long term behavior of the climate system and the sensitivity to forcing changes. Unfortunately, they are subject to large uncertainties, have to deal with a complex proxy-climate structure, and a physically reasonable interpolation between the sparse proxy observations is difficult. Bayesian Hierarchical Models (BHMs) are a class of statistical models that is well suited for spatio-temporal reconstructions of past climate because they permit the inclusion of multiple sources of information (e.g. records from different proxy types, uncertain age information, output from climate simulations) and quantify uncertainties in a statistically rigorous way. BHMs in paleoclimatology typically consist of three stages which are modeled individually and are combined using Bayesian inference techniques. The data stage models the proxy-climate relation (often named transfer function), the process stage models the spatio-temporal distribution of the climate variables of interest, and the prior stage consists of prior distributions of the model parameters. For our BHMs, we translate well-known proxy-climate transfer functions for pollen to a Bayesian framework. In addition, we can include Gaussian distributed local climate information from preprocessed proxy records. The process stage combines physically reasonable spatial structures from prior distributions with proxy records which leads to a multivariate posterior probability distribution for the reconstructed climate variables. The prior distributions that constrain the possible spatial structure of the climate variables are calculated from climate simulation output. We present results from pseudoproxy tests as well as new regional reconstructions of temperatures for the last glacial maximum (LGM, ˜ 21,000 years BP). These reconstructions combine proxy data syntheses with information from climate simulations for the LGM that were performed in the PMIP3 project. The proxy data syntheses consist either of raw pollen data or of normally distributed climate data from preprocessed proxy records. Future extensions of our method contain the inclusion of other proxy types (transfer functions), the implementation of other spatial interpolation techniques, the use of age uncertainties, and the extension to spatio-temporal reconstructions of the last deglaciation. Our work is part of the PalMod project funded by the German Federal Ministry of Education and Science (BMBF).

Probabilistic assessment of compliance with the numerical criteria for fecal coliforms in rivers

NASA Astrophysics Data System (ADS)

Cha, YoonKyung

2017-04-01

Most guidelines for assessing fecal contamination in surface waters suggest that a waterbody is impaired if a certain percent or the geometric mean of samples exceeds the numerical criteria for fecal indicator organisms. However, this raw score approach is not able to account for the uncertainty and variability in the sample statistics. In a Bayesian hierarchical modeling approach, the uncertainty in the mean parameter is expressed as a posterior distribution, and the probability of not violating the criterion is referred to as the confidence of compliance (COC). Further, the spatiotemporal variability in the mean parameter can be quantified by imposing the hierarchical structure on the model. The monitoring data spanning 91 sites across the four major rivers (the Han, Geum, Yeongsan, and Nakdong) of South Korea for the years 2007-2016 were used. The Bayesian hierarchical model was developed for each river to predict the COC with the criteria for fecal coliforms. The established criteria for fecal coliforms are less than 10, 100, 200, and 1,000 CFU/100mL in the river whose water quality goal corresponds to Class Ia, Ib, II, and III, respectively. The model results suggested that the COC varied significantly by site, ranging from 0.0 to 98.9 percent across the four rivers. In the Geum, Yeongsan, and Nakdong Rivers, COC values in the upper river sections were substantially lower than those in the upper river sections. The model suggested that for all four rivers the spatial component, compared with annual and seasonal components, made the largest contribution to the variability in mean fecal coliforms. In all four rivers, mean levels for fecal coliform during the summer (July to September) were distinctly higher than those during other seasons. A decreasing pattern was clearly shown in the Yeongsan River over the recent decade, while monotonic increases or decreases were not shown in other three rivers.

Bayesian dynamic modeling of time series of dengue disease case counts

PubMed Central

López-Quílez, Antonio; Torres-Prieto, Alexander

2017-01-01

The aim of this study is to model the association between weekly time series of dengue case counts and meteorological variables, in a high-incidence city of Colombia, applying Bayesian hierarchical dynamic generalized linear models over the period January 2008 to August 2015. Additionally, we evaluate the model’s short-term performance for predicting dengue cases. The methodology shows dynamic Poisson log link models including constant or time-varying coefficients for the meteorological variables. Calendar effects were modeled using constant or first- or second-order random walk time-varying coefficients. The meteorological variables were modeled using constant coefficients and first-order random walk time-varying coefficients. We applied Markov Chain Monte Carlo simulations for parameter estimation, and deviance information criterion statistic (DIC) for model selection. We assessed the short-term predictive performance of the selected final model, at several time points within the study period using the mean absolute percentage error. The results showed the best model including first-order random walk time-varying coefficients for calendar trend and first-order random walk time-varying coefficients for the meteorological variables. Besides the computational challenges, interpreting the results implies a complete analysis of the time series of dengue with respect to the parameter estimates of the meteorological effects. We found small values of the mean absolute percentage errors at one or two weeks out-of-sample predictions for most prediction points, associated with low volatility periods in the dengue counts. We discuss the advantages and limitations of the dynamic Poisson models for studying the association between time series of dengue disease and meteorological variables. The key conclusion of the study is that dynamic Poisson models account for the dynamic nature of the variables involved in the modeling of time series of dengue disease, producing useful models for decision-making in public health. PMID:28671941

Modelling past land use using archaeological and pollen data

NASA Astrophysics Data System (ADS)

Pirzamanbein, Behnaz; Lindström, johan; Poska, Anneli; Gaillard-Lemdahl, Marie-José

2016-04-01

Accurate maps of past land use are necessary for studying the impact of anthropogenic land-cover changes on climate and biodiversity. We develop a Bayesian hierarchical model to reconstruct the land use using Gaussian Markov random fields. The model uses two observations sets: 1) archaeological data, representing human settlements, urbanization and agricultural findings; and 2) pollen-based land estimates of the three land-cover types Coniferous forest, Broadleaved forest and Unforested/Open land. The pollen based estimates are obtained from the REVEALS model, based on pollen counts from lakes and bogs. Our developed model uses the sparse pollen-based estimations to reconstruct the spatial continuous cover of three land cover types. Using the open-land component and the archaeological data, the extent of land-use is reconstructed. The model is applied on three time periods - centred around 1900 CE, 1000 and, 4000 BCE over Sweden for which both pollen-based estimates and archaeological data are available. To estimate the model parameters and land use, a block updated Markov chain Monte Carlo (MCMC) algorithm is applied. Using the MCMC posterior samples uncertainties in land-use predictions are computed. Due to lack of good historic land use data, model results are evaluated by cross-validation. Keywords. Spatial reconstruction, Gaussian Markov random field, Fossil pollen records, Archaeological data, Human land-use, Prediction uncertainty

A hierarchical model combining distance sampling and time removal to estimate detection probability during avian point counts

USGS Publications Warehouse

Amundson, Courtney L.; Royle, J. Andrew; Handel, Colleen M.

2014-01-01

Imperfect detection during animal surveys biases estimates of abundance and can lead to improper conclusions regarding distribution and population trends. Farnsworth et al. (2005) developed a combined distance-sampling and time-removal model for point-transect surveys that addresses both availability (the probability that an animal is available for detection; e.g., that a bird sings) and perceptibility (the probability that an observer detects an animal, given that it is available for detection). We developed a hierarchical extension of the combined model that provides an integrated analysis framework for a collection of survey points at which both distance from the observer and time of initial detection are recorded. Implemented in a Bayesian framework, this extension facilitates evaluating covariates on abundance and detection probability, incorporating excess zero counts (i.e. zero-inflation), accounting for spatial autocorrelation, and estimating population density. Species-specific characteristics, such as behavioral displays and territorial dispersion, may lead to different patterns of availability and perceptibility, which may, in turn, influence the performance of such hierarchical models. Therefore, we first test our proposed model using simulated data under different scenarios of availability and perceptibility. We then illustrate its performance with empirical point-transect data for a songbird that consistently produces loud, frequent, primarily auditory signals, the Golden-crowned Sparrow (Zonotrichia atricapilla); and for 2 ptarmigan species (Lagopus spp.) that produce more intermittent, subtle, and primarily visual cues. Data were collected by multiple observers along point transects across a broad landscape in southwest Alaska, so we evaluated point-level covariates on perceptibility (observer and habitat), availability (date within season and time of day), and abundance (habitat, elevation, and slope), and included a nested point-within-transect and park-level effect. Our results suggest that this model can provide insight into the detection process during avian surveys and reduce bias in estimates of relative abundance but is best applied to surveys of species with greater availability (e.g., breeding songbirds).

An agglomerative hierarchical clustering approach to visualisation in Bayesian clustering problems

PubMed Central

Dawson, Kevin J.; Belkhir, Khalid

2009-01-01

Clustering problems (including the clustering of individuals into outcrossing populations, hybrid generations, full-sib families and selfing lines) have recently received much attention in population genetics. In these clustering problems, the parameter of interest is a partition of the set of sampled individuals, - the sample partition. In a fully Bayesian approach to clustering problems of this type, our knowledge about the sample partition is represented by a probability distribution on the space of possible sample partitions. Since the number of possible partitions grows very rapidly with the sample size, we can not visualise this probability distribution in its entirety, unless the sample is very small. As a solution to this visualisation problem, we recommend using an agglomerative hierarchical clustering algorithm, which we call the exact linkage algorithm. This algorithm is a special case of the maximin clustering algorithm that we introduced previously. The exact linkage algorithm is now implemented in our software package Partition View. The exact linkage algorithm takes the posterior co-assignment probabilities as input, and yields as output a rooted binary tree, - or more generally, a forest of such trees. Each node of this forest defines a set of individuals, and the node height is the posterior co-assignment probability of this set. This provides a useful visual representation of the uncertainty associated with the assignment of individuals to categories. It is also a useful starting point for a more detailed exploration of the posterior distribution in terms of the co-assignment probabilities. PMID:19337306

A Bayesian hierarchical model with novel prior specifications for estimating HIV testing rates.

PubMed

An, Qian; Kang, Jian; Song, Ruiguang; Hall, H Irene

2016-04-30

Human immunodeficiency virus (HIV) infection is a severe infectious disease actively spreading globally, and acquired immunodeficiency syndrome (AIDS) is an advanced stage of HIV infection. The HIV testing rate, that is, the probability that an AIDS-free HIV infected person seeks a test for HIV during a particular time interval, given no previous positive test has been obtained prior to the start of the time, is an important parameter for public health. In this paper, we propose a Bayesian hierarchical model with two levels of hierarchy to estimate the HIV testing rate using annual AIDS and AIDS-free HIV diagnoses data. At level one, we model the latent number of HIV infections for each year using a Poisson distribution with the intensity parameter representing the HIV incidence rate. At level two, the annual numbers of AIDS and AIDS-free HIV diagnosed cases and all undiagnosed cases stratified by the HIV infections at different years are modeled using a multinomial distribution with parameters including the HIV testing rate. We propose a new class of priors for the HIV incidence rate and HIV testing rate taking into account the temporal dependence of these parameters to improve the estimation accuracy. We develop an efficient posterior computation algorithm based on the adaptive rejection metropolis sampling technique. We demonstrate our model using simulation studies and the analysis of the national HIV surveillance data in the USA. Copyright © 2015 John Wiley & Sons, Ltd.

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

Wainwright, Haruko M.; Flores Orozco, Adrian; Bucker, Matthias

In floodplain environments, a naturally reduced zone (NRZ) is considered to be a common biogeochemical hot spot, having distinct microbial and geochemical characteristics. Although important for understanding their role in mediating floodplain biogeochemical processes, mapping the subsurface distribution of NRZs over the dimensions of a floodplain is challenging, as conventional wellbore data are typically spatially limited and the distribution of NRZs is heterogeneous. In this work, we present an innovative methodology for the probabilistic mapping of NRZs within a three-dimensional (3-D) subsurface domain using induced polarization imaging, which is a noninvasive geophysical technique. Measurements consist of surface geophysical surveys andmore » drilling-recovered sediments at the U.S. Department of Energy field site near Rifle, CO (USA). Inversion of surface time domain-induced polarization (TDIP) data yielded 3-D images of the complex electrical resistivity, in terms of magnitude and phase, which are associated with mineral precipitation and other lithological properties. By extracting the TDIP data values colocated with wellbore lithological logs, we found that the NRZs have a different distribution of resistivity and polarization from the other aquifer sediments. To estimate the spatial distribution of NRZs, we developed a Bayesian hierarchical model to integrate the geophysical and wellbore data. In addition, the resistivity images were used to estimate hydrostratigraphic interfaces under the floodplain. Validation results showed that the integration of electrical imaging and wellbore data using a Bayesian hierarchical model was capable of mapping spatially heterogeneous interfaces and NRZ distributions thereby providing a minimally invasive means to parameterize a hydrobiogeochemical model of the floodplain.« less

Correlation Between Hierarchical Bayesian and Aerosol ...

EPA Pesticide Factsheets

Tools to estimate PM2.5 mass have expanded in recent years, and now include: 1) stationary monitor readings, 2) Community Multi-Scale Air Quality (CMAQ) model estimates, 3) Hierarchical Bayesian (HB) estimates from combined stationary monitor readings and CMAQ model output; and, 4) calibrated Aerosol Optical Depth (AOD) readings from two Moderate Resolution Imaging Spetroradiometer (MODIS) units on National Aeronautics and Space Administration’s (NASA) Terra and Aqua satellites. Case-crossover design and conditional logistic regression were used to determine concentration response (CR) functions for three different PM2.5 levels on asthma emergency department (ED) visits and acute myocardial infarction (MI) inpatient hospitalizations in ninety-nine, 12 km2 grids in Baltimore, MD (2005 data). HB analyses for asthma ED visits produced significant results at 3-day lags for the main effect (OR=1.002, 95% CI=1.000-1.005), and two effect modifiers for females (OR=1.003, 95% CI=1.000-1.006), and non-Caucasian/non-African American persons (OR=1.010, 95% CI=1.001-1.019). HB analyses for acute MI inpatient hospitalizations also consistently produced a significant outcome for persons of other race (OR=1.031, 95% CI=1.006-1.056). Correlation coefficients computed between stationary monitor and satellite AOD PM2.5 values were significant for both asthma (rxy=0.944) and acute MI (rxy=0.940). Both monitor and AOD PM2.5 values were higher in February and June through Aug

Long-range dismount activity classification: LODAC

NASA Astrophysics Data System (ADS)

Garagic, Denis; Peskoe, Jacob; Liu, Fang; Cuevas, Manuel; Freeman, Andrew M.; Rhodes, Bradley J.

2014-06-01

Continuous classification of dismount types (including gender, age, ethnicity) and their activities (such as walking, running) evolving over space and time is challenging. Limited sensor resolution (often exacerbated as a function of platform standoff distance) and clutter from shadows in dense target environments, unfavorable environmental conditions, and the normal properties of real data all contribute to the challenge. The unique and innovative aspect of our approach is a synthesis of multimodal signal processing with incremental non-parametric, hierarchical Bayesian machine learning methods to create a new kind of target classification architecture. This architecture is designed from the ground up to optimally exploit correlations among the multiple sensing modalities (multimodal data fusion) and rapidly and continuously learns (online self-tuning) patterns of distinct classes of dismounts given little a priori information. This increases classification performance in the presence of challenges posed by anti-access/area denial (A2/AD) sensing. To fuse multimodal features, Long-range Dismount Activity Classification (LODAC) develops a novel statistical information theoretic approach for multimodal data fusion that jointly models multimodal data (i.e., a probabilistic model for cross-modal signal generation) and discovers the critical cross-modal correlations by identifying components (features) with maximal mutual information (MI) which is efficiently estimated using non-parametric entropy models. LODAC develops a generic probabilistic pattern learning and classification framework based on a new class of hierarchical Bayesian learning algorithms for efficiently discovering recurring patterns (classes of dismounts) in multiple simultaneous time series (sensor modalities) at multiple levels of feature granularity.

A Bayesian hierarchical approach to galaxy-galaxy lensing

NASA Astrophysics Data System (ADS)

Sonnenfeld, Alessandro; Leauthaud, Alexie

2018-07-01

We present a Bayesian hierarchical inference formalism to study the relation between the properties of dark matter haloes and those of their central galaxies using weak gravitational lensing. Unlike traditional methods, this technique does not resort to stacking the weak lensing signal in bins, and thus allows for a more efficient use of the information content in the data. Our method is particularly useful for constraining scaling relations between two or more galaxy properties and dark matter halo mass, and can also be used to constrain the intrinsic scatter in these scaling relations. We show that, if observational scatter is not properly accounted for, the traditional stacking method can produce biased results when exploring correlations between multiple galaxy properties and halo mass. For example, this bias can affect studies of the joint correlation between galaxy mass, halo mass, and galaxy size, or galaxy colour. In contrast, our method easily and efficiently handles the intrinsic and observational scatter in multiple galaxy properties and halo mass. We test our method on mocks with varying degrees of complexity. We find that we can recover the mean halo mass and concentration, each with a 0.1 dex accuracy, and the intrinsic scatter in halo mass with a 0.05 dex accuracy. In its current version, our method will be most useful for studying the weak lensing signal around central galaxies in groups and clusters, as well as massive galaxies samples with log M* > 11, which have low satellite fractions.

LiDAR based prediction of forest biomass using hierarchical models with spatially varying coefficients

USGS Publications Warehouse

Babcock, Chad; Finley, Andrew O.; Bradford, John B.; Kolka, Randall K.; Birdsey, Richard A.; Ryan, Michael G.

2015-01-01

Many studies and production inventory systems have shown the utility of coupling covariates derived from Light Detection and Ranging (LiDAR) data with forest variables measured on georeferenced inventory plots through regression models. The objective of this study was to propose and assess the use of a Bayesian hierarchical modeling framework that accommodates both residual spatial dependence and non-stationarity of model covariates through the introduction of spatial random effects. We explored this objective using four forest inventory datasets that are part of the North American Carbon Program, each comprising point-referenced measures of above-ground forest biomass and discrete LiDAR. For each dataset, we considered at least five regression model specifications of varying complexity. Models were assessed based on goodness of fit criteria and predictive performance using a 10-fold cross-validation procedure. Results showed that the addition of spatial random effects to the regression model intercept improved fit and predictive performance in the presence of substantial residual spatial dependence. Additionally, in some cases, allowing either some or all regression slope parameters to vary spatially, via the addition of spatial random effects, further improved model fit and predictive performance. In other instances, models showed improved fit but decreased predictive performance—indicating over-fitting and underscoring the need for cross-validation to assess predictive ability. The proposed Bayesian modeling framework provided access to pixel-level posterior predictive distributions that were useful for uncertainty mapping, diagnosing spatial extrapolation issues, revealing missing model covariates, and discovering locally significant parameters.

Bayesian hierarchical modelling of continuous non‐negative longitudinal data with a spike at zero: An application to a study of birds visiting gardens in winter

PubMed Central

Buckland, Stephen T.; King, Ruth; Toms, Mike P.

2015-01-01

The development of methods for dealing with continuous data with a spike at zero has lagged behind those for overdispersed or zero‐inflated count data. We consider longitudinal ecological data corresponding to an annual average of 26 weekly maximum counts of birds, and are hence effectively continuous, bounded below by zero but also with a discrete mass at zero. We develop a Bayesian hierarchical Tweedie regression model that can directly accommodate the excess number of zeros common to this type of data, whilst accounting for both spatial and temporal correlation. Implementation of the model is conducted in a Markov chain Monte Carlo (MCMC) framework, using reversible jump MCMC to explore uncertainty across both parameter and model spaces. This regression modelling framework is very flexible and removes the need to make strong assumptions about mean‐variance relationships a priori. It can also directly account for the spike at zero, whilst being easily applicable to other types of data and other model formulations. Whilst a correlative study such as this cannot prove causation, our results suggest that an increase in an avian predator may have led to an overall decrease in the number of one of its prey species visiting garden feeding stations in the United Kingdom. This may reflect a change in behaviour of house sparrows to avoid feeding stations frequented by sparrowhawks, or a reduction in house sparrow population size as a result of sparrowhawk increase. PMID:25737026

Predicting protein subcellular locations using hierarchical ensemble of Bayesian classifiers based on Markov chains.

PubMed

Bulashevska, Alla; Eils, Roland

2006-06-14

The subcellular location of a protein is closely related to its function. It would be worthwhile to develop a method to predict the subcellular location for a given protein when only the amino acid sequence of the protein is known. Although many efforts have been made to predict subcellular location from sequence information only, there is the need for further research to improve the accuracy of prediction. A novel method called HensBC is introduced to predict protein subcellular location. HensBC is a recursive algorithm which constructs a hierarchical ensemble of classifiers. The classifiers used are Bayesian classifiers based on Markov chain models. We tested our method on six various datasets; among them are Gram-negative bacteria dataset, data for discriminating outer membrane proteins and apoptosis proteins dataset. We observed that our method can predict the subcellular location with high accuracy. Another advantage of the proposed method is that it can improve the accuracy of the prediction of some classes with few sequences in training and is therefore useful for datasets with imbalanced distribution of classes. This study introduces an algorithm which uses only the primary sequence of a protein to predict its subcellular location. The proposed recursive scheme represents an interesting methodology for learning and combining classifiers. The method is computationally efficient and competitive with the previously reported approaches in terms of prediction accuracies as empirical results indicate. The code for the software is available upon request.

A Bayesian Hierarchical Approach to Galaxy-Galaxy Lensing

NASA Astrophysics Data System (ADS)

Sonnenfeld, Alessandro; Leauthaud, Alexie

2018-04-01

We present a Bayesian hierarchical inference formalism to study the relation between the properties of dark matter halos and those of their central galaxies using weak gravitational lensing. Unlike traditional methods, this technique does not resort to stacking the weak lensing signal in bins, and thus allows for a more efficient use of the information content in the data. Our method is particularly useful for constraining scaling relations between two or more galaxy properties and dark matter halo mass, and can also be used to constrain the intrinsic scatter in these scaling relations. We show that, if observational scatter is not properly accounted for, the traditional stacking method can produce biased results when exploring correlations between multiple galaxy properties and halo mass. For example, this bias can affect studies of the joint correlation between galaxy mass, halo mass, and galaxy size, or galaxy colour. In contrast, our method easily and efficiently handles the intrinsic and observational scatter in multiple galaxy properties and halo mass. We test our method on mocks with varying degrees of complexity. We find that we can recover the mean halo mass and concentration, each with a 0.1 dex accuracy, and the intrinsic scatter in halo mass with a 0.05 dex accuracy. In its current version, our method will be most useful for studying the weak lensing signal around central galaxies in groups and clusters, as well as massive galaxies samples with log M* > 11, which have low satellite fractions.

Influence of Climate Change on Flood Hazard using Climate Informed Bayesian Hierarchical Model in Johnson Creek River

NASA Astrophysics Data System (ADS)

Zarekarizi, M.; Moradkhani, H.

2015-12-01

Extreme events are proven to be affected by climate change, influencing hydrologic simulations for which stationarity is usually a main assumption. Studies have discussed that this assumption would lead to large bias in model estimations and higher flood hazard consequently. Getting inspired by the importance of non-stationarity, we determined how the exceedance probabilities have changed over time in Johnson Creek River, Oregon. This could help estimate the probability of failure of a structure that was primarily designed to resist less likely floods according to common practice. Therefore, we built a climate informed Bayesian hierarchical model and non-stationarity was considered in modeling framework. Principle component analysis shows that North Atlantic Oscillation (NAO), Western Pacific Index (WPI) and Eastern Asia (EA) are mostly affecting stream flow in this river. We modeled flood extremes using peaks over threshold (POT) method rather than conventional annual maximum flood (AMF) mainly because it is possible to base the model on more information. We used available threshold selection methods to select a suitable threshold for the study area. Accounting for non-stationarity, model parameters vary through time with climate indices. We developed a couple of model scenarios and chose one which could best explain the variation in data based on performance measures. We also estimated return periods under non-stationarity condition. Results show that ignoring stationarity could increase the flood hazard up to four times which could increase the probability of an in-stream structure being overtopped.

Does Mortality Vary between Asian Subgroups in New Zealand: An Application of Hierarchical Bayesian Modelling

PubMed Central

Jatrana, Santosh; Richardson, Ken; Blakely, Tony; Dayal, Saira

2014-01-01

The aim of this paper was to see whether all-cause and cause-specific mortality rates vary between Asian ethnic subgroups, and whether overseas born Asian subgroup mortality rate ratios varied by nativity and duration of residence. We used hierarchical Bayesian methods to allow for sparse data in the analysis of linked census-mortality data for 25–75 year old New Zealanders. We found directly standardised posterior all-cause and cardiovascular mortality rates were highest for the Indian ethnic group, significantly so when compared with those of Chinese ethnicity. In contrast, cancer mortality rates were lowest for ethnic Indians. Asian overseas born subgroups have about 70% of the mortality rate of their New Zealand born Asian counterparts, a result that showed little variation by Asian subgroup or cause of death. Within the overseas born population, all-cause mortality rates for migrants living 0–9 years in New Zealand were about 60% of the mortality rate of those living more than 25 years in New Zealand regardless of ethnicity. The corresponding figure for cardiovascular mortality rates was 50%. However, while Chinese cancer mortality rates increased with duration of residence, Indian and Other Asian cancer mortality rates did not. Future research on the mechanisms of worsening of health with increased time spent in the host country is required to improve the understanding of the process, and would assist the policy-makers and health planners. PMID:25140523

Comparison of Extreme Precipitation Return Levels using Spatial Bayesian Hierarchical Modeling versus Regional Frequency Analysis

NASA Astrophysics Data System (ADS)

Love, C. A.; Skahill, B. E.; AghaKouchak, A.; Karlovits, G. S.; England, J. F.; Duren, A. M.

2017-12-01

We compare gridded extreme precipitation return levels obtained using spatial Bayesian hierarchical modeling (BHM) with their respective counterparts from a traditional regional frequency analysis (RFA) using the same set of extreme precipitation data. Our study area is the 11,478 square mile Willamette River basin (WRB) located in northwestern Oregon, a major tributary of the Columbia River whose 187 miles long main stem, the Willamette River, flows northward between the Coastal and Cascade Ranges. The WRB contains approximately two ­thirds of Oregon's population and 20 of the 25 most populous cities in the state. The U.S. Army Corps of Engineers (USACE) Portland District operates thirteen dams and extreme precipitation estimates are required to support risk­ informed hydrologic analyses as part of the USACE Dam Safety Program. Our intent is to profile for the USACE an alternate methodology to an RFA that was developed in 2008 due to the lack of an official NOAA Atlas 14 update for the state of Oregon. We analyze 24-hour annual precipitation maxima data for the WRB utilizing the spatial BHM R package "spatial.gev.bma", which has been shown to be efficient in developing coherent maps of extreme precipitation by return level. Our BHM modeling analysis involved application of leave-one-out cross validation (LOO-CV), which not only supported model selection but also a comprehensive assessment of location specific model performance. The LOO-CV results will provide a basis for the BHM RFA comparison.

Dynamic classification of fetal heart rates by hierarchical Dirichlet process mixture models.

PubMed

Yu, Kezi; Quirk, J Gerald; Djurić, Petar M

2017-01-01

In this paper, we propose an application of non-parametric Bayesian (NPB) models for classification of fetal heart rate (FHR) recordings. More specifically, we propose models that are used to differentiate between FHR recordings that are from fetuses with or without adverse outcomes. In our work, we rely on models based on hierarchical Dirichlet processes (HDP) and the Chinese restaurant process with finite capacity (CRFC). Two mixture models were inferred from real recordings, one that represents healthy and another, non-healthy fetuses. The models were then used to classify new recordings and provide the probability of the fetus being healthy. First, we compared the classification performance of the HDP models with that of support vector machines on real data and concluded that the HDP models achieved better performance. Then we demonstrated the use of mixture models based on CRFC for dynamic classification of the performance of (FHR) recordings in a real-time setting.

Dynamic classification of fetal heart rates by hierarchical Dirichlet process mixture models

PubMed Central

Yu, Kezi; Quirk, J. Gerald

2017-01-01

In this paper, we propose an application of non-parametric Bayesian (NPB) models for classification of fetal heart rate (FHR) recordings. More specifically, we propose models that are used to differentiate between FHR recordings that are from fetuses with or without adverse outcomes. In our work, we rely on models based on hierarchical Dirichlet processes (HDP) and the Chinese restaurant process with finite capacity (CRFC). Two mixture models were inferred from real recordings, one that represents healthy and another, non-healthy fetuses. The models were then used to classify new recordings and provide the probability of the fetus being healthy. First, we compared the classification performance of the HDP models with that of support vector machines on real data and concluded that the HDP models achieved better performance. Then we demonstrated the use of mixture models based on CRFC for dynamic classification of the performance of (FHR) recordings in a real-time setting. PMID:28953927

Analyzing Single-Molecule Protein Transportation Experiments via Hierarchical Hidden Markov Models

PubMed Central

Chen, Yang; Shen, Kuang

2017-01-01

To maintain proper cellular functions, over 50% of proteins encoded in the genome need to be transported to cellular membranes. The molecular mechanism behind such a process, often referred to as protein targeting, is not well understood. Single-molecule experiments are designed to unveil the detailed mechanisms and reveal the functions of different molecular machineries involved in the process. The experimental data consist of hundreds of stochastic time traces from the fluorescence recordings of the experimental system. We introduce a Bayesian hierarchical model on top of hidden Markov models (HMMs) to analyze these data and use the statistical results to answer the biological questions. In addition to resolving the biological puzzles and delineating the regulating roles of different molecular complexes, our statistical results enable us to propose a more detailed mechanism for the late stages of the protein targeting process. PMID:28943680

Making Sense of a Negative Clinical Trial Result: A Bayesian Analysis of a Clinical Trial of Lorazepam and Diazepam for Pediatric Status Epilepticus.

PubMed

Chamberlain, Daniel B; Chamberlain, James M

2017-01-01

We demonstrate the application of a Bayesian approach to a recent negative clinical trial result. A Bayesian analysis of such a trial can provide a more useful interpretation of results and can incorporate previous evidence. This was a secondary analysis of the efficacy and safety results of the Pediatric Seizure Study, a randomized clinical trial of lorazepam versus diazepam for pediatric status epilepticus. We included the published results from the only prospective pediatric study of status in a Bayesian hierarchic model, and we performed sensitivity analyses on the amount of pooling between studies. We evaluated 3 summary analyses for the results: superiority, noninferiority (margin <-10%), and practical equivalence (within ±10%). Consistent with the original study's classic analysis of study results, we did not demonstrate superiority of lorazepam over diazepam. There is a 95% probability that the true efficacy of lorazepam is in the range of 66% to 80%. For both the efficacy and safety outcomes, there was greater than 95% probability that lorazepam is noninferior to diazepam, and there was greater than 90% probability that the 2 medications are practically equivalent. The results were largely driven by the current study because of the sample sizes of our study (n=273) and the previous pediatric study (n=61). Because Bayesian analysis estimates the probability of one or more hypotheses, such an approach can provide more useful information about the meaning of the results of a negative trial outcome. In the case of pediatric status epilepticus, it is highly likely that lorazepam is noninferior and practically equivalent to diazepam. Copyright © 2016 American College of Emergency Physicians. Published by Elsevier Inc. All rights reserved.

Informative Bayesian Type A uncertainty evaluation, especially applicable to a small number of observations

NASA Astrophysics Data System (ADS)

Cox, M.; Shirono, K.

2017-10-01

A criticism levelled at the Guide to the Expression of Uncertainty in Measurement (GUM) is that it is based on a mixture of frequentist and Bayesian thinking. In particular, the GUM’s Type A (statistical) uncertainty evaluations are frequentist, whereas the Type B evaluations, using state-of-knowledge distributions, are Bayesian. In contrast, making the GUM fully Bayesian implies, among other things, that a conventional objective Bayesian approach to Type A uncertainty evaluation for a number n of observations leads to the impractical consequence that n must be at least equal to 4, thus presenting a difficulty for many metrologists. This paper presents a Bayesian analysis of Type A uncertainty evaluation that applies for all n ≥slant 2 , as in the frequentist analysis in the current GUM. The analysis is based on assuming that the observations are drawn from a normal distribution (as in the conventional objective Bayesian analysis), but uses an informative prior based on lower and upper bounds for the standard deviation of the sampling distribution for the quantity under consideration. The main outcome of the analysis is a closed-form mathematical expression for the factor by which the standard deviation of the mean observation should be multiplied to calculate the required standard uncertainty. Metrological examples are used to illustrate the approach, which is straightforward to apply using a formula or look-up table.

Bayesian Nonlinear Assimilation of Eulerian and Lagrangian Coastal Flow Data

DTIC Science & Technology

2015-09-30

Lagrangian Coastal Flow Data Dr. Pierre F.J. Lermusiaux Department of Mechanical Engineering Center for Ocean Science and Engineering Massachusetts...Develop and apply theory, schemes and computational systems for rigorous Bayesian nonlinear assimilation of Eulerian and Lagrangian coastal flow data...coastal ocean fields, both in Eulerian and Lagrangian forms. - Further develop and implement our GMM-DO schemes for robust Bayesian nonlinear estimation

The Variability and Interpretation of Earthquake Source Mechanisms in The Geysers Geothermal Field From a Bayesian Standpoint Based on the Choice of a Noise Model

NASA Astrophysics Data System (ADS)

Mustać, Marija; Tkalčić, Hrvoje; Burky, Alexander L.

2018-01-01

Moment tensor (MT) inversion studies of events in The Geysers geothermal field mostly focused on microseismicity and found a large number of earthquakes with significant non-double-couple (non-DC) seismic radiation. Here we concentrate on the largest events in the area in recent years using a hierarchical Bayesian MT inversion. Initially, we show that the non-DC components of the MT can be reliably retrieved using regional waveform data from a small number of stations. Subsequently, we present results for a number of events and show that accounting for noise correlations can lead to retrieval of a lower isotropic (ISO) component and significantly different focal mechanisms. We compute the Bayesian evidence to compare solutions obtained with different assumptions of the noise covariance matrix. Although a diagonal covariance matrix produces a better waveform fit, inversions that account for noise correlations via an empirically estimated noise covariance matrix account for interdependences of data errors and are preferred from a Bayesian point of view. This implies that improper treatment of data noise in waveform inversions can result in fitting the noise and misinterpreting the non-DC components. Finally, one of the analyzed events is characterized as predominantly DC, while the others still have significant non-DC components, probably as a result of crack opening, which is a reasonable hypothesis for The Geysers geothermal field geological setting.

Cross-validation to select Bayesian hierarchical models in phylogenetics.

PubMed

Duchêne, Sebastián; Duchêne, David A; Di Giallonardo, Francesca; Eden, John-Sebastian; Geoghegan, Jemma L; Holt, Kathryn E; Ho, Simon Y W; Holmes, Edward C

2016-05-26

Recent developments in Bayesian phylogenetic models have increased the range of inferences that can be drawn from molecular sequence data. Accordingly, model selection has become an important component of phylogenetic analysis. Methods of model selection generally consider the likelihood of the data under the model in question. In the context of Bayesian phylogenetics, the most common approach involves estimating the marginal likelihood, which is typically done by integrating the likelihood across model parameters, weighted by the prior. Although this method is accurate, it is sensitive to the presence of improper priors. We explored an alternative approach based on cross-validation that is widely used in evolutionary analysis. This involves comparing models according to their predictive performance. We analysed simulated data and a range of viral and bacterial data sets using a cross-validation approach to compare a variety of molecular clock and demographic models. Our results show that cross-validation can be effective in distinguishing between strict- and relaxed-clock models and in identifying demographic models that allow growth in population size over time. In most of our empirical data analyses, the model selected using cross-validation was able to match that selected using marginal-likelihood estimation. The accuracy of cross-validation appears to improve with longer sequence data, particularly when distinguishing between relaxed-clock models. Cross-validation is a useful method for Bayesian phylogenetic model selection. This method can be readily implemented even when considering complex models where selecting an appropriate prior for all parameters may be difficult.

Bayesian least squares deconvolution

NASA Astrophysics Data System (ADS)

Asensio Ramos, A.; Petit, P.

2015-11-01

Aims: We develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods: We consider LSD under the Bayesian framework and we introduce a flexible Gaussian process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results: We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.

Bayesian statistics in medicine: a 25 year review.

PubMed

Ashby, Deborah

2006-11-15

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

Host Star Dependence of Small Planet Mass–Radius Distributions

NASA Astrophysics Data System (ADS)

Neil, Andrew R.; Rogers, Leslie A.

2018-05-01

The planet formation environment around M dwarf stars is different than around G dwarf stars. The longer hot protostellar phase, activity levels and lower protoplanetary disk mass of M dwarfs all may leave imprints on the composition distribution of planets. We use hierarchical Bayesian modeling conditioned on the sample of transiting planets with radial velocity mass measurements to explore small planet mass–radius distributions that depend on host star mass. We find that the current mass–radius data set is consistent with no host star mass dependence. These models are then applied to the Kepler planet radius distribution to calculate the mass distribution of close-orbiting planets and how it varies with host star mass. We find that the average heavy element mass per star at short orbits is higher for M dwarfs compared to FGK dwarfs, in agreement with previous studies. This work will facilitate comparisons between microlensing planet surveys and Kepler, and will provide an analysis framework that can readily be updated as more M dwarf planets are discovered by ongoing and future surveys such as K2 and the Transiting Exoplanet Survey Satellite.

A utility-based design for randomized comparative trials with ordinal outcomes and prognostic subgroups.

PubMed

Murray, Thomas A; Yuan, Ying; Thall, Peter F; Elizondo, Joan H; Hofstetter, Wayne L

2018-01-22

A design is proposed for randomized comparative trials with ordinal outcomes and prognostic subgroups. The design accounts for patient heterogeneity by allowing possibly different comparative conclusions within subgroups. The comparative testing criterion is based on utilities for the levels of the ordinal outcome and a Bayesian probability model. Designs based on two alternative models that include treatment-subgroup interactions are considered, the proportional odds model and a non-proportional odds model with a hierarchical prior that shrinks toward the proportional odds model. A third design that assumes homogeneity and ignores possible treatment-subgroup interactions also is considered. The three approaches are applied to construct group sequential designs for a trial of nutritional prehabilitation versus standard of care for esophageal cancer patients undergoing chemoradiation and surgery, including both untreated patients and salvage patients whose disease has recurred following previous therapy. A simulation study is presented that compares the three designs, including evaluation of within-subgroup type I and II error probabilities under a variety of scenarios including different combinations of treatment-subgroup interactions. © 2018, The International Biometric Society.

Effects of multiple levels of social organization on survival and abundance.

PubMed

Ward, Eric J; Semmens, Brice X; Holmes, Elizabeth E; Balcomb Iii, Ken C

2011-04-01

Identifying how social organization shapes individual behavior, survival, and fecundity of animals that live in groups can inform conservation efforts and improve forecasts of population abundance, even when the mechanism responsible for group-level differences is unknown. We constructed a hierarchical Bayesian model to quantify the relative variability in survival rates among different levels of social organization (matrilines and pods) of an endangered population of killer whales (Orcinus orca). Individual killer whales often participate in group activities such as prey sharing and cooperative hunting. The estimated age-specific survival probabilities and survivorship curves differed considerably among pods and to a lesser extent among matrilines (within pods). Across all pods, males had lower life expectancy than females. Differences in survival between pods may be caused by a combination of factors that vary across the population's range, including reduced prey availability, contaminants in prey, and human activity. Our modeling approach could be applied to demographic rates for other species and for parameters other than survival, including reproduction, prey selection, movement, and detection probabilities. Conservation Biology ©2010 Society for Conservation Biology. No claim to original US government works.

A multivariate multilevel Gaussian model with a mixed effects structure in the mean and covariance part.

PubMed

Li, Baoyue; Bruyneel, Luk; Lesaffre, Emmanuel

2014-05-20

A traditional Gaussian hierarchical model assumes a nested multilevel structure for the mean and a constant variance at each level. We propose a Bayesian multivariate multilevel factor model that assumes a multilevel structure for both the mean and the covariance matrix. That is, in addition to a multilevel structure for the mean we also assume that the covariance matrix depends on covariates and random effects. This allows to explore whether the covariance structure depends on the values of the higher levels and as such models heterogeneity in the variances and correlation structure of the multivariate outcome across the higher level values. The approach is applied to the three-dimensional vector of burnout measurements collected on nurses in a large European study to answer the research question whether the covariance matrix of the outcomes depends on recorded system-level features in the organization of nursing care, but also on not-recorded factors that vary with countries, hospitals, and nursing units. Simulations illustrate the performance of our modeling approach. Copyright © 2013 John Wiley & Sons, Ltd.

Model-based estimation of individual fitness

USGS Publications Warehouse

Link, W.A.; Cooch, E.G.; Cam, E.

2002-01-01

Fitness is the currency of natural selection, a measure of the propagation rate of genotypes into future generations. Its various definitions have the common feature that they are functions of survival and fertility rates. At the individual level, the operative level for natural selection, these rates must be understood as latent features, genetically determined propensities existing at birth. This conception of rates requires that individual fitness be defined and estimated by consideration of the individual in a modelled relation to a group of similar individuals; the only alternative is to consider a sample of size one, unless a clone of identical individuals is available. We present hierarchical models describing individual heterogeneity in survival and fertility rates and allowing for associations between these rates at the individual level. We apply these models to an analysis of life histories of Kittiwakes (Rissa tridactyla) observed at several colonies on the Brittany coast of France. We compare Bayesian estimation of the population distribution of individual fitness with estimation based on treating individual life histories in isolation, as samples of size one (e.g. McGraw and Caswell, 1996).

Causal assessment of surrogacy in a meta-analysis of colorectal cancer trials

PubMed Central

Li, Yun; Taylor, Jeremy M.G.; Elliott, Michael R.; Sargent, Daniel J.

2011-01-01

When the true end points (T) are difficult or costly to measure, surrogate markers (S) are often collected in clinical trials to help predict the effect of the treatment (Z). There is great interest in understanding the relationship among S, T, and Z. A principal stratification (PS) framework has been proposed by Frangakis and Rubin (2002) to study their causal associations. In this paper, we extend the framework to a multiple trial setting and propose a Bayesian hierarchical PS model to assess surrogacy. We apply the method to data from a large collection of colon cancer trials in which S and T are binary. We obtain the trial-specific causal measures among S, T, and Z, as well as their overall population-level counterparts that are invariant across trials. The method allows for information sharing across trials and reduces the nonidentifiability problem. We examine the frequentist properties of our model estimates and the impact of the monotonicity assumption using simulations. We also illustrate the challenges in evaluating surrogacy in the counterfactual framework that result from nonidentifiability. PMID:21252079

Model-based estimation of individual fitness

USGS Publications Warehouse

Link, W.A.; Cooch, E.G.; Cam, E.

2002-01-01

Fitness is the currency of natural selection, a measure of the propagation rate of genotypes into future generations. Its various definitions have the common feature that they are functions of survival and fertility rates. At the individual level, the operative level for natural selection, these rates must be understood as latent features, genetically determined propensities existing at birth. This conception of rates requires that individual fitness be defined and estimated by consideration of the individual in a modelled relation to a group of similar individuals; the only alternative is to consider a sample of size one, unless a clone of identical individuals is available. We present hierarchical models describing individual heterogeneity in survival and fertility rates and allowing for associations between these rates at the individual level. We apply these models to an analysis of life histories of Kittiwakes (Rissa tridactyla ) observed at several colonies on the Brittany coast of France. We compare Bayesian estimation of the population distribution of individual fitness with estimation based on treating individual life histories in isolation, as samples of size one (e.g. McGraw & Caswell, 1996).

Predicting summer residential electricity demand across the U.S.A using climate information

NASA Astrophysics Data System (ADS)

Sun, X.; Wang, S.; Lall, U.

2017-12-01

We developed a Bayesian Hierarchical model to predict monthly residential per capita electricity consumption at the state level across the USA using climate information. The summer period was selected since cooling requirements may be directly associated with electricity use, while for winter a mix of energy sources may be used to meet heating needs. Historical monthly electricity consumption data from 1990 to 2013 were used to build a predictive model with a set of corresponding climate and non-climate covariates. A clustering analysis was performed first to identify groups of states that had similar temporal patterns for the cooling degree days of each state. Then, a partial pooling model was applied to each cluster to assess the sensitivity of monthly per capita residential electricity demand to each predictor (including cooling-degree-days, gross domestic product (GDP) per capita, per capita electricity demand of previous month and previous year, and the residential electricity price). The sensitivity of residential electricity to cooling-degree-days has an identifiable geographic distribution with higher values in northeastern United States.

Quantifying the Strength of General Factors in Psychopathology: A Comparison of CFA with Maximum Likelihood Estimation, BSEM, and ESEM/EFA Bifactor Approaches.

PubMed

Murray, Aja Louise; Booth, Tom; Eisner, Manuel; Obsuth, Ingrid; Ribeaud, Denis

2018-05-22

Whether or not importance should be placed on an all-encompassing general factor of psychopathology (or p factor) in classifying, researching, diagnosing, and treating psychiatric disorders depends (among other issues) on the extent to which comorbidity is symptom-general rather than staying largely within the confines of narrower transdiagnostic factors such as internalizing and externalizing. In this study, we compared three methods of estimating p factor strength. We compared omega hierarchical and explained common variance calculated from confirmatory factor analysis (CFA) bifactor models with maximum likelihood (ML) estimation, from exploratory structural equation modeling/exploratory factor analysis models with a bifactor rotation, and from Bayesian structural equation modeling (BSEM) bifactor models. Our simulation results suggested that BSEM with small variance priors on secondary loadings might be the preferred option. However, CFA with ML also performed well provided secondary loadings were modeled. We provide two empirical examples of applying the three methodologies using a normative sample of youth (z-proso, n = 1,286) and a university counseling sample (n = 359).

A powerful and flexible statistical framework for testing hypotheses of allele-specific gene expression from RNA-seq data

PubMed Central

Skelly, Daniel A.; Johansson, Marnie; Madeoy, Jennifer; Wakefield, Jon; Akey, Joshua M.

2011-01-01

Variation in gene expression is thought to make a significant contribution to phenotypic diversity among individuals within populations. Although high-throughput cDNA sequencing offers a unique opportunity to delineate the genome-wide architecture of regulatory variation, new statistical methods need to be developed to capitalize on the wealth of information contained in RNA-seq data sets. To this end, we developed a powerful and flexible hierarchical Bayesian model that combines information across loci to allow both global and locus-specific inferences about allele-specific expression (ASE). We applied our methodology to a large RNA-seq data set obtained in a diploid hybrid of two diverse Saccharomyces cerevisiae strains, as well as to RNA-seq data from an individual human genome. Our statistical framework accurately quantifies levels of ASE with specified false-discovery rates, achieving high reproducibility between independent sequencing platforms. We pinpoint loci that show unusual and biologically interesting patterns of ASE, including allele-specific alternative splicing and transcription termination sites. Our methodology provides a rigorous, quantitative, and high-resolution tool for profiling ASE across whole genomes. PMID:21873452

Statistical tools for analysis and modeling of cosmic populations and astronomical time series: CUDAHM and TSE

NASA Astrophysics Data System (ADS)

Loredo, Thomas; Budavari, Tamas; Scargle, Jeffrey D.

2018-01-01

This presentation provides an overview of open-source software packages addressing two challenging classes of astrostatistics problems. (1) CUDAHM is a C++ framework for hierarchical Bayesian modeling of cosmic populations, leveraging graphics processing units (GPUs) to enable applying this computationally challenging paradigm to large datasets. CUDAHM is motivated by measurement error problems in astronomy, where density estimation and linear and nonlinear regression must be addressed for populations of thousands to millions of objects whose features are measured with possibly complex uncertainties, potentially including selection effects. An example calculation demonstrates accurate GPU-accelerated luminosity function estimation for simulated populations of $10^6$ objects in about two hours using a single NVIDIA Tesla K40c GPU. (2) Time Series Explorer (TSE) is a collection of software in Python and MATLAB for exploratory analysis and statistical modeling of astronomical time series. It comprises a library of stand-alone functions and classes, as well as an application environment for interactive exploration of times series data. The presentation will summarize key capabilities of this emerging project, including new algorithms for analysis of irregularly-sampled time series.

Dynamic social networks based on movement

USGS Publications Warehouse

Scharf, Henry; Hooten, Mevin B.; Fosdick, Bailey K.; Johnson, Devin S.; London, Joshua M.; Durban, John W.

2016-01-01

Network modeling techniques provide a means for quantifying social structure in populations of individuals. Data used to define social connectivity are often expensive to collect and based on case-specific, ad hoc criteria. Moreover, in applications involving animal social networks, collection of these data is often opportunistic and can be invasive. Frequently, the social network of interest for a given population is closely related to the way individuals move. Thus, telemetry data, which are minimally invasive and relatively inexpensive to collect, present an alternative source of information. We develop a framework for using telemetry data to infer social relationships among animals. To achieve this, we propose a Bayesian hierarchical model with an underlying dynamic social network controlling movement of individuals via two mechanisms: an attractive effect and an aligning effect. We demonstrate the model and its ability to accurately identify complex social behavior in simulation, and apply our model to telemetry data arising from killer whales. Using auxiliary information about the study population, we investigate model validity and find the inferred dynamic social network is consistent with killer whale ecology and expert knowledge.

Bayesian multimodel inference for dose-response studies

USGS Publications Warehouse

Link, W.A.; Albers, P.H.

2007-01-01

Statistical inference in dose?response studies is model-based: The analyst posits a mathematical model of the relation between exposure and response, estimates parameters of the model, and reports conclusions conditional on the model. Such analyses rarely include any accounting for the uncertainties associated with model selection. The Bayesian inferential system provides a convenient framework for model selection and multimodel inference. In this paper we briefly describe the Bayesian paradigm and Bayesian multimodel inference. We then present a family of models for multinomial dose?response data and apply Bayesian multimodel inferential methods to the analysis of data on the reproductive success of American kestrels (Falco sparveriuss) exposed to various sublethal dietary concentrations of methylmercury.

Understanding movement data and movement processes: current and emerging directions.

PubMed

Schick, Robert S; Loarie, Scott R; Colchero, Fernando; Best, Benjamin D; Boustany, Andre; Conde, Dalia A; Halpin, Patrick N; Joppa, Lucas N; McClellan, Catherine M; Clark, James S

2008-12-01

Animal movement has been the focus on much theoretical and empirical work in ecology over the last 25 years. By studying the causes and consequences of individual movement, ecologists have gained greater insight into the behavior of individuals and the spatial dynamics of populations at increasingly higher levels of organization. In particular, ecologists have focused on the interaction between individuals and their environment in an effort to understand future impacts from habitat loss and climate change. Tools to examine this interaction have included: fractal analysis, first passage time, Lévy flights, multi-behavioral analysis, hidden markov models, and state-space models. Concurrent with the development of movement models has been an increase in the sophistication and availability of hierarchical bayesian models. In this review we bring these two threads together by using hierarchical structures as a framework for reviewing individual models. We synthesize emerging themes in movement ecology, and propose a new hierarchical model for animal movement that builds on these emerging themes. This model moves away from traditional random walks, and instead focuses inference on how moving animals with complex behavior interact with their landscape and make choices about its suitability.

Bayesian Inference for Functional Dynamics Exploring in fMRI Data.

PubMed

Guo, Xuan; Liu, Bing; Chen, Le; Chen, Guantao; Pan, Yi; Zhang, Jing

2016-01-01

This paper aims to review state-of-the-art Bayesian-inference-based methods applied to functional magnetic resonance imaging (fMRI) data. Particularly, we focus on one specific long-standing challenge in the computational modeling of fMRI datasets: how to effectively explore typical functional interactions from fMRI time series and the corresponding boundaries of temporal segments. Bayesian inference is a method of statistical inference which has been shown to be a powerful tool to encode dependence relationships among the variables with uncertainty. Here we provide an introduction to a group of Bayesian-inference-based methods for fMRI data analysis, which were designed to detect magnitude or functional connectivity change points and to infer their functional interaction patterns based on corresponding temporal boundaries. We also provide a comparison of three popular Bayesian models, that is, Bayesian Magnitude Change Point Model (BMCPM), Bayesian Connectivity Change Point Model (BCCPM), and Dynamic Bayesian Variable Partition Model (DBVPM), and give a summary of their applications. We envision that more delicate Bayesian inference models will be emerging and play increasingly important roles in modeling brain functions in the years to come.

A hierarchical perspective on the diversity of butterfly species' responses to weather in the Sierra Nevada Mountains.

PubMed

Nice, Chris C; Forister, Matthew L; Gompert, Zachariah; Fordyce, James A; Shapiro, Arthur M

2014-08-01

An important and largely unaddressed issue in studies of biotic-abiotic relationships is the extent to which closely related species, or species living in similar habitats, have similar responses to weather. We addressed this by applying a hierarchical, Bayesian analytical framework to a long-term data set for butterflies which allowed us to simultaneously investigate responses of the entire fauna and individual species. A small number of variables had community-level effects. In particular, higher total annual snow depth had a positive effect on butterfly occurrences, while spring minimum temperature and El Niño-Southern Oscillation (ENSO) sea-surface variables for April-May had negative standardized coefficients. Our most important finding was that variables with large impacts at the community-level did not necessarily have a consistent response across all species. Species-level responses were much more similar to each other for snow depth compared to the other variables with strong community effects. This variation in species-level responses to weather variables raises important complications for the prediction of biotic responses to shifting climatic conditions. In addition, we found that clear associations with weather can be detected when considering ecologically delimited subsets of the community. For example, resident species and non-ruderal species had a much more unified response to weather variables compared to non-resident species and ruderal species, which suggests local adaptation to climate. These results highlight the complexity of biotic-abiotic interactions and confront that complexity with methodological advances that allow ecologists to understand communities and shifting climates while simultaneously revealing species-specific variation in response to climate.

Search for Patterns of Functional Specificity in the Brain: A Nonparametric Hierarchical Bayesian Model for Group fMRI Data

PubMed Central

Sridharan, Ramesh; Vul, Edward; Hsieh, Po-Jang; Kanwisher, Nancy; Golland, Polina

2012-01-01

Functional MRI studies have uncovered a number of brain areas that demonstrate highly specific functional patterns. In the case of visual object recognition, small, focal regions have been characterized with selectivity for visual categories such as human faces. In this paper, we develop an algorithm that automatically learns patterns of functional specificity from fMRI data in a group of subjects. The method does not require spatial alignment of functional images from different subjects. The algorithm is based on a generative model that comprises two main layers. At the lower level, we express the functional brain response to each stimulus as a binary activation variable. At the next level, we define a prior over sets of activation variables in all subjects. We use a Hierarchical Dirichlet Process as the prior in order to learn the patterns of functional specificity shared across the group, which we call functional systems, and estimate the number of these systems. Inference based on our model enables automatic discovery and characterization of dominant and consistent functional systems. We apply the method to data from a visual fMRI study comprised of 69 distinct stimulus images. The discovered system activation profiles correspond to selectivity for a number of image categories such as faces, bodies, and scenes. Among systems found by our method, we identify new areas that are deactivated by face stimuli. In empirical comparisons with perviously proposed exploratory methods, our results appear superior in capturing the structure in the space of visual categories of stimuli. PMID:21884803

Moving beyond qualitative evaluations of Bayesian models of cognition.

PubMed

Hemmer, Pernille; Tauber, Sean; Steyvers, Mark

2015-06-01

Bayesian models of cognition provide a powerful way to understand the behavior and goals of individuals from a computational point of view. Much of the focus in the Bayesian cognitive modeling approach has been on qualitative model evaluations, where predictions from the models are compared to data that is often averaged over individuals. In many cognitive tasks, however, there are pervasive individual differences. We introduce an approach to directly infer individual differences related to subjective mental representations within the framework of Bayesian models of cognition. In this approach, Bayesian data analysis methods are used to estimate cognitive parameters and motivate the inference process within a Bayesian cognitive model. We illustrate this integrative Bayesian approach on a model of memory. We apply the model to behavioral data from a memory experiment involving the recall of heights of people. A cross-validation analysis shows that the Bayesian memory model with inferred subjective priors predicts withheld data better than a Bayesian model where the priors are based on environmental statistics. In addition, the model with inferred priors at the individual subject level led to the best overall generalization performance, suggesting that individual differences are important to consider in Bayesian models of cognition.

Tmax Determined Using a Bayesian Estimation Deconvolution Algorithm Applied to Bolus Tracking Perfusion Imaging: A Digital Phantom Validation Study.

PubMed

Uwano, Ikuko; Sasaki, Makoto; Kudo, Kohsuke; Boutelier, Timothé; Kameda, Hiroyuki; Mori, Futoshi; Yamashita, Fumio

2017-01-10

The Bayesian estimation algorithm improves the precision of bolus tracking perfusion imaging. However, this algorithm cannot directly calculate Tmax, the time scale widely used to identify ischemic penumbra, because Tmax is a non-physiological, artificial index that reflects the tracer arrival delay (TD) and other parameters. We calculated Tmax from the TD and mean transit time (MTT) obtained by the Bayesian algorithm and determined its accuracy in comparison with Tmax obtained by singular value decomposition (SVD) algorithms. The TD and MTT maps were generated by the Bayesian algorithm applied to digital phantoms with time-concentration curves that reflected a range of values for various perfusion metrics using a global arterial input function. Tmax was calculated from the TD and MTT using constants obtained by a linear least-squares fit to Tmax obtained from the two SVD algorithms that showed the best benchmarks in a previous study. Correlations between the Tmax values obtained by the Bayesian and SVD methods were examined. The Bayesian algorithm yielded accurate TD and MTT values relative to the true values of the digital phantom. Tmax calculated from the TD and MTT values with the least-squares fit constants showed excellent correlation (Pearson's correlation coefficient = 0.99) and agreement (intraclass correlation coefficient = 0.99) with Tmax obtained from SVD algorithms. Quantitative analyses of Tmax values calculated from Bayesian-estimation algorithm-derived TD and MTT from a digital phantom correlated and agreed well with Tmax values determined using SVD algorithms.

[Bayesian statistics in medicine -- part II: main applications and inference].

PubMed

Montomoli, C; Nichelatti, M

2008-01-01

Bayesian statistics is not only used when one is dealing with 2-way tables, but it can be used for inferential purposes. Using the basic concepts presented in the first part, this paper aims to give a simple overview of Bayesian methods by introducing its foundation (Bayes' theorem) and then applying this rule to a very simple practical example; whenever possible, the elementary processes at the basis of analysis are compared to those of frequentist (classical) statistical analysis. The Bayesian reasoning is naturally connected to medical activity, since it appears to be quite similar to a diagnostic process.

The Bayesian approach to reporting GSR analysis results: some first-hand experiences

NASA Astrophysics Data System (ADS)

Charles, Sebastien; Nys, Bart

2010-06-01

The use of Bayesian principles in the reporting of forensic findings has been a matter of interest for some years. Recently, also the GSR community is gradually exploring the advantages of this method, or rather approach, for writing reports. Since last year, our GSR group is adapting reporting procedures to the use of Bayesian principles. The police and magistrates find the reports more directly accessible and useful in their part of the criminal investigation. In the lab we find that, through applying the Bayesian principles, unnecessary analyses can be eliminated and thus time can be freed on the instruments.

F-MAP: A Bayesian approach to infer the gene regulatory network using external hints

PubMed Central

Shahdoust, Maryam; Mahjub, Hossein; Sadeghi, Mehdi

2017-01-01

The Common topological features of related species gene regulatory networks suggest reconstruction of the network of one species by using the further information from gene expressions profile of related species. We present an algorithm to reconstruct the gene regulatory network named; F-MAP, which applies the knowledge about gene interactions from related species. Our algorithm sets a Bayesian framework to estimate the precision matrix of one species microarray gene expressions dataset to infer the Gaussian Graphical model of the network. The conjugate Wishart prior is used and the information from related species is applied to estimate the hyperparameters of the prior distribution by using the factor analysis. Applying the proposed algorithm on six related species of drosophila shows that the precision of reconstructed networks is improved considerably compared to the precision of networks constructed by other Bayesian approaches. PMID:28938012

Constraint of soil moisture on CO2 efflux from tundra lichen, moss, and tussock in Council, Alaska, using a hierarchical Bayesian model

NASA Astrophysics Data System (ADS)

Kim, Y.; Nishina, K.; Chae, N.; Park, S. J.; Yoon, Y. J.; Lee, B. Y.

2014-10-01

The tundra ecosystem is quite vulnerable to drastic climate change in the Arctic, and the quantification of carbon dynamics is of significant importance regarding thawing permafrost, changes to the snow-covered period and snow and shrub community extent, and the decline of sea ice in the Arctic. Here, CO2 efflux measurements using a manual chamber system within a 40 m × 40 m (5 m interval; 81 total points) plot were conducted within dominant tundra vegetation on the Seward Peninsula of Alaska, during the growing seasons of 2011 and 2012, for the assessment of driving parameters of CO2 efflux. We applied a hierarchical Bayesian (HB) model - a function of soil temperature, soil moisture, vegetation type, and thaw depth - to quantify the effects of environmental factors on CO2 efflux and to estimate growing season CO2 emissions. Our results showed that average CO2 efflux in 2011 was 1.4 times higher than in 2012, resulting from the distinct difference in soil moisture between the 2 years. Tussock-dominated CO2 efflux is 1.4 to 2.3 times higher than those measured in lichen and moss communities, revealing tussock as a significant CO2 source in the Arctic, with a wide area distribution on the circumpolar scale. CO2 efflux followed soil temperature nearly exponentially from both the observed data and the posterior medians of the HB model. This reveals that soil temperature regulates the seasonal variation of CO2 efflux and that soil moisture contributes to the interannual variation of CO2 efflux for the two growing seasons in question. Obvious changes in soil moisture during the growing seasons of 2011 and 2012 resulted in an explicit difference between CO2 effluxes - 742 and 539 g CO2 m-2 period-1 for 2011 and 2012, respectively, suggesting the 2012 CO2 emission rate was reduced to 27% (95% credible interval: 17-36%) of the 2011 emission, due to higher soil moisture from severe rain. The estimated growing season CO2 emission rate ranged from 0.86 Mg CO2 in 2012 to 1.20 Mg CO2 in 2011 within a 40 m × 40 m plot, corresponding to 86 and 80% of annual CO2 emission rates within the western Alaska tundra ecosystem, estimated from the temperature dependence of CO2 efflux. Therefore, this HB model can be readily applied to observed CO2 efflux, as it demands only four environmental factors and can also be effective for quantitatively assessing the driving parameters of CO2 efflux.

Bayesian Analysis of High Dimensional Classification

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Subhadeep; Liang, Faming

2009-12-01

Modern data mining and bioinformatics have presented an important playground for statistical learning techniques, where the number of input variables is possibly much larger than the sample size of the training data. In supervised learning, logistic regression or probit regression can be used to model a binary output and form perceptron classification rules based on Bayesian inference. In these cases , there is a lot of interest in searching for sparse model in High Dimensional regression(/classification) setup. we first discuss two common challenges for analyzing high dimensional data. The first one is the curse of dimensionality. The complexity of many existing algorithms scale exponentially with the dimensionality of the space and by virtue of that algorithms soon become computationally intractable and therefore inapplicable in many real applications. secondly, multicollinearities among the predictors which severely slowdown the algorithm. In order to make Bayesian analysis operational in high dimension we propose a novel 'Hierarchical stochastic approximation monte carlo algorithm' (HSAMC), which overcomes the curse of dimensionality, multicollinearity of predictors in high dimension and also it possesses the self-adjusting mechanism to avoid the local minima separated by high energy barriers. Models and methods are illustrated by simulation inspired from from the feild of genomics. Numerical results indicate that HSAMC can work as a general model selection sampler in high dimensional complex model space.

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.

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