Bayesian parameter estimation of a k-ε model for accurate jet-in-crossflow simulations

DOE PAGES

Ray, Jaideep; Lefantzi, Sophia; Arunajatesan, Srinivasan; ...

2016-05-31

Reynolds-averaged Navier–Stokes models are not very accurate for high-Reynolds-number compressible jet-in-crossflow interactions. The inaccuracy arises from the use of inappropriate model parameters and model-form errors in the Reynolds-averaged Navier–Stokes model. In this study, the hypothesis is pursued that Reynolds-averaged Navier–Stokes predictions can be significantly improved by using parameters inferred from experimental measurements of a supersonic jet interacting with a transonic crossflow.

Bayesian Image Segmentations by Potts Prior and Loopy Belief Propagation

NASA Astrophysics Data System (ADS)

Tanaka, Kazuyuki; Kataoka, Shun; Yasuda, Muneki; Waizumi, Yuji; Hsu, Chiou-Ting

2014-12-01

This paper presents a Bayesian image segmentation model based on Potts prior and loopy belief propagation. The proposed Bayesian model involves several terms, including the pairwise interactions of Potts models, and the average vectors and covariant matrices of Gauss distributions in color image modeling. These terms are often referred to as hyperparameters in statistical machine learning theory. In order to determine these hyperparameters, we propose a new scheme for hyperparameter estimation based on conditional maximization of entropy in the Potts prior. The algorithm is given based on loopy belief propagation. In addition, we compare our conditional maximum entropy framework with the conventional maximum likelihood framework, and also clarify how the first order phase transitions in loopy belief propagations for Potts models influence our hyperparameter estimation procedures.

Encoding probabilistic brain atlases using Bayesian inference.

PubMed

Van Leemput, Koen

2009-06-01

This paper addresses the problem of creating probabilistic brain atlases from manually labeled training data. Probabilistic atlases are typically constructed by counting the relative frequency of occurrence of labels in corresponding locations across the training images. However, such an "averaging" approach generalizes poorly to unseen cases when the number of training images is limited, and provides no principled way of aligning the training datasets using deformable registration. In this paper, we generalize the generative image model implicitly underlying standard "average" atlases, using mesh-based representations endowed with an explicit deformation model. Bayesian inference is used to infer the optimal model parameters from the training data, leading to a simultaneous group-wise registration and atlas estimation scheme that encompasses standard averaging as a special case. We also use Bayesian inference to compare alternative atlas models in light of the training data, and show how this leads to a data compression problem that is intuitive to interpret and computationally feasible. Using this technique, we automatically determine the optimal amount of spatial blurring, the best deformation field flexibility, and the most compact mesh representation. We demonstrate, using 2-D training datasets, that the resulting models are better at capturing the structure in the training data than conventional probabilistic atlases. We also present experiments of the proposed atlas construction technique in 3-D, and show the resulting atlases' potential in fully-automated, pulse sequence-adaptive segmentation of 36 neuroanatomical structures in brain MRI scans.

Hyperspectral remote sensing of plant biochemistry using Bayesian model averaging with variable and band selection

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

Zhao, Kaiguang; Valle, Denis; Popescu, Sorin

2013-05-15

Model specification remains challenging in spectroscopy of plant biochemistry, as exemplified by the availability of various spectral indices or band combinations for estimating the same biochemical. This lack of consensus in model choice across applications argues for a paradigm shift in hyperspectral methods to address model uncertainty and misspecification. We demonstrated one such method using Bayesian model averaging (BMA), which performs variable/band selection and quantifies the relative merits of many candidate models to synthesize a weighted average model with improved predictive performances. The utility of BMA was examined using a portfolio of 27 foliage spectral–chemical datasets representing over 80 speciesmore » across the globe to estimate multiple biochemical properties, including nitrogen, hydrogen, carbon, cellulose, lignin, chlorophyll (a or b), carotenoid, polar and nonpolar extractives, leaf mass per area, and equivalent water thickness. We also compared BMA with partial least squares (PLS) and stepwise multiple regression (SMR). Results showed that all the biochemicals except carotenoid were accurately estimated from hyerspectral data with R2 values > 0.80.« less

Metainference: A Bayesian inference method for heterogeneous systems.

PubMed

Bonomi, Massimiliano; Camilloni, Carlo; Cavalli, Andrea; Vendruscolo, Michele

2016-01-01

Modeling a complex system is almost invariably a challenging task. The incorporation of experimental observations can be used to improve the quality of a model and thus to obtain better predictions about the behavior of the corresponding system. This approach, however, is affected by a variety of different errors, especially when a system simultaneously populates an ensemble of different states and experimental data are measured as averages over such states. To address this problem, we present a Bayesian inference method, called "metainference," that is able to deal with errors in experimental measurements and with experimental measurements averaged over multiple states. To achieve this goal, metainference models a finite sample of the distribution of models using a replica approach, in the spirit of the replica-averaging modeling based on the maximum entropy principle. To illustrate the method, we present its application to a heterogeneous model system and to the determination of an ensemble of structures corresponding to the thermal fluctuations of a protein molecule. Metainference thus provides an approach to modeling complex systems with heterogeneous components and interconverting between different states by taking into account all possible sources of errors.

Reducing the Uncertainty in Atlantic Meridional Overturning Circulation Projections Using Bayesian Model Averaging

NASA Astrophysics Data System (ADS)

Olson, R.; An, S. I.

2016-12-01

Atlantic Meridional Overturning Circulation (AMOC) in the ocean might slow down in the future, which can lead to a host of climatic effects in North Atlantic and throughout the world. Despite improvements in climate models and availability of new observations, AMOC projections remain uncertain. Here we constrain CMIP5 multi-model ensemble output with observations of a recently developed AMOC index to provide improved Bayesian predictions of future AMOC. Specifically, we first calculate yearly AMOC index loosely based on Rahmstorf et al. (2015) for years 1880—2004 for both observations, and the CMIP5 models for which relevant output is available. We then assign a weight to each model based on a Bayesian Model Averaging method that accounts for differential model skill in terms of both mean state and variability. We include the temporal autocorrelation in climate model errors, and account for the uncertainty in the parameters of our statistical model. We use the weights to provide future weighted projections of AMOC, and compare them to un-weighted ones. Our projections use bootstrapping to account for uncertainty in internal AMOC variability. We also perform spectral and other statistical analyses to show that AMOC index variability, both in models and in observations, is consistent with red noise. Our results improve on and complement previous work by using a new ensemble of climate models, a different observational metric, and an improved Bayesian weighting method that accounts for differential model skill at reproducing internal variability. Reference: Rahmstorf, S., Box, J. E., Feulner, G., Mann, M. E., Robinson, A., Rutherford, S., & Schaffernicht, E. J. (2015). Exceptional twentieth-century slowdown in atlantic ocean overturning circulation. Nature Climate Change, 5(5), 475-480. doi:10.1038/nclimate2554

A Bayesian network model for predicting pregnancy after in vitro fertilization.

PubMed

Corani, G; Magli, C; Giusti, A; Gianaroli, L; Gambardella, L M

2013-11-01

We present a Bayesian network model for predicting the outcome of in vitro fertilization (IVF). The problem is characterized by a particular missingness process; we propose a simple but effective averaging approach which improves parameter estimates compared to the traditional MAP estimation. We present results with generated data and the analysis of a real data set. Moreover, we assess by means of a simulation study the effectiveness of the model in supporting the selection of the embryos to be transferred. © 2013 Elsevier Ltd. All rights reserved.

Bayesian model selection: Evidence estimation based on DREAM simulation and bridge sampling

NASA Astrophysics Data System (ADS)

Volpi, Elena; Schoups, Gerrit; Firmani, Giovanni; Vrugt, Jasper A.

2017-04-01

Bayesian inference has found widespread application in Earth and Environmental Systems Modeling, providing an effective tool for prediction, data assimilation, parameter estimation, uncertainty analysis and hypothesis testing. Under multiple competing hypotheses, the Bayesian approach also provides an attractive alternative to traditional information criteria (e.g. AIC, BIC) for model selection. The key variable for Bayesian model selection is the evidence (or marginal likelihood) that is the normalizing constant in the denominator of Bayes theorem; while it is fundamental for model selection, the evidence is not required for Bayesian inference. It is computed for each hypothesis (model) by averaging the likelihood function over the prior parameter distribution, rather than maximizing it as by information criteria; the larger a model evidence the more support it receives among a collection of hypothesis as the simulated values assign relatively high probability density to the observed data. Hence, the evidence naturally acts as an Occam's razor, preferring simpler and more constrained models against the selection of over-fitted ones by information criteria that incorporate only the likelihood maximum. Since it is not particularly easy to estimate the evidence in practice, Bayesian model selection via the marginal likelihood has not yet found mainstream use. We illustrate here the properties of a new estimator of the Bayesian model evidence, which provides robust and unbiased estimates of the marginal likelihood; the method is coined Gaussian Mixture Importance Sampling (GMIS). GMIS uses multidimensional numerical integration of the posterior parameter distribution via bridge sampling (a generalization of importance sampling) of a mixture distribution fitted to samples of the posterior distribution derived from the DREAM algorithm (Vrugt et al., 2008; 2009). Some illustrative examples are presented to show the robustness and superiority of the GMIS estimator with respect to other commonly used approaches in the literature.

a Bayesian Synthesis of Predictions from Different Models for Setting Water Quality Criteria

NASA Astrophysics Data System (ADS)

Arhonditsis, G. B.; Ecological Modelling Laboratory

2011-12-01

Skeptical views of the scientific value of modelling argue that there is no true model of an ecological system, but rather several adequate descriptions of different conceptual basis and structure. In this regard, rather than picking the single "best-fit" model to predict future system responses, we can use Bayesian model averaging to synthesize the forecasts from different models. Hence, by acknowledging that models from different areas of the complexity spectrum have different strengths and weaknesses, the Bayesian model averaging is an appealing approach to improve the predictive capacity and to overcome the ambiguity surrounding the model selection or the risk of basing ecological forecasts on a single model. Our study addresses this question using a complex ecological model, developed by Ramin et al. (2011; Environ Modell Softw 26, 337-353) to guide the water quality criteria setting process in the Hamilton Harbour (Ontario, Canada), along with a simpler plankton model that considers the interplay among phosphate, detritus, and generic phytoplankton and zooplankton state variables. This simple approach is more easily subjected to detailed sensitivity analysis and also has the advantage of fewer unconstrained parameters. Using Markov Chain Monte Carlo simulations, we calculate the relative mean standard error to assess the posterior support of the two models from the existing data. Predictions from the two models are then combined using the respective standard error estimates as weights in a weighted model average. The model averaging approach is used to examine the robustness of predictive statements made from our earlier work regarding the response of Hamilton Harbour to the different nutrient loading reduction strategies. The two eutrophication models are then used in conjunction with the SPAtially Referenced Regressions On Watershed attributes (SPARROW) watershed model. The Bayesian nature of our work is used: (i) to alleviate problems of spatiotemporal resolution mismatch between watershed and receiving waterbody models; and (ii) to overcome the conceptual or scale misalignment between processes of interest and supporting information. The proposed Bayesian approach provides an effective means of empirically estimating the relation between in-stream measurements of nutrient fluxes and the sources/sinks of nutrients within the watershed, while explicitly accounting for the uncertainty associated with the existing knowledge from the system along with the different types of spatial correlation typically underlying the parameter estimation of watershed models. Our modelling exercise offers the first estimates of the export coefficients and the delivery rates from the different subcatchments and thus generates testable hypotheses regarding the nutrient export "hot spots" in the studied watershed. Finally, we conduct modeling experiments that evaluate the potential improvement of the model parameter estimates and the decrease of the predictive uncertainty, if the uncertainty associated with the contemporary nutrient loading estimates is reduced. The lessons learned from this study will contribute towards the development of integrated modelling frameworks.

Spatio-temporal interpolation of precipitation during monsoon periods in Pakistan

NASA Astrophysics Data System (ADS)

Hussain, Ijaz; Spöck, Gunter; Pilz, Jürgen; Yu, Hwa-Lung

2010-08-01

Spatio-temporal estimation of precipitation over a region is essential to the modeling of hydrologic processes for water resources management. The changes of magnitude and space-time heterogeneity of rainfall observations make space-time estimation of precipitation a challenging task. In this paper we propose a Box-Cox transformed hierarchical Bayesian multivariate spatio-temporal interpolation method for the skewed response variable. The proposed method is applied to estimate space-time monthly precipitation in the monsoon periods during 1974-2000, and 27-year monthly average precipitation data are obtained from 51 stations in Pakistan. The results of transformed hierarchical Bayesian multivariate spatio-temporal interpolation are compared to those of non-transformed hierarchical Bayesian interpolation by using cross-validation. The software developed by [11] is used for Bayesian non-stationary multivariate space-time interpolation. It is observed that the transformed hierarchical Bayesian method provides more accuracy than the non-transformed hierarchical Bayesian method.

Influence of Averaging Preprocessing on Image Analysis with a Markov Random Field Model

NASA Astrophysics Data System (ADS)

Sakamoto, Hirotaka; Nakanishi-Ohno, Yoshinori; Okada, Masato

2018-02-01

This paper describes our investigations into the influence of averaging preprocessing on the performance of image analysis. Averaging preprocessing involves a trade-off: image averaging is often undertaken to reduce noise while the number of image data available for image analysis is decreased. We formulated a process of generating image data by using a Markov random field (MRF) model to achieve image analysis tasks such as image restoration and hyper-parameter estimation by a Bayesian approach. According to the notions of Bayesian inference, posterior distributions were analyzed to evaluate the influence of averaging. There are three main results. First, we found that the performance of image restoration with a predetermined value for hyper-parameters is invariant regardless of whether averaging is conducted. We then found that the performance of hyper-parameter estimation deteriorates due to averaging. Our analysis of the negative logarithm of the posterior probability, which is called the free energy based on an analogy with statistical mechanics, indicated that the confidence of hyper-parameter estimation remains higher without averaging. Finally, we found that when the hyper-parameters are estimated from the data, the performance of image restoration worsens as averaging is undertaken. We conclude that averaging adversely influences the performance of image analysis through hyper-parameter estimation.

ENSURF: multi-model sea level forecast - implementation and validation results for the IBIROOS and Western Mediterranean regions

NASA Astrophysics Data System (ADS)

Pérez, B.; Brouwer, R.; Beckers, J.; Paradis, D.; Balseiro, C.; Lyons, K.; Cure, M.; Sotillo, M. G.; Hackett, B.; Verlaan, M.; Fanjul, E. A.

2012-03-01

ENSURF (Ensemble SURge Forecast) is a multi-model application for sea level forecast that makes use of several storm surge or circulation models and near-real time tide gauge data in the region, with the following main goals: 1. providing easy access to existing forecasts, as well as to its performance and model validation, by means of an adequate visualization tool; 2. generation of better forecasts of sea level, including confidence intervals, by means of the Bayesian Model Average technique (BMA). The Bayesian Model Average technique generates an overall forecast probability density function (PDF) by making a weighted average of the individual forecasts PDF's; the weights represent the Bayesian likelihood that a model will give the correct forecast and are continuously updated based on the performance of the models during a recent training period. This implies the technique needs the availability of sea level data from tide gauges in near-real time. The system was implemented for the European Atlantic facade (IBIROOS region) and Western Mediterranean coast based on the MATROOS visualization tool developed by Deltares. Results of validation of the different models and BMA implementation for the main harbours are presented for these regions where this kind of activity is performed for the first time. The system is currently operational at Puertos del Estado and has proved to be useful in the detection of calibration problems in some of the circulation models, in the identification of the systematic differences between baroclinic and barotropic models for sea level forecasts and to demonstrate the feasibility of providing an overall probabilistic forecast, based on the BMA method.

Bayesian model averaging method for evaluating associations between air pollution and respiratory mortality: a time-series study

PubMed Central

Fang, Xin; Li, Runkui; Kan, Haidong; Bottai, Matteo; Fang, Fang

2016-01-01

Objective To demonstrate an application of Bayesian model averaging (BMA) with generalised additive mixed models (GAMM) and provide a novel modelling technique to assess the association between inhalable coarse particles (PM10) and respiratory mortality in time-series studies. Design A time-series study using regional death registry between 2009 and 2010. Setting 8 districts in a large metropolitan area in Northern China. Participants 9559 permanent residents of the 8 districts who died of respiratory diseases between 2009 and 2010. Main outcome measures Per cent increase in daily respiratory mortality rate (MR) per interquartile range (IQR) increase of PM10 concentration and corresponding 95% confidence interval (CI) in single-pollutant and multipollutant (including NOx, CO) models. Results The Bayesian model averaged GAMM (GAMM+BMA) and the optimal GAMM of PM10, multipollutants and principal components (PCs) of multipollutants showed comparable results for the effect of PM10 on daily respiratory MR, that is, one IQR increase in PM10 concentration corresponded to 1.38% vs 1.39%, 1.81% vs 1.83% and 0.87% vs 0.88% increase, respectively, in daily respiratory MR. However, GAMM+BMA gave slightly but noticeable wider CIs for the single-pollutant model (−1.09 to 4.28 vs −1.08 to 3.93) and the PCs-based model (−2.23 to 4.07 vs −2.03 vs 3.88). The CIs of the multiple-pollutant model from two methods are similar, that is, −1.12 to 4.85 versus −1.11 versus 4.83. Conclusions The BMA method may represent a useful tool for modelling uncertainty in time-series studies when evaluating the effect of air pollution on fatal health outcomes. PMID:27531727

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.

Comparing interval estimates for small sample ordinal CFA models

PubMed Central

Natesan, Prathiba

2015-01-01

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

Comparing interval estimates for small sample ordinal CFA models.

PubMed

Natesan, Prathiba

2015-01-01

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

Metainference: A Bayesian inference method for heterogeneous systems

PubMed Central

Bonomi, Massimiliano; Camilloni, Carlo; Cavalli, Andrea; Vendruscolo, Michele

2016-01-01

Modeling a complex system is almost invariably a challenging task. The incorporation of experimental observations can be used to improve the quality of a model and thus to obtain better predictions about the behavior of the corresponding system. This approach, however, is affected by a variety of different errors, especially when a system simultaneously populates an ensemble of different states and experimental data are measured as averages over such states. To address this problem, we present a Bayesian inference method, called “metainference,” that is able to deal with errors in experimental measurements and with experimental measurements averaged over multiple states. To achieve this goal, metainference models a finite sample of the distribution of models using a replica approach, in the spirit of the replica-averaging modeling based on the maximum entropy principle. To illustrate the method, we present its application to a heterogeneous model system and to the determination of an ensemble of structures corresponding to the thermal fluctuations of a protein molecule. Metainference thus provides an approach to modeling complex systems with heterogeneous components and interconverting between different states by taking into account all possible sources of errors. PMID:26844300

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).

Multi-Model Ensemble Wake Vortex Prediction

NASA Technical Reports Server (NTRS)

Koerner, Stephan; Holzaepfel, Frank; Ahmad, Nash'at N.

2015-01-01

Several multi-model ensemble methods are investigated for predicting wake vortex transport and decay. This study is a joint effort between National Aeronautics and Space Administration and Deutsches Zentrum fuer Luft- und Raumfahrt to develop a multi-model ensemble capability using their wake models. An overview of different multi-model ensemble methods and their feasibility for wake applications is presented. The methods include Reliability Ensemble Averaging, Bayesian Model Averaging, and Monte Carlo Simulations. The methodologies are evaluated using data from wake vortex field experiments.

Data free inference with processed data products

DOE PAGES

Chowdhary, K.; Najm, H. N.

2014-07-12

Here, we consider the context of probabilistic inference of model parameters given error bars or confidence intervals on model output values, when the data is unavailable. We introduce a class of algorithms in a Bayesian framework, relying on maximum entropy arguments and approximate Bayesian computation methods, to generate consistent data with the given summary statistics. Once we obtain consistent data sets, we pool the respective posteriors, to arrive at a single, averaged density on the parameters. This approach allows us to perform accurate forward uncertainty propagation consistent with the reported statistics.

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.

A Bayesian model averaging approach for estimating the relative risk of mortality associated with heat waves in 105 U.S. cities.

PubMed

Bobb, Jennifer F; Dominici, Francesca; Peng, Roger D

2011-12-01

Estimating the risks heat waves pose to human health is a critical part of assessing the future impact of climate change. In this article, we propose a flexible class of time series models to estimate the relative risk of mortality associated with heat waves and conduct Bayesian model averaging (BMA) to account for the multiplicity of potential models. Applying these methods to data from 105 U.S. cities for the period 1987-2005, we identify those cities having a high posterior probability of increased mortality risk during heat waves, examine the heterogeneity of the posterior distributions of mortality risk across cities, assess sensitivity of the results to the selection of prior distributions, and compare our BMA results to a model selection approach. Our results show that no single model best predicts risk across the majority of cities, and that for some cities heat-wave risk estimation is sensitive to model choice. Although model averaging leads to posterior distributions with increased variance as compared to statistical inference conditional on a model obtained through model selection, we find that the posterior mean of heat wave mortality risk is robust to accounting for model uncertainty over a broad class of models. © 2011, The International Biometric Society.

Model Uncertainty and Bayesian Model Averaged Benchmark Dose Estimation for Continuous Data

EPA Science Inventory

The benchmark dose (BMD) approach has gained acceptance as a valuable risk assessment tool, but risk assessors still face significant challenges associated with selecting an appropriate BMD/BMDL estimate from the results of a set of acceptable dose-response models. Current approa...

Predicting Football Matches Results using Bayesian Networks for English Premier League (EPL)

NASA Astrophysics Data System (ADS)

Razali, Nazim; Mustapha, Aida; Yatim, Faiz Ahmad; Aziz, Ruhaya Ab

2017-08-01

The issues of modeling asscoiation football prediction model has become increasingly popular in the last few years and many different approaches of prediction models have been proposed with the point of evaluating the attributes that lead a football team to lose, draw or win the match. There are three types of approaches has been considered for predicting football matches results which include statistical approaches, machine learning approaches and Bayesian approaches. Lately, many studies regarding football prediction models has been produced using Bayesian approaches. This paper proposes a Bayesian Networks (BNs) to predict the results of football matches in term of home win (H), away win (A) and draw (D). The English Premier League (EPL) for three seasons of 2010-2011, 2011-2012 and 2012-2013 has been selected and reviewed. K-fold cross validation has been used for testing the accuracy of prediction model. The required information about the football data is sourced from a legitimate site at http://www.football-data.co.uk. BNs achieved predictive accuracy of 75.09% in average across three seasons. It is hoped that the results could be used as the benchmark output for future research in predicting football matches results.

Bayesian block-diagonal variable selection and model averaging

PubMed Central

Papaspiliopoulos, O.; Rossell, D.

2018-01-01

Summary We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general designs. In block-diagonal designs our approach returns the most probable model of any given size without resorting to numerical integration. The algorithm also provides a novel and efficient solution to the frequentist best subset selection problem for block-diagonal designs. Posterior probabilities for any number of models are obtained by evaluating a single one-dimensional integral, and other quantities of interest such as variable inclusion probabilities and model-averaged regression estimates are obtained by an adaptive, deterministic one-dimensional numerical integration. The overall computational cost scales linearly with the number of blocks, which can be processed in parallel, and exponentially with the block size, rendering it most adequate in situations where predictors are organized in many moderately-sized blocks. For general designs, we approximate the Gram matrix by a block-diagonal matrix using spectral clustering and propose an iterative algorithm that capitalizes on the block-diagonal algorithms to explore efficiently the model space. All methods proposed in this paper are implemented in the R library mombf. PMID:29861501

BUMPER v1.0: a Bayesian user-friendly model for palaeo-environmental reconstruction

NASA Astrophysics Data System (ADS)

Holden, Philip B.; Birks, H. John B.; Brooks, Stephen J.; Bush, Mark B.; Hwang, Grace M.; Matthews-Bird, Frazer; Valencia, Bryan G.; van Woesik, Robert

2017-02-01

We describe the Bayesian user-friendly model for palaeo-environmental reconstruction (BUMPER), a Bayesian transfer function for inferring past climate and other environmental variables from microfossil assemblages. BUMPER is fully self-calibrating, straightforward to apply, and computationally fast, requiring ˜ 2 s to build a 100-taxon model from a 100-site training set on a standard personal computer. We apply the model's probabilistic framework to generate thousands of artificial training sets under ideal assumptions. We then use these to demonstrate the sensitivity of reconstructions to the characteristics of the training set, considering assemblage richness, taxon tolerances, and the number of training sites. We find that a useful guideline for the size of a training set is to provide, on average, at least 10 samples of each taxon. We demonstrate general applicability to real data, considering three different organism types (chironomids, diatoms, pollen) and different reconstructed variables. An identically configured model is used in each application, the only change being the input files that provide the training-set environment and taxon-count data. The performance of BUMPER is shown to be comparable with weighted average partial least squares (WAPLS) in each case. Additional artificial datasets are constructed with similar characteristics to the real data, and these are used to explore the reasons for the differing performances of the different training sets.

Bayesian propensity scores for high-dimensional causal inference: A comparison of drug-eluting to bare-metal coronary stents.

PubMed

Spertus, Jacob V; Normand, Sharon-Lise T

2018-04-23

High-dimensional data provide many potential confounders that may bolster the plausibility of the ignorability assumption in causal inference problems. Propensity score methods are powerful causal inference tools, which are popular in health care research and are particularly useful for high-dimensional data. Recent interest has surrounded a Bayesian treatment of propensity scores in order to flexibly model the treatment assignment mechanism and summarize posterior quantities while incorporating variance from the treatment model. We discuss methods for Bayesian propensity score analysis of binary treatments, focusing on modern methods for high-dimensional Bayesian regression and the propagation of uncertainty. We introduce a novel and simple estimator for the average treatment effect that capitalizes on conjugacy of the beta and binomial distributions. Through simulations, we show the utility of horseshoe priors and Bayesian additive regression trees paired with our new estimator, while demonstrating the importance of including variance from the treatment regression model. An application to cardiac stent data with almost 500 confounders and 9000 patients illustrates approaches and facilitates comparison with existing alternatives. As measured by a falsifiability endpoint, we improved confounder adjustment compared with past observational research of the same problem. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

How robust are the estimated effects of air pollution on health? Accounting for model uncertainty using Bayesian model averaging.

PubMed

Pannullo, Francesca; Lee, Duncan; Waclawski, Eugene; Leyland, Alastair H

2016-08-01

The long-term impact of air pollution on human health can be estimated from small-area ecological studies in which the health outcome is regressed against air pollution concentrations and other covariates, such as socio-economic deprivation. Socio-economic deprivation is multi-factorial and difficult to measure, and includes aspects of income, education, and housing as well as others. However, these variables are potentially highly correlated, meaning one can either create an overall deprivation index, or use the individual characteristics, which can result in a variety of pollution-health effects. Other aspects of model choice may affect the pollution-health estimate, such as the estimation of pollution, and spatial autocorrelation model. Therefore, we propose a Bayesian model averaging approach to combine the results from multiple statistical models to produce a more robust representation of the overall pollution-health effect. We investigate the relationship between nitrogen dioxide concentrations and cardio-respiratory mortality in West Central Scotland between 2006 and 2012. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

Bayesian model averaging method for evaluating associations between air pollution and respiratory mortality: a time-series study.

PubMed

Fang, Xin; Li, Runkui; Kan, Haidong; Bottai, Matteo; Fang, Fang; Cao, Yang

2016-08-16

To demonstrate an application of Bayesian model averaging (BMA) with generalised additive mixed models (GAMM) and provide a novel modelling technique to assess the association between inhalable coarse particles (PM10) and respiratory mortality in time-series studies. A time-series study using regional death registry between 2009 and 2010. 8 districts in a large metropolitan area in Northern China. 9559 permanent residents of the 8 districts who died of respiratory diseases between 2009 and 2010. Per cent increase in daily respiratory mortality rate (MR) per interquartile range (IQR) increase of PM10 concentration and corresponding 95% confidence interval (CI) in single-pollutant and multipollutant (including NOx, CO) models. The Bayesian model averaged GAMM (GAMM+BMA) and the optimal GAMM of PM10, multipollutants and principal components (PCs) of multipollutants showed comparable results for the effect of PM10 on daily respiratory MR, that is, one IQR increase in PM10 concentration corresponded to 1.38% vs 1.39%, 1.81% vs 1.83% and 0.87% vs 0.88% increase, respectively, in daily respiratory MR. However, GAMM+BMA gave slightly but noticeable wider CIs for the single-pollutant model (-1.09 to 4.28 vs -1.08 to 3.93) and the PCs-based model (-2.23 to 4.07 vs -2.03 vs 3.88). The CIs of the multiple-pollutant model from two methods are similar, that is, -1.12 to 4.85 versus -1.11 versus 4.83. The BMA method may represent a useful tool for modelling uncertainty in time-series studies when evaluating the effect of air pollution on fatal health outcomes. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/

Bayesian approach to non-Gaussian field statistics for diffusive broadband terahertz pulses.

PubMed

Pearce, Jeremy; Jian, Zhongping; Mittleman, Daniel M

2005-11-01

We develop a closed-form expression for the probability distribution function for the field components of a diffusive broadband wave propagating through a random medium. We consider each spectral component to provide an individual observation of a random variable, the configurationally averaged spectral intensity. Since the intensity determines the variance of the field distribution at each frequency, this random variable serves as the Bayesian prior that determines the form of the non-Gaussian field statistics. This model agrees well with experimental results.

Exploiting Cross-sensitivity by Bayesian Decoding of Mixed Potential Sensor Arrays

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

Kreller, Cortney

LANL mixed-potential electrochemical sensor (MPES) device arrays were coupled with advanced Bayesian inference treatment of the physical model of relevant sensor-analyte interactions. We demonstrated that our approach could be used to uniquely discriminate the composition of ternary gas sensors with three discreet MPES sensors with an average error of less than 2%. We also observed that the MPES exhibited excellent stability over a year of operation at elevated temperatures in the presence of test gases.

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.

K-ε Turbulence Model Parameter Estimates Using an Approximate Self-similar Jet-in-Crossflow Solution

DOE PAGES

DeChant, Lawrence; Ray, Jaideep; Lefantzi, Sophia; ...

2017-06-09

The k-ε turbulence model has been described as perhaps “the most widely used complete turbulence model.” This family of heuristic Reynolds Averaged Navier-Stokes (RANS) turbulence closures is supported by a suite of model parameters that have been estimated by demanding the satisfaction of well-established canonical flows such as homogeneous shear flow, log-law behavior, etc. While this procedure does yield a set of so-called nominal parameters, it is abundantly clear that they do not provide a universally satisfactory turbulence model that is capable of simulating complex flows. Recent work on the Bayesian calibration of the k-ε model using jet-in-crossflow wind tunnelmore » data has yielded parameter estimates that are far more predictive than nominal parameter values. In this paper, we develop a self-similar asymptotic solution for axisymmetric jet-in-crossflow interactions and derive analytical estimates of the parameters that were inferred using Bayesian calibration. The self-similar method utilizes a near field approach to estimate the turbulence model parameters while retaining the classical far-field scaling to model flow field quantities. Our parameter values are seen to be far more predictive than the nominal values, as checked using RANS simulations and experimental measurements. They are also closer to the Bayesian estimates than the nominal parameters. A traditional simplified jet trajectory model is explicitly related to the turbulence model parameters and is shown to yield good agreement with measurement when utilizing the analytical derived turbulence model coefficients. Finally, the close agreement between the turbulence model coefficients obtained via Bayesian calibration and the analytically estimated coefficients derived in this paper is consistent with the contention that the Bayesian calibration approach is firmly rooted in the underlying physical description.« less

Accounting for uncertainty in health economic decision models by using model averaging.

PubMed

Jackson, Christopher H; Thompson, Simon G; Sharples, Linda D

2009-04-01

Health economic decision models are subject to considerable uncertainty, much of which arises from choices between several plausible model structures, e.g. choices of covariates in a regression model. Such structural uncertainty is rarely accounted for formally in decision models but can be addressed by model averaging. We discuss the most common methods of averaging models and the principles underlying them. We apply them to a comparison of two surgical techniques for repairing abdominal aortic aneurysms. In model averaging, competing models are usually either weighted by using an asymptotically consistent model assessment criterion, such as the Bayesian information criterion, or a measure of predictive ability, such as Akaike's information criterion. We argue that the predictive approach is more suitable when modelling the complex underlying processes of interest in health economics, such as individual disease progression and response to treatment.

Metadata Creation Tool Content Template For Data Stewards

EPA Science Inventory

A space-time Bayesian fusion model (McMillan, Holland, Morara, and Feng, 2009) is used to provide daily, gridded predictive PM_2.5 (daily average) and O₃ (daily 8-hr maximum) surfaces for 2001-2005. The fusion model uses both air quality monitoring data from ...

Using Bayes Model Averaging for Wind Power Forecasts

NASA Astrophysics Data System (ADS)

Preede Revheim, Pål; Beyer, Hans Georg

2014-05-01

For operational purposes predictions of the forecasts of the lumped output of groups of wind farms spread over larger geographic areas will often be of interest. A naive approach is to make forecasts for each individual site and sum them up to get the group forecast. It is however well documented that a better choice is to use a model that also takes advantage of spatial smoothing effects. It might however be the case that some sites tends to more accurately reflect the total output of the region, either in general or for certain wind directions. It will then be of interest giving these a greater influence over the group forecast. Bayesian model averaging (BMA) is a statistical post-processing method for producing probabilistic forecasts from ensembles. Raftery et al. [1] show how BMA can be used for statistical post processing of forecast ensembles, producing PDFs of future weather quantities. The BMA predictive PDF of a future weather quantity is a weighted average of the ensemble members' PDFs, where the weights can be interpreted as posterior probabilities and reflect the ensemble members' contribution to overall forecasting skill over a training period. In Revheim and Beyer [2] the BMA procedure used in Sloughter, Gneiting and Raftery [3] were found to produce fairly accurate PDFs for the future mean wind speed of a group of sites from the single sites wind speeds. However, when the procedure was attempted applied to wind power it resulted in either problems with the estimation of the parameters (mainly caused by longer consecutive periods of no power production) or severe underestimation (mainly caused by problems with reflecting the power curve). In this paper the problems that arose when applying BMA to wind power forecasting is met through two strategies. First, the BMA procedure is run with a combination of single site wind speeds and single site wind power production as input. This solves the problem with longer consecutive periods where the input data does not contain information, but it has the disadvantage of nearly doubling the number of model parameters to be estimated. Second, the BMA procedure is run with group mean wind power as the response variable instead of group mean wind speed. This also solves the problem with longer consecutive periods without information in the input data, but it leaves the power curve to also be estimated from the data. [1] Raftery, A. E., et al. (2005). Using Bayesian Model Averaging to Calibrate Forecast Ensembles. Monthly Weather Review, 133, 1155-1174. [2]Revheim, P. P. and H. G. Beyer (2013). Using Bayesian Model Averaging for wind farm group forecasts. EWEA Wind Power Forecasting Technology Workshop,Rotterdam, 4-5 December 2013. [3]Sloughter, J. M., T. Gneiting and A. E. Raftery (2010). Probabilistic Wind Speed Forecasting Using Ensembles and Bayesian Model Averaging. Journal of the American Statistical Association, Vol. 105, No. 489, 25-35

Multimodel Ensemble Methods for Prediction of Wake-Vortex Transport and Decay Originating NASA

NASA Technical Reports Server (NTRS)

Korner, Stephan; Ahmad, Nashat N.; Holzapfel, Frank; VanValkenburg, Randal L.

2017-01-01

Several multimodel ensemble methods are selected and further developed to improve the deterministic and probabilistic prediction skills of individual wake-vortex transport and decay models. The different multimodel ensemble methods are introduced, and their suitability for wake applications is demonstrated. The selected methods include direct ensemble averaging, Bayesian model averaging, and Monte Carlo simulation. The different methodologies are evaluated employing data from wake-vortex field measurement campaigns conducted in the United States and Germany.

Model-Averaged ℓ1 Regularization using Markov Chain Monte Carlo Model Composition

PubMed Central

Fraley, Chris; Percival, Daniel

2014-01-01

Bayesian Model Averaging (BMA) is an effective technique for addressing model uncertainty in variable selection problems. However, current BMA approaches have computational difficulty dealing with data in which there are many more measurements (variables) than samples. This paper presents a method for combining ℓ1 regularization and Markov chain Monte Carlo model composition techniques for BMA. By treating the ℓ1 regularization path as a model space, we propose a method to resolve the model uncertainty issues arising in model averaging from solution path point selection. We show that this method is computationally and empirically effective for regression and classification in high-dimensional datasets. We apply our technique in simulations, as well as to some applications that arise in genomics. PMID:25642001

Application Bayesian Model Averaging method for ensemble system for Poland

NASA Astrophysics Data System (ADS)

Guzikowski, Jakub; Czerwinska, Agnieszka

2014-05-01

The aim of the project is to evaluate methods for generating numerical ensemble weather prediction using a meteorological data from The Weather Research & Forecasting Model and calibrating this data by means of Bayesian Model Averaging (WRF BMA) approach. We are constructing height resolution short range ensemble forecasts using meteorological data (temperature) generated by nine WRF's models. WRF models have 35 vertical levels and 2.5 km x 2.5 km horizontal resolution. The main emphasis is that the used ensemble members has a different parameterization of the physical phenomena occurring in the boundary layer. To calibrate an ensemble forecast we use Bayesian Model Averaging (BMA) approach. The BMA predictive Probability Density Function (PDF) is a weighted average of predictive PDFs associated with each individual ensemble member, with weights that reflect the member's relative skill. For test we chose a case with heat wave and convective weather conditions in Poland area from 23th July to 1st August 2013. From 23th July to 29th July 2013 temperature oscillated below or above 30 Celsius degree in many meteorology stations and new temperature records were added. During this time the growth of the hospitalized patients with cardiovascular system problems was registered. On 29th July 2013 an advection of moist tropical air masses was recorded in the area of Poland causes strong convection event with mesoscale convection system (MCS). MCS caused local flooding, damage to the transport infrastructure, destroyed buildings, trees and injuries and direct threat of life. Comparison of the meteorological data from ensemble system with the data recorded on 74 weather stations localized in Poland is made. We prepare a set of the model - observations pairs. Then, the obtained data from single ensemble members and median from WRF BMA system are evaluated on the basis of the deterministic statistical error Root Mean Square Error (RMSE), Mean Absolute Error (MAE). To evaluation probabilistic data The Brier Score (BS) and Continuous Ranked Probability Score (CRPS) were used. Finally comparison between BMA calibrated data and data from ensemble members will be displayed.

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

PubMed Central

Raviv, Ofri; Ahissar, Merav; Loewenstein, Yonatan

2012-01-01

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

Accounting for uncertainty in health economic decision models by using model averaging

PubMed Central

Jackson, Christopher H; Thompson, Simon G; Sharples, Linda D

2009-01-01

Health economic decision models are subject to considerable uncertainty, much of which arises from choices between several plausible model structures, e.g. choices of covariates in a regression model. Such structural uncertainty is rarely accounted for formally in decision models but can be addressed by model averaging. We discuss the most common methods of averaging models and the principles underlying them. We apply them to a comparison of two surgical techniques for repairing abdominal aortic aneurysms. In model averaging, competing models are usually either weighted by using an asymptotically consistent model assessment criterion, such as the Bayesian information criterion, or a measure of predictive ability, such as Akaike's information criterion. We argue that the predictive approach is more suitable when modelling the complex underlying processes of interest in health economics, such as individual disease progression and response to treatment. PMID:19381329

Dynamic Model Averaging in Large Model Spaces Using Dynamic Occam's Window.

PubMed

Onorante, Luca; Raftery, Adrian E

2016-01-01

Bayesian model averaging has become a widely used approach to accounting for uncertainty about the structural form of the model generating the data. When data arrive sequentially and the generating model can change over time, Dynamic Model Averaging (DMA) extends model averaging to deal with this situation. Often in macroeconomics, however, many candidate explanatory variables are available and the number of possible models becomes too large for DMA to be applied in its original form. We propose a new method for this situation which allows us to perform DMA without considering the whole model space, but using a subset of models and dynamically optimizing the choice of models at each point in time. This yields a dynamic form of Occam's window. We evaluate the method in the context of the problem of nowcasting GDP in the Euro area. We find that its forecasting performance compares well with that of other methods.

Dynamic Model Averaging in Large Model Spaces Using Dynamic Occam’s Window*

PubMed Central

Onorante, Luca; Raftery, Adrian E.

2015-01-01

Bayesian model averaging has become a widely used approach to accounting for uncertainty about the structural form of the model generating the data. When data arrive sequentially and the generating model can change over time, Dynamic Model Averaging (DMA) extends model averaging to deal with this situation. Often in macroeconomics, however, many candidate explanatory variables are available and the number of possible models becomes too large for DMA to be applied in its original form. We propose a new method for this situation which allows us to perform DMA without considering the whole model space, but using a subset of models and dynamically optimizing the choice of models at each point in time. This yields a dynamic form of Occam’s window. We evaluate the method in the context of the problem of nowcasting GDP in the Euro area. We find that its forecasting performance compares well with that of other methods. PMID:26917859

Enhancing Flood Prediction Reliability Using Bayesian Model Averaging

NASA Astrophysics Data System (ADS)

Liu, Z.; Merwade, V.

2017-12-01

Uncertainty analysis is an indispensable part of modeling the hydrology and hydrodynamics of non-idealized environmental systems. Compared to reliance on prediction from one model simulation, using on ensemble of predictions that consider uncertainty from different sources is more reliable. In this study, Bayesian model averaging (BMA) is applied to Black River watershed in Arkansas and Missouri by combining multi-model simulations to get reliable deterministic water stage and probabilistic inundation extent predictions. The simulation ensemble is generated from 81 LISFLOOD-FP subgrid model configurations that include uncertainty from channel shape, channel width, channel roughness and discharge. Model simulation outputs are trained with observed water stage data during one flood event, and BMA prediction ability is validated for another flood event. Results from this study indicate that BMA does not always outperform all members in the ensemble, but it provides relatively robust deterministic flood stage predictions across the basin. Station based BMA (BMA_S) water stage prediction has better performance than global based BMA (BMA_G) prediction which is superior to the ensemble mean prediction. Additionally, high-frequency flood inundation extent (probability greater than 60%) in BMA_G probabilistic map is more accurate than the probabilistic flood inundation extent based on equal weights.

Using Bayesian Model Averaging (BMA) to calibrate probabilistic surface temperature forecasts over Iran

NASA Astrophysics Data System (ADS)

Soltanzadeh, I.; Azadi, M.; Vakili, G. A.

2011-07-01

Using Bayesian Model Averaging (BMA), an attempt was made to obtain calibrated probabilistic numerical forecasts of 2-m temperature over Iran. The ensemble employs three limited area models (WRF, MM5 and HRM), with WRF used with five different configurations. Initial and boundary conditions for MM5 and WRF are obtained from the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) and for HRM the initial and boundary conditions come from analysis of Global Model Europe (GME) of the German Weather Service. The resulting ensemble of seven members was run for a period of 6 months (from December 2008 to May 2009) over Iran. The 48-h raw ensemble outputs were calibrated using BMA technique for 120 days using a 40 days training sample of forecasts and relative verification data. The calibrated probabilistic forecasts were assessed using rank histogram and attribute diagrams. Results showed that application of BMA improved the reliability of the raw ensemble. Using the weighted ensemble mean forecast as a deterministic forecast it was found that the deterministic-style BMA forecasts performed usually better than the best member's deterministic forecast.

Iowa radon leukaemia study: a hierarchical population risk model for spatially correlated exposure measured with error.

PubMed

Smith, Brian J; Zhang, Lixun; Field, R William

2007-11-10

This paper presents a Bayesian model that allows for the joint prediction of county-average radon levels and estimation of the associated leukaemia risk. The methods are motivated by radon data from an epidemiologic study of residential radon in Iowa that include 2726 outdoor and indoor measurements. Prediction of county-average radon is based on a geostatistical model for the radon data which assumes an underlying continuous spatial process. In the radon model, we account for uncertainties due to incomplete spatial coverage, spatial variability, characteristic differences between homes, and detector measurement error. The predicted radon averages are, in turn, included as a covariate in Poisson models for incident cases of acute lymphocytic (ALL), acute myelogenous (AML), chronic lymphocytic (CLL), and chronic myelogenous (CML) leukaemias reported to the Iowa cancer registry from 1973 to 2002. Since radon and leukaemia risk are modelled simultaneously in our approach, the resulting risk estimates accurately reflect uncertainties in the predicted radon exposure covariate. Posterior mean (95 per cent Bayesian credible interval) estimates of the relative risk associated with a 1 pCi/L increase in radon for ALL, AML, CLL, and CML are 0.91 (0.78-1.03), 1.01 (0.92-1.12), 1.06 (0.96-1.16), and 1.12 (0.98-1.27), respectively. Copyright 2007 John Wiley & Sons, Ltd.

Model weights and the foundations of multimodel inference

USGS Publications Warehouse

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

2006-01-01

Statistical thinking in wildlife biology and ecology has been profoundly influenced by the introduction of AIC (Akaike?s information criterion) as a tool for model selection and as a basis for model averaging. In this paper, we advocate the Bayesian paradigm as a broader framework for multimodel inference, one in which model averaging and model selection are naturally linked, and in which the performance of AIC-based tools is naturally evaluated. Prior model weights implicitly associated with the use of AIC are seen to highly favor complex models: in some cases, all but the most highly parameterized models in the model set are virtually ignored a priori. We suggest the usefulness of the weighted BIC (Bayesian information criterion) as a computationally simple alternative to AIC, based on explicit selection of prior model probabilities rather than acceptance of default priors associated with AIC. We note, however, that both procedures are only approximate to the use of exact Bayes factors. We discuss and illustrate technical difficulties associated with Bayes factors, and suggest approaches to avoiding these difficulties in the context of model selection for a logistic regression. Our example highlights the predisposition of AIC weighting to favor complex models and suggests a need for caution in using the BIC for computing approximate posterior model weights.

Double the dates and go for Bayes - Impacts of model choice, dating density and quality on chronologies

NASA Astrophysics Data System (ADS)

Blaauw, Maarten; Christen, J. Andrés; Bennett, K. D.; Reimer, Paula J.

2018-05-01

Reliable chronologies are essential for most Quaternary studies, but little is known about how age-depth model choice, as well as dating density and quality, affect the precision and accuracy of chronologies. A meta-analysis suggests that most existing late-Quaternary studies contain fewer than one date per millennium, and provide millennial-scale precision at best. We use existing and simulated sediment cores to estimate what dating density and quality are required to obtain accurate chronologies at a desired precision. For many sites, a doubling in dating density would significantly improve chronologies and thus their value for reconstructing and interpreting past environmental changes. Commonly used classical age-depth models stop becoming more precise after a minimum dating density is reached, but the precision of Bayesian age-depth models which take advantage of chronological ordering continues to improve with more dates. Our simulations show that classical age-depth models severely underestimate uncertainty and are inaccurate at low dating densities, and also perform poorly at high dating densities. On the other hand, Bayesian age-depth models provide more realistic precision estimates, including at low to average dating densities, and are much more robust against dating scatter and outliers. Indeed, Bayesian age-depth models outperform classical ones at all tested dating densities, qualities and time-scales. We recommend that chronologies should be produced using Bayesian age-depth models taking into account chronological ordering and based on a minimum of 2 dates per millennium.

Testing averaged cosmology with type Ia supernovae and BAO data

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

Santos, B.; Alcaniz, J.S.; Coley, A.A.

An important problem in precision cosmology is the determination of the effects of averaging and backreaction on observational predictions, particularly in view of the wealth of new observational data and improved statistical techniques. In this paper, we discuss the observational viability of a class of averaged cosmologies which consist of a simple parametrized phenomenological two-scale backreaction model with decoupled spatial curvature parameters. We perform a Bayesian model selection analysis and find that this class of averaged phenomenological cosmological models is favored with respect to the standard ΛCDM cosmological scenario when a joint analysis of current SNe Ia and BAO datamore » is performed. In particular, the analysis provides observational evidence for non-trivial spatial curvature.« less

An empirical investigation on different methods of economic growth rate forecast and its behavior from fifteen countries across five continents

NASA Astrophysics Data System (ADS)

Yin, Yip Chee; Hock-Eam, Lim

2012-09-01

Our empirical results show that we can predict GDP growth rate more accurately in continent with fewer large economies, compared to smaller economies like Malaysia. This difficulty is very likely positively correlated with subsidy or social security policies. The stage of economic development and level of competiveness also appears to have interactive effects on this forecast stability. These results are generally independent of the forecasting procedures. Countries with high stability in their economic growth, forecasting by model selection is better than model averaging. Overall forecast weight averaging (FWA) is a better forecasting procedure in most countries. FWA also outperforms simple model averaging (SMA) and has the same forecasting ability as Bayesian model averaging (BMA) in almost all countries.

Model selection on solid ground: Rigorous comparison of nine ways to evaluate Bayesian model evidence

PubMed Central

Schöniger, Anneli; Wöhling, Thomas; Samaniego, Luis; Nowak, Wolfgang

2014-01-01

Bayesian model selection or averaging objectively ranks a number of plausible, competing conceptual models based on Bayes' theorem. It implicitly performs an optimal trade-off between performance in fitting available data and minimum model complexity. The procedure requires determining Bayesian model evidence (BME), which is the likelihood of the observed data integrated over each model's parameter space. The computation of this integral is highly challenging because it is as high-dimensional as the number of model parameters. Three classes of techniques to compute BME are available, each with its own challenges and limitations: (1) Exact and fast analytical solutions are limited by strong assumptions. (2) Numerical evaluation quickly becomes unfeasible for expensive models. (3) Approximations known as information criteria (ICs) such as the AIC, BIC, or KIC (Akaike, Bayesian, or Kashyap information criterion, respectively) yield contradicting results with regard to model ranking. Our study features a theory-based intercomparison of these techniques. We further assess their accuracy in a simplistic synthetic example where for some scenarios an exact analytical solution exists. In more challenging scenarios, we use a brute-force Monte Carlo integration method as reference. We continue this analysis with a real-world application of hydrological model selection. This is a first-time benchmarking of the various methods for BME evaluation against true solutions. Results show that BME values from ICs are often heavily biased and that the choice of approximation method substantially influences the accuracy of model ranking. For reliable model selection, bias-free numerical methods should be preferred over ICs whenever computationally feasible. PMID:25745272

Pricing and hedging derivative securities with neural networks: Bayesian regularization, early stopping, and bagging.

PubMed

Gençay, R; Qi, M

2001-01-01

We study the effectiveness of cross validation, Bayesian regularization, early stopping, and bagging to mitigate overfitting and improving generalization for pricing and hedging derivative securities with daily S&P 500 index daily call options from January 1988 to December 1993. Our results indicate that Bayesian regularization can generate significantly smaller pricing and delta-hedging errors than the baseline neural-network (NN) model and the Black-Scholes model for some years. While early stopping does not affect the pricing errors, it significantly reduces the hedging error (HE) in four of the six years we investigated. Although computationally most demanding, bagging seems to provide the most accurate pricing and delta hedging. Furthermore, the standard deviation of the MSPE of bagging is far less than that of the baseline model in all six years, and the standard deviation of the average HE of bagging is far less than that of the baseline model in five out of six years. We conclude that they be used at least in cases when no appropriate hints are available.

Comparing methods of measuring geographic patterns in temporal trends: an application to county-level heart disease mortality in the United States, 1973 to 2010.

PubMed

Vaughan, Adam S; Kramer, Michael R; Waller, Lance A; Schieb, Linda J; Greer, Sophia; Casper, Michele

2015-05-01

To demonstrate the implications of choosing analytical methods for quantifying spatiotemporal trends, we compare the assumptions, implementation, and outcomes of popular methods using county-level heart disease mortality in the United States between 1973 and 2010. We applied four regression-based approaches (joinpoint regression, both aspatial and spatial generalized linear mixed models, and Bayesian space-time model) and compared resulting inferences for geographic patterns of local estimates of annual percent change and associated uncertainty. The average local percent change in heart disease mortality from each method was -4.5%, with the Bayesian model having the smallest range of values. The associated uncertainty in percent change differed markedly across the methods, with the Bayesian space-time model producing the narrowest range of variance (0.0-0.8). The geographic pattern of percent change was consistent across methods with smaller declines in the South Central United States and larger declines in the Northeast and Midwest. However, the geographic patterns of uncertainty differed markedly between methods. The similarity of results, including geographic patterns, for magnitude of percent change across these methods validates the underlying spatial pattern of declines in heart disease mortality. However, marked differences in degree of uncertainty indicate that Bayesian modeling offers substantially more precise estimates. Copyright © 2015 Elsevier Inc. All rights reserved.

On the predictive information criteria for model determination in seismic hazard analysis

NASA Astrophysics Data System (ADS)

Varini, Elisa; Rotondi, Renata

2016-04-01

Many statistical tools have been developed for evaluating, understanding, and comparing models, from both frequentist and Bayesian perspectives. In particular, the problem of model selection can be addressed according to whether the primary goal is explanation or, alternatively, prediction. In the former case, the criteria for model selection are defined over the parameter space whose physical interpretation can be difficult; in the latter case, they are defined over the space of the observations, which has a more direct physical meaning. In the frequentist approaches, model selection is generally based on an asymptotic approximation which may be poor for small data sets (e.g. the F-test, the Kolmogorov-Smirnov test, etc.); moreover, these methods often apply under specific assumptions on models (e.g. models have to be nested in the likelihood ratio test). In the Bayesian context, among the criteria for explanation, the ratio of the observed marginal densities for two competing models, named Bayes Factor (BF), is commonly used for both model choice and model averaging (Kass and Raftery, J. Am. Stat. Ass., 1995). But BF does not apply to improper priors and, even when the prior is proper, it is not robust to the specification of the prior. These limitations can be extended to two famous penalized likelihood methods as the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), since they are proved to be approximations of -2log BF . In the perspective that a model is as good as its predictions, the predictive information criteria aim at evaluating the predictive accuracy of Bayesian models or, in other words, at estimating expected out-of-sample prediction error using a bias-correction adjustment of within-sample error (Gelman et al., Stat. Comput., 2014). In particular, the Watanabe criterion is fully Bayesian because it averages the predictive distribution over the posterior distribution of parameters rather than conditioning on a point estimate, but it is hardly applicable to data which are not independent given parameters (Watanabe, J. Mach. Learn. Res., 2010). A solution is given by Ando and Tsay criterion where the joint density may be decomposed into the product of the conditional densities (Ando and Tsay, Int. J. Forecast., 2010). The above mentioned criteria are global summary measures of model performance, but more detailed analysis could be required to discover the reasons for poor global performance. In this latter case, a retrospective predictive analysis is performed on each individual observation. In this study we performed the Bayesian analysis of Italian data sets by four versions of a long-term hazard model known as the stress release model (Vere-Jones, J. Physics Earth, 1978; Bebbington and Harte, Geophys. J. Int., 2003; Varini and Rotondi, Environ. Ecol. Stat., 2015). Then we illustrate the results on their performance evaluated by Bayes Factor, predictive information criteria and retrospective predictive analysis.

Advancing understanding of affect labeling with dynamic causal modeling

PubMed Central

Torrisi, Salvatore J.; Lieberman, Matthew D.; Bookheimer, Susan Y.; Altshuler, Lori L.

2013-01-01

Mechanistic understandings of forms of incidental emotion regulation have implications for basic and translational research in the affective sciences. In this study we applied Dynamic Causal Modeling (DCM) for fMRI to a common paradigm of labeling facial affect to elucidate prefrontal to subcortical influences. Four brain regions were used to model affect labeling, including right ventrolateral prefrontal cortex (vlPFC), amygdala and Broca’s area. 64 models were compared, for each of 45 healthy subjects. Family level inference split the model space to a likely driving input and Bayesian Model Selection within the winning family of 32 models revealed a strong pattern of endogenous network connectivity. Modulatory effects of labeling were most prominently observed following Bayesian Model Averaging, with the dampening influence on amygdala originating from Broca’s area but much more strongly from right vlPFC. These results solidify and extend previous correlation and regression-based estimations of negative corticolimbic coupling. PMID:23774393

Bayesian analyses of time-interval data for environmental radiation monitoring.

PubMed

Luo, Peng; Sharp, Julia L; DeVol, Timothy A

2013-01-01

Time-interval (time difference between two consecutive pulses) analysis based on the principles of Bayesian inference was investigated for online radiation monitoring. Using experimental and simulated data, Bayesian analysis of time-interval data [Bayesian (ti)] was compared with Bayesian and a conventional frequentist analysis of counts in a fixed count time [Bayesian (cnt) and single interval test (SIT), respectively]. The performances of the three methods were compared in terms of average run length (ARL) and detection probability for several simulated detection scenarios. Experimental data were acquired with a DGF-4C system in list mode. Simulated data were obtained using Monte Carlo techniques to obtain a random sampling of the Poisson distribution. All statistical algorithms were developed using the R Project for statistical computing. Bayesian analysis of time-interval information provided a similar detection probability as Bayesian analysis of count information, but the authors were able to make a decision with fewer pulses at relatively higher radiation levels. In addition, for the cases with very short presence of the source (< count time), time-interval information is more sensitive to detect a change than count information since the source data is averaged by the background data over the entire count time. The relationships of the source time, change points, and modifications to the Bayesian approach for increasing detection probability are presented.

A Bayesian model averaging approach with non-informative priors for cost-effectiveness analyses.

PubMed

Conigliani, Caterina

2010-07-20

We consider the problem of assessing new and existing technologies for their cost-effectiveness in the case where data on both costs and effects are available from a clinical trial, and we address it by means of the cost-effectiveness acceptability curve. The main difficulty in these analyses is that cost data usually exhibit highly skew and heavy-tailed distributions, so that it can be extremely difficult to produce realistic probabilistic models for the underlying population distribution. Here, in order to integrate the uncertainty about the model into the analysis of cost data and into cost-effectiveness analyses, we consider an approach based on Bayesian model averaging (BMA) in the particular case of weak prior informations about the unknown parameters of the different models involved in the procedure. The main consequence of this assumption is that the marginal densities required by BMA are undetermined. However, in accordance with the theory of partial Bayes factors and in particular of fractional Bayes factors, we suggest replacing each marginal density with a ratio of integrals that can be efficiently computed via path sampling. Copyright (c) 2010 John Wiley & Sons, Ltd.

A Bayesian model averaging approach to examining changes in quality of life among returning Iraq and Afghanistan Veterans

PubMed Central

Stock, Eileen M.; Kimbrel, Nathan A.; Meyer, Eric C.; Copeland, Laurel A.; Monte, Ralph; Zeber, John E.; Gulliver, Suzy Bird; Morissette, Sandra B.

2016-01-01

Many Veterans from the conflicts in Iraq and Afghanistan return home with physical and psychological impairments that impact their ability to enjoy normal life activities and diminish their quality of life (QoL). The present research aimed to identify predictors of QoL over an 8-month period using Bayesian model averaging (BMA), which is a statistical technique useful for maximizing power with smaller sample sizes. A sample of 117 Iraq and Afghanistan Veterans receiving care in a southwestern healthcare system was recruited, and BMA examined the impact of key demographics (e.g., age, gender), diagnoses (e.g., depression), and treatment modalities (e.g., individual therapy, medication) on QoL over time. Multiple imputation based on Gibbs sampling was employed for incomplete data (6.4% missingness). Average follow-up QoL scores were significantly lower than at baseline (73.2 initial vs 69.5 4-month and 68.3 8-month). Employment was associated with increased QoL during each follow-up, while posttraumatic stress disorder and black race were inversely related. Additionally, predictive models indicated that depression, income, treatment for a medical condition, and group psychotherapy were strong negative predictors of 4-month QoL but not 8-month QoL. PMID:24942672

Learning classification trees

NASA Technical Reports Server (NTRS)

Buntine, Wray

1991-01-01

Algorithms for learning classification trees have had successes in artificial intelligence and statistics over many years. How a tree learning algorithm can be derived from Bayesian decision theory is outlined. This introduces Bayesian techniques for splitting, smoothing, and tree averaging. The splitting rule turns out to be similar to Quinlan's information gain splitting rule, while smoothing and averaging replace pruning. Comparative experiments with reimplementations of a minimum encoding approach, Quinlan's C4 and Breiman et al. Cart show the full Bayesian algorithm is consistently as good, or more accurate than these other approaches though at a computational price.

Bayesian effect estimation accounting for adjustment uncertainty.

PubMed

Wang, Chi; Parmigiani, Giovanni; Dominici, Francesca

2012-09-01

Model-based estimation of the effect of an exposure on an outcome is generally sensitive to the choice of which confounding factors are included in the model. We propose a new approach, which we call Bayesian adjustment for confounding (BAC), to estimate the effect of an exposure of interest on the outcome, while accounting for the uncertainty in the choice of confounders. Our approach is based on specifying two models: (1) the outcome as a function of the exposure and the potential confounders (the outcome model); and (2) the exposure as a function of the potential confounders (the exposure model). We consider Bayesian variable selection on both models and link the two by introducing a dependence parameter, ω, denoting the prior odds of including a predictor in the outcome model, given that the same predictor is in the exposure model. In the absence of dependence (ω= 1), BAC reduces to traditional Bayesian model averaging (BMA). In simulation studies, we show that BAC, with ω > 1, estimates the exposure effect with smaller bias than traditional BMA, and improved coverage. We, then, compare BAC, a recent approach of Crainiceanu, Dominici, and Parmigiani (2008, Biometrika 95, 635-651), and traditional BMA in a time series data set of hospital admissions, air pollution levels, and weather variables in Nassau, NY for the period 1999-2005. Using each approach, we estimate the short-term effects of on emergency admissions for cardiovascular diseases, accounting for confounding. This application illustrates the potentially significant pitfalls of misusing variable selection methods in the context of adjustment uncertainty. © 2012, The International Biometric Society.

A Bayesian model averaging method for the derivation of reservoir operating rules

NASA Astrophysics Data System (ADS)

Zhang, Jingwen; Liu, Pan; Wang, Hao; Lei, Xiaohui; Zhou, Yanlai

2015-09-01

Because the intrinsic dynamics among optimal decision making, inflow processes and reservoir characteristics are complex, functional forms of reservoir operating rules are always determined subjectively. As a result, the uncertainty of selecting form and/or model involved in reservoir operating rules must be analyzed and evaluated. In this study, we analyze the uncertainty of reservoir operating rules using the Bayesian model averaging (BMA) model. Three popular operating rules, namely piecewise linear regression, surface fitting and a least-squares support vector machine, are established based on the optimal deterministic reservoir operation. These individual models provide three-member decisions for the BMA combination, enabling the 90% release interval to be estimated by the Markov Chain Monte Carlo simulation. A case study of China's the Baise reservoir shows that: (1) the optimal deterministic reservoir operation, superior to any reservoir operating rules, is used as the samples to derive the rules; (2) the least-squares support vector machine model is more effective than both piecewise linear regression and surface fitting; (3) BMA outperforms any individual model of operating rules based on the optimal trajectories. It is revealed that the proposed model can reduce the uncertainty of operating rules, which is of great potential benefit in evaluating the confidence interval of decisions.

Bayesian Maximum Entropy Integration of Ozone Observations and Model Predictions: A National Application.

PubMed

Xu, Yadong; Serre, Marc L; Reyes, Jeanette; Vizuete, William

2016-04-19

To improve ozone exposure estimates for ambient concentrations at a national scale, we introduce our novel Regionalized Air Quality Model Performance (RAMP) approach to integrate chemical transport model (CTM) predictions with the available ozone observations using the Bayesian Maximum Entropy (BME) framework. The framework models the nonlinear and nonhomoscedastic relation between air pollution observations and CTM predictions and for the first time accounts for variability in CTM model performance. A validation analysis using only noncollocated data outside of a validation radius rv was performed and the R(2) between observations and re-estimated values for two daily metrics, the daily maximum 8-h average (DM8A) and the daily 24-h average (D24A) ozone concentrations, were obtained with the OBS scenario using ozone observations only in contrast with the RAMP and a Constant Air Quality Model Performance (CAMP) scenarios. We show that, by accounting for the spatial and temporal variability in model performance, our novel RAMP approach is able to extract more information in terms of R(2) increase percentage, with over 12 times for the DM8A and over 3.5 times for the D24A ozone concentrations, from CTM predictions than the CAMP approach assuming that model performance does not change across space and time.

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

PubMed Central

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

2010-01-01

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

Bayesian regression models outperform partial least squares methods for predicting milk components and technological properties using infrared spectral data

PubMed Central

Ferragina, A.; de los Campos, G.; Vazquez, A. I.; Cecchinato, A.; Bittante, G.

2017-01-01

The aim of this study was to assess the performance of Bayesian models commonly used for genomic selection to predict “difficult-to-predict” dairy traits, such as milk fatty acid (FA) expressed as percentage of total fatty acids, and technological properties, such as fresh cheese yield and protein recovery, using Fourier-transform infrared (FTIR) spectral data. Our main hypothesis was that Bayesian models that can estimate shrinkage and perform variable selection may improve our ability to predict FA traits and technological traits above and beyond what can be achieved using the current calibration models (e.g., partial least squares, PLS). To this end, we assessed a series of Bayesian methods and compared their prediction performance with that of PLS. The comparison between models was done using the same sets of data (i.e., same samples, same variability, same spectral treatment) for each trait. Data consisted of 1,264 individual milk samples collected from Brown Swiss cows for which gas chromatographic FA composition, milk coagulation properties, and cheese-yield traits were available. For each sample, 2 spectra in the infrared region from 5,011 to 925 cm−1 were available and averaged before data analysis. Three Bayesian models: Bayesian ridge regression (Bayes RR), Bayes A, and Bayes B, and 2 reference models: PLS and modified PLS (MPLS) procedures, were used to calibrate equations for each of the traits. The Bayesian models used were implemented in the R package BGLR (http://cran.r-project.org/web/packages/BGLR/index.html), whereas the PLS and MPLS were those implemented in the WinISI II software (Infrasoft International LLC, State College, PA). Prediction accuracy was estimated for each trait and model using 25 replicates of a training-testing validation procedure. Compared with PLS, which is currently the most widely used calibration method, MPLS and the 3 Bayesian methods showed significantly greater prediction accuracy. Accuracy increased in moving from calibration to external validation methods, and in moving from PLS and MPLS to Bayesian methods, particularly Bayes A and Bayes B. The maximum R2 value of validation was obtained with Bayes B and Bayes A. For the FA, C10:0 (% of each FA on total FA basis) had the highest R2 (0.75, achieved with Bayes A and Bayes B), and among the technological traits, fresh cheese yield R2 of 0.82 (achieved with Bayes B). These 2 methods have proven to be useful instruments in shrinking and selecting very informative wavelengths and inferring the structure and functions of the analyzed traits. We conclude that Bayesian models are powerful tools for deriving calibration equations, and, importantly, these equations can be easily developed using existing open-source software. As part of our study, we provide scripts based on the open source R software BGLR, which can be used to train customized prediction equations for other traits or populations. PMID:26387015

Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier–Stokes simulations: A data-driven, physics-informed Bayesian approach

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

Xiao, H., E-mail: hengxiao@vt.edu; Wu, J.-L.; Wang, J.-X.

Despite their well-known limitations, Reynolds-Averaged Navier–Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering analysis, design and optimization. While the predictive capability of RANS models depends on many factors, for many practical flows the turbulence models are by far the largest source of uncertainty. As RANS models are used in the design and safety evaluation of many mission-critical systems such as airplanes and nuclear power plants, quantifying their model-form uncertainties has significant implications in enabling risk-informed decision-making. In this work we develop a data-driven, physics-informed Bayesian framework for quantifying model-form uncertainties in RANS simulations.more » Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to assimilate the prior knowledge and observation data in a Bayesian framework, and to propagate them to posterior distributions of velocities and other Quantities of Interest (QoIs). We use two representative cases, the flow over periodic hills and the flow in a square duct, to evaluate the performance of the proposed framework. Both cases are challenging for standard RANS turbulence models. Simulation results suggest that, even with very sparse observations, the obtained posterior mean velocities and other QoIs have significantly better agreement with the benchmark data compared to the baseline results. At most locations the posterior distribution adequately captures the true model error within the developed model form uncertainty bounds. The framework is a major improvement over existing black-box, physics-neutral methods for model-form uncertainty quantification, where prior knowledge and details of the models are not exploited. This approach has potential implications in many fields in which the governing equations are well understood but the model uncertainty comes from unresolved physical processes. - Highlights: • Proposed a physics–informed framework to quantify uncertainty in RANS simulations. • Framework incorporates physical prior knowledge and observation data. • Based on a rigorous Bayesian framework yet fully utilizes physical model. • Applicable for many complex physical systems beyond turbulent flows.« less

A statistical model for combustion resonance from a DI diesel engine with applications

NASA Astrophysics Data System (ADS)

Bodisco, Timothy; Low Choy, Samantha; Masri, Assaad; Brown, Richard J.

2015-08-01

Introduced in this paper is a Bayesian model for isolating the resonant frequency from combustion chamber resonance. The model shown in this paper focused on characterising the initial rise in the resonant frequency to investigate the rise of in-cylinder bulk temperature associated with combustion. By resolving the model parameters, it is possible to determine: the start of pre-mixed combustion, the start of diffusion combustion, the initial resonant frequency, the resonant frequency as a function of crank angle, the in-cylinder bulk temperature as a function of crank angle and the trapped mass as a function of crank angle. The Bayesian method allows for individual cycles to be examined without cycle-averaging-allowing inter-cycle variability studies. Results are shown for a turbo-charged, common-rail compression ignition engine run at 2000 rpm and full load.

Estimation of Model's Marginal likelihood Using Adaptive Sparse Grid Surrogates in Bayesian Model Averaging

NASA Astrophysics Data System (ADS)

Zeng, X.

2015-12-01

A large number of model executions are required to obtain alternative conceptual models' predictions and their posterior probabilities in Bayesian model averaging (BMA). The posterior model probability is estimated through models' marginal likelihood and prior probability. The heavy computation burden hinders the implementation of BMA prediction, especially for the elaborated marginal likelihood estimator. For overcoming the computation burden of BMA, an adaptive sparse grid (SG) stochastic collocation method is used to build surrogates for alternative conceptual models through the numerical experiment of a synthetical groundwater model. BMA predictions depend on model posterior weights (or marginal likelihoods), and this study also evaluated four marginal likelihood estimators, including arithmetic mean estimator (AME), harmonic mean estimator (HME), stabilized harmonic mean estimator (SHME), and thermodynamic integration estimator (TIE). The results demonstrate that TIE is accurate in estimating conceptual models' marginal likelihoods. The BMA-TIE has better predictive performance than other BMA predictions. TIE has high stability for estimating conceptual model's marginal likelihood. The repeated estimated conceptual model's marginal likelihoods by TIE have significant less variability than that estimated by other estimators. In addition, the SG surrogates are efficient to facilitate BMA predictions, especially for BMA-TIE. The number of model executions needed for building surrogates is 4.13%, 6.89%, 3.44%, and 0.43% of the required model executions of BMA-AME, BMA-HME, BMA-SHME, and BMA-TIE, respectively.

Impact of censoring on learning Bayesian networks in survival modelling.

PubMed

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

2009-11-01

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

Climate Projections from the NARCliM Project: Bayesian Model Averaging of Maximum Temperature Projections

NASA Astrophysics Data System (ADS)

Olson, R.; Evans, J. P.; Fan, Y.

2015-12-01

NARCliM (NSW/ACT Regional Climate Modelling Project) is a regional climate project for Australia and the surrounding region. It dynamically downscales 4 General Circulation Models (GCMs) using three Regional Climate Models (RCMs) to provide climate projections for the CORDEX-AustralAsia region at 50 km resolution, and for south-east Australia at 10 km resolution. The project differs from previous work in the level of sophistication of model selection. Specifically, the selection process for GCMs included (i) conducting literature review to evaluate model performance, (ii) analysing model independence, and (iii) selecting models that span future temperature and precipitation change space. RCMs for downscaling the GCMs were chosen based on their performance for several precipitation events over South-East Australia, and on model independence.Bayesian Model Averaging (BMA) provides a statistically consistent framework for weighing the models based on their likelihood given the available observations. These weights are used to provide probability distribution functions (pdfs) for model projections. We develop a BMA framework for constructing probabilistic climate projections for spatially-averaged variables from the NARCliM project. The first step in the procedure is smoothing model output in order to exclude the influence of internal climate variability. Our statistical model for model-observations residuals is a homoskedastic iid process. Comparing RCMs with Australian Water Availability Project (AWAP) observations is used to determine model weights through Monte Carlo integration. Posterior pdfs of statistical parameters of model-data residuals are obtained using Markov Chain Monte Carlo. The uncertainty in the properties of the model-data residuals is fully accounted for when constructing the projections. We present the preliminary results of the BMA analysis for yearly maximum temperature for New South Wales state planning regions for the period 2060-2079.

Numerical Demons in Monte Carlo Estimation of Bayesian Model Evidence with Application to Soil Respiration Models

NASA Astrophysics Data System (ADS)

Elshall, A. S.; Ye, M.; Niu, G. Y.; Barron-Gafford, G.

2016-12-01

Bayesian multimodel inference is increasingly being used in hydrology. Estimating Bayesian model evidence (BME) is of central importance in many Bayesian multimodel analysis such as Bayesian model averaging and model selection. BME is the overall probability of the model in reproducing the data, accounting for the trade-off between the goodness-of-fit and the model complexity. Yet estimating BME is challenging, especially for high dimensional problems with complex sampling space. Estimating BME using the Monte Carlo numerical methods is preferred, as the methods yield higher accuracy than semi-analytical solutions (e.g. Laplace approximations, BIC, KIC, etc.). However, numerical methods are prone the numerical demons arising from underflow of round off errors. Although few studies alluded to this issue, to our knowledge this is the first study that illustrates these numerical demons. We show that the precision arithmetic can become a threshold on likelihood values and Metropolis acceptance ratio, which results in trimming parameter regions (when likelihood function is less than the smallest floating point number that a computer can represent) and corrupting of the empirical measures of the random states of the MCMC sampler (when using log-likelihood function). We consider two of the most powerful numerical estimators of BME that are the path sampling method of thermodynamic integration (TI) and the importance sampling method of steppingstone sampling (SS). We also consider the two most widely used numerical estimators, which are the prior sampling arithmetic mean (AS) and posterior sampling harmonic mean (HM). We investigate the vulnerability of these four estimators to the numerical demons. Interesting, the most biased estimator, namely the HM, turned out to be the least vulnerable. While it is generally assumed that AM is a bias-free estimator that will always approximate the true BME by investing in computational effort, we show that arithmetic underflow can hamper AM resulting in severe underestimation of BME. TI turned out to be the most vulnerable, resulting in BME overestimation. Finally, we show how SS can be largely invariant to rounding errors, yielding the most accurate and computational efficient results. These research results are useful for MC simulations to estimate Bayesian model evidence.

Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier-Stokes simulations: A data-driven, physics-informed Bayesian approach

NASA Astrophysics Data System (ADS)

Xiao, H.; Wu, J.-L.; Wang, J.-X.; Sun, R.; Roy, C. J.

2016-11-01

Despite their well-known limitations, Reynolds-Averaged Navier-Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering analysis, design and optimization. While the predictive capability of RANS models depends on many factors, for many practical flows the turbulence models are by far the largest source of uncertainty. As RANS models are used in the design and safety evaluation of many mission-critical systems such as airplanes and nuclear power plants, quantifying their model-form uncertainties has significant implications in enabling risk-informed decision-making. In this work we develop a data-driven, physics-informed Bayesian framework for quantifying model-form uncertainties in RANS simulations. Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to assimilate the prior knowledge and observation data in a Bayesian framework, and to propagate them to posterior distributions of velocities and other Quantities of Interest (QoIs). We use two representative cases, the flow over periodic hills and the flow in a square duct, to evaluate the performance of the proposed framework. Both cases are challenging for standard RANS turbulence models. Simulation results suggest that, even with very sparse observations, the obtained posterior mean velocities and other QoIs have significantly better agreement with the benchmark data compared to the baseline results. At most locations the posterior distribution adequately captures the true model error within the developed model form uncertainty bounds. The framework is a major improvement over existing black-box, physics-neutral methods for model-form uncertainty quantification, where prior knowledge and details of the models are not exploited. This approach has potential implications in many fields in which the governing equations are well understood but the model uncertainty comes from unresolved physical processes.

Robust Bayesian Experimental Design for Conceptual Model Discrimination

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Bayesian ensemble refinement by replica simulations and reweighting.

PubMed

Hummer, Gerhard; Köfinger, Jürgen

2015-12-28

We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be characterized by integrating a wide range of experimental data, including measurements of ensemble-averaged observables. We start from a Bayesian formulation in which the posterior is a functional that ranks different configuration space distributions. By maximizing this posterior, we derive an optimal Bayesian ensemble distribution. For discrete configurations, this optimal distribution is identical to that obtained by the maximum entropy "ensemble refinement of SAXS" (EROS) formulation. Bayesian replica ensemble refinement enhances the sampling of relevant configurations by imposing restraints on averages of observables in coupled replica molecular dynamics simulations. We show that the strength of the restraints should scale linearly with the number of replicas to ensure convergence to the optimal Bayesian result in the limit of infinitely many replicas. In the "Bayesian inference of ensembles" method, we combine the replica and EROS approaches to accelerate the convergence. An adaptive algorithm can be used to sample directly from the optimal ensemble, without replicas. We discuss the incorporation of single-molecule measurements and dynamic observables such as relaxation parameters. The theoretical analysis of different Bayesian ensemble refinement approaches provides a basis for practical applications and a starting point for further investigations.

Bayesian ensemble refinement by replica simulations and reweighting

NASA Astrophysics Data System (ADS)

Hummer, Gerhard; Köfinger, Jürgen

2015-12-01

We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be characterized by integrating a wide range of experimental data, including measurements of ensemble-averaged observables. We start from a Bayesian formulation in which the posterior is a functional that ranks different configuration space distributions. By maximizing this posterior, we derive an optimal Bayesian ensemble distribution. For discrete configurations, this optimal distribution is identical to that obtained by the maximum entropy "ensemble refinement of SAXS" (EROS) formulation. Bayesian replica ensemble refinement enhances the sampling of relevant configurations by imposing restraints on averages of observables in coupled replica molecular dynamics simulations. We show that the strength of the restraints should scale linearly with the number of replicas to ensure convergence to the optimal Bayesian result in the limit of infinitely many replicas. In the "Bayesian inference of ensembles" method, we combine the replica and EROS approaches to accelerate the convergence. An adaptive algorithm can be used to sample directly from the optimal ensemble, without replicas. We discuss the incorporation of single-molecule measurements and dynamic observables such as relaxation parameters. The theoretical analysis of different Bayesian ensemble refinement approaches provides a basis for practical applications and a starting point for further investigations.

Joint analysis of input and parametric uncertainties in watershed water quality modeling: A formal Bayesian approach

NASA Astrophysics Data System (ADS)

Han, Feng; Zheng, Yi

2018-06-01

Significant Input uncertainty is a major source of error in watershed water quality (WWQ) modeling. It remains challenging to address the input uncertainty in a rigorous Bayesian framework. This study develops the Bayesian Analysis of Input and Parametric Uncertainties (BAIPU), an approach for the joint analysis of input and parametric uncertainties through a tight coupling of Markov Chain Monte Carlo (MCMC) analysis and Bayesian Model Averaging (BMA). The formal likelihood function for this approach is derived considering a lag-1 autocorrelated, heteroscedastic, and Skew Exponential Power (SEP) distributed error model. A series of numerical experiments were performed based on a synthetic nitrate pollution case and on a real study case in the Newport Bay Watershed, California. The Soil and Water Assessment Tool (SWAT) and Differential Evolution Adaptive Metropolis (DREAM(ZS)) were used as the representative WWQ model and MCMC algorithm, respectively. The major findings include the following: (1) the BAIPU can be implemented and used to appropriately identify the uncertain parameters and characterize the predictive uncertainty; (2) the compensation effect between the input and parametric uncertainties can seriously mislead the modeling based management decisions, if the input uncertainty is not explicitly accounted for; (3) the BAIPU accounts for the interaction between the input and parametric uncertainties and therefore provides more accurate calibration and uncertainty results than a sequential analysis of the uncertainties; and (4) the BAIPU quantifies the credibility of different input assumptions on a statistical basis and can be implemented as an effective inverse modeling approach to the joint inference of parameters and inputs.

A MOVING AVERAGE BAYESIAN MODEL FOR SPATIAL SURFACE AND COVERAGE PREDICTION FROM ENVIRONMENTAL POINT-SOURCE DATA

EPA Science Inventory

This paper addresses the general problem of estimating at arbitrary locations the value of an unobserved quantity that varies over space, such as ozone concentration in air or nitrate concentrations in surface groundwater, on the basis of approximate measurements of the quantity ...

Bayesian model evidence as a model evaluation metric

NASA Astrophysics Data System (ADS)

Guthke, Anneli; Höge, Marvin; Nowak, Wolfgang

2017-04-01

When building environmental systems models, we are typically confronted with the questions of how to choose an appropriate model (i.e., which processes to include or neglect) and how to measure its quality. Various metrics have been proposed that shall guide the modeller towards a most robust and realistic representation of the system under study. Criteria for evaluation often address aspects of accuracy (absence of bias) or of precision (absence of unnecessary variance) and need to be combined in a meaningful way in order to address the inherent bias-variance dilemma. We suggest using Bayesian model evidence (BME) as a model evaluation metric that implicitly performs a tradeoff between bias and variance. BME is typically associated with model weights in the context of Bayesian model averaging (BMA). However, it can also be seen as a model evaluation metric in a single-model context or in model comparison. It combines a measure for goodness of fit with a penalty for unjustifiable complexity. Unjustifiable refers to the fact that the appropriate level of model complexity is limited by the amount of information available for calibration. Derived in a Bayesian context, BME naturally accounts for measurement errors in the calibration data as well as for input and parameter uncertainty. BME is therefore perfectly suitable to assess model quality under uncertainty. We will explain in detail and with schematic illustrations what BME measures, i.e. how complexity is defined in the Bayesian setting and how this complexity is balanced with goodness of fit. We will further discuss how BME compares to other model evaluation metrics that address accuracy and precision such as the predictive logscore or other model selection criteria such as the AIC, BIC or KIC. Although computationally more expensive than other metrics or criteria, BME represents an appealing alternative because it provides a global measure of model quality. Even if not applicable to each and every case, we aim at stimulating discussion about how to judge the quality of hydrological models in the presence of uncertainty in general by dissecting the mechanism behind BME.

REMOVING BIASES IN RESOLVED STELLAR MASS MAPS OF GALAXY DISKS THROUGH SUCCESSIVE BAYESIAN MARGINALIZATION

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

Martínez-García, Eric E.; González-Lópezlira, Rosa A.; Bruzual A, Gustavo

2017-01-20

Stellar masses of galaxies are frequently obtained by fitting stellar population synthesis models to galaxy photometry or spectra. The state of the art method resolves spatial structures within a galaxy to assess the total stellar mass content. In comparison to unresolved studies, resolved methods yield, on average, higher fractions of stellar mass for galaxies. In this work we improve the current method in order to mitigate a bias related to the resolved spatial distribution derived for the mass. The bias consists in an apparent filamentary mass distribution and a spatial coincidence between mass structures and dust lanes near spiral arms.more » The improved method is based on iterative Bayesian marginalization, through a new algorithm we have named Bayesian Successive Priors (BSP). We have applied BSP to M51 and to a pilot sample of 90 spiral galaxies from the Ohio State University Bright Spiral Galaxy Survey. By quantitatively comparing both methods, we find that the average fraction of stellar mass missed by unresolved studies is only half what previously thought. In contrast with the previous method, the output BSP mass maps bear a better resemblance to near-infrared images.« less

Bayesian dose-response analysis for epidemiological studies with complex uncertainty in dose estimation.

PubMed

Kwon, Deukwoo; Hoffman, F Owen; Moroz, Brian E; Simon, Steven L

2016-02-10

Most conventional risk analysis methods rely on a single best estimate of exposure per person, which does not allow for adjustment for exposure-related uncertainty. Here, we propose a Bayesian model averaging method to properly quantify the relationship between radiation dose and disease outcomes by accounting for shared and unshared uncertainty in estimated dose. Our Bayesian risk analysis method utilizes multiple realizations of sets (vectors) of doses generated by a two-dimensional Monte Carlo simulation method that properly separates shared and unshared errors in dose estimation. The exposure model used in this work is taken from a study of the risk of thyroid nodules among a cohort of 2376 subjects who were exposed to fallout from nuclear testing in Kazakhstan. We assessed the performance of our method through an extensive series of simulations and comparisons against conventional regression risk analysis methods. When the estimated doses contain relatively small amounts of uncertainty, the Bayesian method using multiple a priori plausible draws of dose vectors gave similar results to the conventional regression-based methods of dose-response analysis. However, when large and complex mixtures of shared and unshared uncertainties are present, the Bayesian method using multiple dose vectors had significantly lower relative bias than conventional regression-based risk analysis methods and better coverage, that is, a markedly increased capability to include the true risk coefficient within the 95% credible interval of the Bayesian-based risk estimate. An evaluation of the dose-response using our method is presented for an epidemiological study of thyroid disease following radiation exposure. Copyright © 2015 John Wiley & Sons, Ltd.

Selectivity curves of the capture of mangrove crab (Ucides cordatus) on the northern coast of Brazil using bayesian inference.

PubMed

Furtado-Junior, I; Abrunhosa, F A; Holanda, F C A F; Tavares, M C S

2016-06-01

Fishing selectivity of the mangrove crab Ucides cordatus in the north coast of Brazil can be defined as the fisherman's ability to capture and select individuals from a certain size or sex (or a combination of these factors) which suggests an empirical selectivity. Considering this hypothesis, we calculated the selectivity curves for males and females crabs using the logit function of the logistic model in the formulation. The Bayesian inference consisted of obtaining the posterior distribution by applying the Markov chain Monte Carlo (MCMC) method to software R using the OpenBUGS, BRugs, and R2WinBUGS libraries. The estimated results of width average carapace selection for males and females compared with previous studies reporting the average width of the carapace of sexual maturity allow us to confirm the hypothesis that most mature individuals do not suffer from fishing pressure; thus, ensuring their sustainability.

Bayesian regression models outperform partial least squares methods for predicting milk components and technological properties using infrared spectral data.

PubMed

Ferragina, A; de los Campos, G; Vazquez, A I; Cecchinato, A; Bittante, G

2015-11-01

The aim of this study was to assess the performance of Bayesian models commonly used for genomic selection to predict "difficult-to-predict" dairy traits, such as milk fatty acid (FA) expressed as percentage of total fatty acids, and technological properties, such as fresh cheese yield and protein recovery, using Fourier-transform infrared (FTIR) spectral data. Our main hypothesis was that Bayesian models that can estimate shrinkage and perform variable selection may improve our ability to predict FA traits and technological traits above and beyond what can be achieved using the current calibration models (e.g., partial least squares, PLS). To this end, we assessed a series of Bayesian methods and compared their prediction performance with that of PLS. The comparison between models was done using the same sets of data (i.e., same samples, same variability, same spectral treatment) for each trait. Data consisted of 1,264 individual milk samples collected from Brown Swiss cows for which gas chromatographic FA composition, milk coagulation properties, and cheese-yield traits were available. For each sample, 2 spectra in the infrared region from 5,011 to 925 cm(-1) were available and averaged before data analysis. Three Bayesian models: Bayesian ridge regression (Bayes RR), Bayes A, and Bayes B, and 2 reference models: PLS and modified PLS (MPLS) procedures, were used to calibrate equations for each of the traits. The Bayesian models used were implemented in the R package BGLR (http://cran.r-project.org/web/packages/BGLR/index.html), whereas the PLS and MPLS were those implemented in the WinISI II software (Infrasoft International LLC, State College, PA). Prediction accuracy was estimated for each trait and model using 25 replicates of a training-testing validation procedure. Compared with PLS, which is currently the most widely used calibration method, MPLS and the 3 Bayesian methods showed significantly greater prediction accuracy. Accuracy increased in moving from calibration to external validation methods, and in moving from PLS and MPLS to Bayesian methods, particularly Bayes A and Bayes B. The maximum R(2) value of validation was obtained with Bayes B and Bayes A. For the FA, C10:0 (% of each FA on total FA basis) had the highest R(2) (0.75, achieved with Bayes A and Bayes B), and among the technological traits, fresh cheese yield R(2) of 0.82 (achieved with Bayes B). These 2 methods have proven to be useful instruments in shrinking and selecting very informative wavelengths and inferring the structure and functions of the analyzed traits. We conclude that Bayesian models are powerful tools for deriving calibration equations, and, importantly, these equations can be easily developed using existing open-source software. As part of our study, we provide scripts based on the open source R software BGLR, which can be used to train customized prediction equations for other traits or populations. Copyright © 2015 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

ENSURF: multi-model sea level forecast - implementation and validation results for the IBIROOS and Western Mediterranean regions

NASA Astrophysics Data System (ADS)

Pérez, B.; Brower, R.; Beckers, J.; Paradis, D.; Balseiro, C.; Lyons, K.; Cure, M.; Sotillo, M. G.; Hacket, B.; Verlaan, M.; Alvarez Fanjul, E.

2011-04-01

ENSURF (Ensemble SURge Forecast) is a multi-model application for sea level forecast that makes use of existing storm surge or circulation models today operational in Europe, as well as near-real time tide gauge data in the region, with the following main goals: - providing an easy access to existing forecasts, as well as to its performance and model validation, by means of an adequate visualization tool - generation of better forecasts of sea level, including confidence intervals, by means of the Bayesian Model Average Technique (BMA) The system was developed and implemented within ECOOP (C.No. 036355) European Project for the NOOS and the IBIROOS regions, based on MATROOS visualization tool developed by Deltares. Both systems are today operational at Deltares and Puertos del Estado respectively. The Bayesian Modelling Average technique generates an overall forecast probability density function (PDF) by making a weighted average of the individual forecasts PDF's; the weights represent the probability that a model will give the correct forecast PDF and are determined and updated operationally based on the performance of the models during a recent training period. This implies the technique needs the availability of sea level data from tide gauges in near-real time. Results of validation of the different models and BMA implementation for the main harbours will be presented for the IBIROOS and Western Mediterranean regions, where this kind of activity is performed for the first time. The work has proved to be useful to detect problems in some of the circulation models not previously well calibrated with sea level data, to identify the differences on baroclinic and barotropic models for sea level applications and to confirm the general improvement of the BMA forecasts.

Improved Determination of the Myelin Water Fraction in Human Brain using Magnetic Resonance Imaging through Bayesian Analysis of mcDESPOT

PubMed Central

Bouhrara, Mustapha; Spencer, Richard G.

2015-01-01

Myelin water fraction (MWF) mapping with magnetic resonance imaging has led to the ability to directly observe myelination and demyelination in both the developing brain and in disease. Multicomponent driven equilibrium single pulse observation of T1 and T2 (mcDESPOT) has been proposed as a rapid approach for multicomponent relaxometry and has been applied to map MWF in human brain. However, even for the simplest two-pool signal model consisting of MWF and non-myelin-associated water, the dimensionality of the parameter space for obtaining MWF estimates remains high. This renders parameter estimation difficult, especially at low-to-moderate signal-to-noise ratios (SNR), due to the presence of local minima and the flatness of the fit residual energy surface used for parameter determination using conventional nonlinear least squares (NLLS)-based algorithms. In this study, we introduce three Bayesian approaches for analysis of the mcDESPOT signal model to determine MWF. Given the high dimensional nature of mcDESPOT signal model, and, thereby, the high dimensional marginalizations over nuisance parameters needed to derive the posterior probability distribution of MWF parameter, the introduced Bayesian analyses use different approaches to reduce the dimensionality of the parameter space. The first approach uses normalization by average signal amplitude, and assumes that noise can be accurately estimated from signal-free regions of the image. The second approach likewise uses average amplitude normalization, but incorporates a full treatment of noise as an unknown variable through marginalization. The third approach does not use amplitude normalization and incorporates marginalization over both noise and signal amplitude. Through extensive Monte Carlo numerical simulations and analysis of in-vivo human brain datasets exhibiting a range of SNR and spatial resolution, we demonstrated the markedly improved accuracy and precision in the estimation of MWF using these Bayesian methods as compared to the stochastic region contraction (SRC) implementation of NLLS. PMID:26499810

Quantifying the uncertainty of nonpoint source attribution in distributed water quality models: A Bayesian assessment of SWAT's sediment export predictions

NASA Astrophysics Data System (ADS)

Wellen, Christopher; Arhonditsis, George B.; Long, Tanya; Boyd, Duncan

2014-11-01

Spatially distributed nonpoint source watershed models are essential tools to estimate the magnitude and sources of diffuse pollution. However, little work has been undertaken to understand the sources and ramifications of the uncertainty involved in their use. In this study we conduct the first Bayesian uncertainty analysis of the water quality components of the SWAT model, one of the most commonly used distributed nonpoint source models. Working in Southern Ontario, we apply three Bayesian configurations for calibrating SWAT to Redhill Creek, an urban catchment, and Grindstone Creek, an agricultural one. We answer four interrelated questions: can SWAT determine suspended sediment sources with confidence when end of basin data is used for calibration? How does uncertainty propagate from the discharge submodel to the suspended sediment submodels? Do the estimated sediment sources vary when different calibration approaches are used? Can we combine the knowledge gained from different calibration approaches? We show that: (i) despite reasonable fit at the basin outlet, the simulated sediment sources are subject to uncertainty sufficient to undermine the typical approach of reliance on a single, best fit simulation; (ii) more than a third of the uncertainty of sediment load predictions may stem from the discharge submodel; (iii) estimated sediment sources do vary significantly across the three statistical configurations of model calibration despite end-of-basin predictions being virtually identical; and (iv) Bayesian model averaging is an approach that can synthesize predictions when a number of adequate distributed models make divergent source apportionments. We conclude with recommendations for future research to reduce the uncertainty encountered when using distributed nonpoint source models for source apportionment.

Bayesian estimation of self-similarity exponent

NASA Astrophysics Data System (ADS)

Makarava, Natallia; Benmehdi, Sabah; Holschneider, Matthias

2011-08-01

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

Bayesian multimodel inference of soil microbial respiration models: Theory, application and future prospective

NASA Astrophysics Data System (ADS)

Elshall, A. S.; Ye, M.; Niu, G. Y.; Barron-Gafford, G.

2015-12-01

Models in biogeoscience involve uncertainties in observation data, model inputs, model structure, model processes and modeling scenarios. To accommodate for different sources of uncertainty, multimodal analysis such as model combination, model selection, model elimination or model discrimination are becoming more popular. To illustrate theoretical and practical challenges of multimodal analysis, we use an example about microbial soil respiration modeling. Global soil respiration releases more than ten times more carbon dioxide to the atmosphere than all anthropogenic emissions. Thus, improving our understanding of microbial soil respiration is essential for improving climate change models. This study focuses on a poorly understood phenomena, which is the soil microbial respiration pulses in response to episodic rainfall pulses (the "Birch effect"). We hypothesize that the "Birch effect" is generated by the following three mechanisms. To test our hypothesis, we developed and assessed five evolving microbial-enzyme models against field measurements from a semiarid Savannah that is characterized by pulsed precipitation. These five model evolve step-wise such that the first model includes none of these three mechanism, while the fifth model includes the three mechanisms. The basic component of Bayesian multimodal analysis is the estimation of marginal likelihood to rank the candidate models based on their overall likelihood with respect to observation data. The first part of the study focuses on using this Bayesian scheme to discriminate between these five candidate models. The second part discusses some theoretical and practical challenges, which are mainly the effect of likelihood function selection and the marginal likelihood estimation methods on both model ranking and Bayesian model averaging. The study shows that making valid inference from scientific data is not a trivial task, since we are not only uncertain about the candidate scientific models, but also about the statistical methods that are used to discriminate between these models.

Bayesian Monte Carlo and Maximum Likelihood Approach for ...

EPA Pesticide Factsheets

Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood estimation (BMCML) to calibrate a lake oxygen recovery model. We first derive an analytical solution of the differential equation governing lake-averaged oxygen dynamics as a function of time-variable wind speed. Statistical inferences on model parameters and predictive uncertainty are then drawn by Bayesian conditioning of the analytical solution on observed daily wind speed and oxygen concentration data obtained from an earlier study during two recovery periods on a eutrophic lake in upper state New York. The model is calibrated using oxygen recovery data for one year and statistical inferences were validated using recovery data for another year. Compared with essentially two-step, regression and optimization approach, the BMCML results are more comprehensive and performed relatively better in predicting the observed temporal dissolved oxygen levels (DO) in the lake. BMCML also produced comparable calibration and validation results with those obtained using popular Markov Chain Monte Carlo technique (MCMC) and is computationally simpler and easier to implement than the MCMC. Next, using the calibrated model, we derive an optimal relationship between liquid film-transfer coefficien

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

ERIC Educational Resources Information Center

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

2011-01-01

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

SU-F-R-44: Modeling Lung SBRT Tumor Response Using Bayesian Network Averaging

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

Diamant, A; Ybarra, N; Seuntjens, J

2016-06-15

Purpose: The prediction of tumor control after a patient receives lung SBRT (stereotactic body radiation therapy) has proven to be challenging, due to the complex interactions between an individual’s biology and dose-volume metrics. Many of these variables have predictive power when combined, a feature that we exploit using a graph modeling approach based on Bayesian networks. This provides a probabilistic framework that allows for accurate and visually intuitive predictive modeling. The aim of this study is to uncover possible interactions between an individual patient’s characteristics and generate a robust model capable of predicting said patient’s treatment outcome. Methods: We investigatedmore » a cohort of 32 prospective patients from multiple institutions whom had received curative SBRT to the lung. The number of patients exhibiting tumor failure was observed to be 7 (event rate of 22%). The serum concentration of 5 biomarkers previously associated with NSCLC (non-small cell lung cancer) was measured pre-treatment. A total of 21 variables were analyzed including: dose-volume metrics with BED (biologically effective dose) correction and clinical variables. A Markov Chain Monte Carlo technique estimated the posterior probability distribution of the potential graphical structures. The probability of tumor failure was then estimated by averaging the top 100 graphs and applying Baye’s rule. Results: The optimal Bayesian model generated throughout this study incorporated the PTV volume, the serum concentration of the biomarker EGFR (epidermal growth factor receptor) and prescription BED. This predictive model recorded an area under the receiver operating characteristic curve of 0.94(1), providing better performance compared to competing methods in other literature. Conclusion: The use of biomarkers in conjunction with dose-volume metrics allows for the generation of a robust predictive model. The preliminary results of this report demonstrate that it is possible to accurately model the prognosis of an individual lung SBRT patient’s treatment.« less

Bayesian model averaging using particle filtering and Gaussian mixture modeling: Theory, concepts, and simulation experiments

NASA Astrophysics Data System (ADS)

Rings, Joerg; Vrugt, Jasper A.; Schoups, Gerrit; Huisman, Johan A.; Vereecken, Harry

2012-05-01

Bayesian model averaging (BMA) is a standard method for combining predictive distributions from different models. In recent years, this method has enjoyed widespread application and use in many fields of study to improve the spread-skill relationship of forecast ensembles. The BMA predictive probability density function (pdf) of any quantity of interest is a weighted average of pdfs centered around the individual (possibly bias-corrected) forecasts, where the weights are equal to posterior probabilities of the models generating the forecasts, and reflect the individual models skill over a training (calibration) period. The original BMA approach presented by Raftery et al. (2005) assumes that the conditional pdf of each individual model is adequately described with a rather standard Gaussian or Gamma statistical distribution, possibly with a heteroscedastic variance. Here we analyze the advantages of using BMA with a flexible representation of the conditional pdf. A joint particle filtering and Gaussian mixture modeling framework is presented to derive analytically, as closely and consistently as possible, the evolving forecast density (conditional pdf) of each constituent ensemble member. The median forecasts and evolving conditional pdfs of the constituent models are subsequently combined using BMA to derive one overall predictive distribution. This paper introduces the theory and concepts of this new ensemble postprocessing method, and demonstrates its usefulness and applicability by numerical simulation of the rainfall-runoff transformation using discharge data from three different catchments in the contiguous United States. The revised BMA method receives significantly lower-prediction errors than the original default BMA method (due to filtering) with predictive uncertainty intervals that are substantially smaller but still statistically coherent (due to the use of a time-variant conditional pdf).

Evaluating and improving count-based population inference: A case study from 31 years of monitoring Sandhill Cranes

USGS Publications Warehouse

Gerber, Brian D.; Kendall, William L.

2017-01-01

Monitoring animal populations can be difficult. Limited resources often force monitoring programs to rely on unadjusted or smoothed counts as an index of abundance. Smoothing counts is commonly done using a moving-average estimator to dampen sampling variation. These indices are commonly used to inform management decisions, although their reliability is often unknown. We outline a process to evaluate the biological plausibility of annual changes in population counts and indices from a typical monitoring scenario and compare results with a hierarchical Bayesian time series (HBTS) model. We evaluated spring and fall counts, fall indices, and model-based predictions for the Rocky Mountain population (RMP) of Sandhill Cranes (Antigone canadensis) by integrating juvenile recruitment, harvest, and survival into a stochastic stage-based population model. We used simulation to evaluate population indices from the HBTS model and the commonly used 3-yr moving average estimator. We found counts of the RMP to exhibit biologically unrealistic annual change, while the fall population index was largely biologically realistic. HBTS model predictions suggested that the RMP changed little over 31 yr of monitoring, but the pattern depended on assumptions about the observational process. The HBTS model fall population predictions were biologically plausible if observed crane harvest mortality was compensatory up to natural mortality, as empirical evidence suggests. Simulations indicated that the predicted mean of the HBTS model was generally a more reliable estimate of the true population than population indices derived using a moving 3-yr average estimator. Practitioners could gain considerable advantages from modeling population counts using a hierarchical Bayesian autoregressive approach. Advantages would include: (1) obtaining measures of uncertainty; (2) incorporating direct knowledge of the observational and population processes; (3) accommodating missing years of data; and (4) forecasting population size.

Bayesian optimization of the Community Land Model simulated biosphere-atmosphere exchange using CO 2 observations from a dense tower network and aircraft campaigns over Oregon

DOE PAGES

Schmidt, Andres; Law, Beverly E.; Göckede, Mathias; ...

2016-09-15

Here, the vast forests and natural areas of the Pacific Northwest comprise one of the most productive ecosystems in the northern hemisphere. The heterogeneous landscape of Oregon poses a particular challenge to ecosystem models. We present a framework using a scaling factor Bayesian inversion to improve the modeled atmosphere-biosphere exchange of carbon dioxide. Observations from 5 CO/CO 2 towers, eddy covariance towers, and airborne campaigns were used to constrain the Community Land Model CLM4.5 simulated terrestrial CO 2 exchange at a high spatial and temporal resolution (1/24°, 3-hourly). To balance aggregation errors and the degrees of freedom in the inversemore » modeling system, we applied an unsupervised clustering approach for the spatial structuring of our model domain. Data from flight campaigns were used to quantify the uncertainty introduced by the Lagrangian particle dispersion model that was applied for the inversions. The average annual statewide net ecosystem productivity (NEP) was increased by 32% to 29.7 TgC per year by assimilating the tropospheric mixing ratio data. The associated uncertainty was decreased by 28.4% to 29%, on average over the entire Oregon model domain with the lowest uncertainties of 11% in western Oregon. The largest differences between posterior and prior CO 2 fluxes were found for the Coast Range ecoregion of Oregon that also exhibits the highest availability of atmospheric observations and associated footprints. In this area, covered by highly productive Douglas-fir forest, the differences between the prior and posterior estimate of NEP averaged 3.84 TgC per year during the study period from 2012 through 2014.« less

Bayesian optimization of the Community Land Model simulated biosphere-atmosphere exchange using CO 2 observations from a dense tower network and aircraft campaigns over Oregon

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

Schmidt, Andres; Law, Beverly E.; Göckede, Mathias

Here, the vast forests and natural areas of the Pacific Northwest comprise one of the most productive ecosystems in the northern hemisphere. The heterogeneous landscape of Oregon poses a particular challenge to ecosystem models. We present a framework using a scaling factor Bayesian inversion to improve the modeled atmosphere-biosphere exchange of carbon dioxide. Observations from 5 CO/CO 2 towers, eddy covariance towers, and airborne campaigns were used to constrain the Community Land Model CLM4.5 simulated terrestrial CO 2 exchange at a high spatial and temporal resolution (1/24°, 3-hourly). To balance aggregation errors and the degrees of freedom in the inversemore » modeling system, we applied an unsupervised clustering approach for the spatial structuring of our model domain. Data from flight campaigns were used to quantify the uncertainty introduced by the Lagrangian particle dispersion model that was applied for the inversions. The average annual statewide net ecosystem productivity (NEP) was increased by 32% to 29.7 TgC per year by assimilating the tropospheric mixing ratio data. The associated uncertainty was decreased by 28.4% to 29%, on average over the entire Oregon model domain with the lowest uncertainties of 11% in western Oregon. The largest differences between posterior and prior CO 2 fluxes were found for the Coast Range ecoregion of Oregon that also exhibits the highest availability of atmospheric observations and associated footprints. In this area, covered by highly productive Douglas-fir forest, the differences between the prior and posterior estimate of NEP averaged 3.84 TgC per year during the study period from 2012 through 2014.« less

Value of information analysis for interventional and counterfactual Bayesian networks in forensic medical sciences.

PubMed

Constantinou, Anthony Costa; Yet, Barbaros; Fenton, Norman; Neil, Martin; Marsh, William

2016-01-01

Inspired by real-world examples from the forensic medical sciences domain, we seek to determine whether a decision about an interventional action could be subject to amendments on the basis of some incomplete information within the model, and whether it would be worthwhile for the decision maker to seek further information prior to suggesting a decision. The method is based on the underlying principle of Value of Information to enhance decision analysis in interventional and counterfactual Bayesian networks. The method is applied to two real-world Bayesian network models (previously developed for decision support in forensic medical sciences) to examine the average gain in terms of both Value of Information (average relative gain ranging from 11.45% and 59.91%) and decision making (potential amendments in decision making ranging from 0% to 86.8%). We have shown how the method becomes useful for decision makers, not only when decision making is subject to amendments on the basis of some unknown risk factors, but also when it is not. Knowing that a decision outcome is independent of one or more unknown risk factors saves us from the trouble of seeking information about the particular set of risk factors. Further, we have also extended the assessment of this implication to the counterfactual case and demonstrated how answers about interventional actions are expected to change when some unknown factors become known, and how useful this becomes in forensic medical science. Copyright © 2015 Elsevier B.V. All rights reserved.

Goal-oriented Site Characterization in Hydrogeological Applications: An Overview

NASA Astrophysics Data System (ADS)

Nowak, W.; de Barros, F.; Rubin, Y.

2011-12-01

In this study, we address the importance of goal-oriented site characterization. Given the multiple sources of uncertainty in hydrogeological applications, information needs of modeling, prediction and decision support should be satisfied with efficient and rational field campaigns. In this work, we provide an overview of an optimal sampling design framework based on Bayesian decision theory, statistical parameter inference and Bayesian model averaging. It optimizes the field sampling campaign around decisions on environmental performance metrics (e.g., risk, arrival times, etc.) while accounting for parametric and model uncertainty in the geostatistical characterization, in forcing terms, and measurement error. The appealing aspects of the framework lie on its goal-oriented character and that it is directly linked to the confidence in a specified decision. We illustrate how these concepts could be applied in a human health risk problem where uncertainty from both hydrogeological and health parameters are accounted.

Bayesian Ensemble Trees (BET) for Clustering and Prediction in Heterogeneous Data

PubMed Central

Duan, Leo L.; Clancy, John P.; Szczesniak, Rhonda D.

2016-01-01

We propose a novel “tree-averaging” model that utilizes the ensemble of classification and regression trees (CART). Each constituent tree is estimated with a subset of similar data. We treat this grouping of subsets as Bayesian Ensemble Trees (BET) and model them as a Dirichlet process. We show that BET determines the optimal number of trees by adapting to the data heterogeneity. Compared with the other ensemble methods, BET requires much fewer trees and shows equivalent prediction accuracy using weighted averaging. Moreover, each tree in BET provides variable selection criterion and interpretation for each subset. We developed an efficient estimating procedure with improved estimation strategies in both CART and mixture models. We demonstrate these advantages of BET with simulations and illustrate the approach with a real-world data example involving regression of lung function measurements obtained from patients with cystic fibrosis. Supplemental materials are available online. PMID:27524872

Evaluating Bayesian spatial methods for modelling species distributions with clumped and restricted occurrence data.

PubMed

Redding, David W; Lucas, Tim C D; Blackburn, Tim M; Jones, Kate E

2017-01-01

Statistical approaches for inferring the spatial distribution of taxa (Species Distribution Models, SDMs) commonly rely on available occurrence data, which is often clumped and geographically restricted. Although available SDM methods address some of these factors, they could be more directly and accurately modelled using a spatially-explicit approach. Software to fit models with spatial autocorrelation parameters in SDMs are now widely available, but whether such approaches for inferring SDMs aid predictions compared to other methodologies is unknown. Here, within a simulated environment using 1000 generated species' ranges, we compared the performance of two commonly used non-spatial SDM methods (Maximum Entropy Modelling, MAXENT and boosted regression trees, BRT), to a spatial Bayesian SDM method (fitted using R-INLA), when the underlying data exhibit varying combinations of clumping and geographic restriction. Finally, we tested how any recommended methodological settings designed to account for spatially non-random patterns in the data impact inference. Spatial Bayesian SDM method was the most consistently accurate method, being in the top 2 most accurate methods in 7 out of 8 data sampling scenarios. Within high-coverage sample datasets, all methods performed fairly similarly. When sampling points were randomly spread, BRT had a 1-3% greater accuracy over the other methods and when samples were clumped, the spatial Bayesian SDM method had a 4%-8% better AUC score. Alternatively, when sampling points were restricted to a small section of the true range all methods were on average 10-12% less accurate, with greater variation among the methods. Model inference under the recommended settings to account for autocorrelation was not impacted by clumping or restriction of data, except for the complexity of the spatial regression term in the spatial Bayesian model. Methods, such as those made available by R-INLA, can be successfully used to account for spatial autocorrelation in an SDM context and, by taking account of random effects, produce outputs that can better elucidate the role of covariates in predicting species occurrence. Given that it is often unclear what the drivers are behind data clumping in an empirical occurrence dataset, or indeed how geographically restricted these data are, spatially-explicit Bayesian SDMs may be the better choice when modelling the spatial distribution of target species.

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.

Improved prediction of tacrolimus concentrations early after kidney transplantation using theory-based pharmacokinetic modelling.

PubMed

Størset, Elisabet; Holford, Nick; Hennig, Stefanie; Bergmann, Troels K; Bergan, Stein; Bremer, Sara; Åsberg, Anders; Midtvedt, Karsten; Staatz, Christine E

2014-09-01

The aim was to develop a theory-based population pharmacokinetic model of tacrolimus in adult kidney transplant recipients and to externally evaluate this model and two previous empirical models. Data were obtained from 242 patients with 3100 tacrolimus whole blood concentrations. External evaluation was performed by examining model predictive performance using Bayesian forecasting. Pharmacokinetic disposition parameters were estimated based on tacrolimus plasma concentrations, predicted from whole blood concentrations, haematocrit and literature values for tacrolimus binding to red blood cells. Disposition parameters were allometrically scaled to fat free mass. Tacrolimus whole blood clearance/bioavailability standardized to haematocrit of 45% and fat free mass of 60 kg was estimated to be 16.1 l h−1 [95% CI 12.6, 18.0 l h−1]. Tacrolimus clearance was 30% higher (95% CI 13, 46%) and bioavailability 18% lower (95% CI 2, 29%) in CYP3A5 expressers compared with non-expressers. An Emax model described decreasing tacrolimus bioavailability with increasing prednisolone dose. The theory-based model was superior to the empirical models during external evaluation displaying a median prediction error of −1.2% (95% CI −3.0, 0.1%). Based on simulation, Bayesian forecasting led to 65% (95% CI 62, 68%) of patients achieving a tacrolimus average steady-state concentration within a suggested acceptable range. A theory-based population pharmacokinetic model was superior to two empirical models for prediction of tacrolimus concentrations and seemed suitable for Bayesian prediction of tacrolimus doses early after kidney transplantation.

Order-Constrained Reference Priors with Implications for Bayesian Isotonic Regression, Analysis of Covariance and Spatial Models

NASA Astrophysics Data System (ADS)

Gong, Maozhen

Selecting an appropriate prior distribution is a fundamental issue in Bayesian Statistics. In this dissertation, under the framework provided by Berger and Bernardo, I derive the reference priors for several models which include: Analysis of Variance (ANOVA)/Analysis of Covariance (ANCOVA) models with a categorical variable under common ordering constraints, the conditionally autoregressive (CAR) models and the simultaneous autoregressive (SAR) models with a spatial autoregression parameter rho considered. The performances of reference priors for ANOVA/ANCOVA models are evaluated by simulation studies with comparisons to Jeffreys' prior and Least Squares Estimation (LSE). The priors are then illustrated in a Bayesian model of the "Risk of Type 2 Diabetes in New Mexico" data, where the relationship between the type 2 diabetes risk (through Hemoglobin A1c) and different smoking levels is investigated. In both simulation studies and real data set modeling, the reference priors that incorporate internal order information show good performances and can be used as default priors. The reference priors for the CAR and SAR models are also illustrated in the "1999 SAT State Average Verbal Scores" data with a comparison to a Uniform prior distribution. Due to the complexity of the reference priors for both CAR and SAR models, only a portion (12 states in the Midwest) of the original data set is considered. The reference priors can give a different marginal posterior distribution compared to a Uniform prior, which provides an alternative for prior specifications for areal data in Spatial statistics.

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

NASA Astrophysics Data System (ADS)

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

2008-12-01

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

Development and comparison of Bayesian modularization method in uncertainty assessment of hydrological models

NASA Astrophysics Data System (ADS)

Li, L.; Xu, C.-Y.; Engeland, K.

2012-04-01

With respect to model calibration, parameter estimation and analysis of uncertainty sources, different approaches have been used in hydrological models. Bayesian method is one of the most widely used methods for uncertainty assessment of hydrological models, which incorporates different sources of information into a single analysis through Bayesian theorem. However, none of these applications can well treat the uncertainty in extreme flows of hydrological models' simulations. This study proposes a Bayesian modularization method approach in uncertainty assessment of conceptual hydrological models by considering the extreme flows. It includes a comprehensive comparison and evaluation of uncertainty assessments by a new Bayesian modularization method approach and traditional Bayesian models using the Metropolis Hasting (MH) algorithm with the daily hydrological model WASMOD. Three likelihood functions are used in combination with traditional Bayesian: the AR (1) plus Normal and time period independent model (Model 1), the AR (1) plus Normal and time period dependent model (Model 2) and the AR (1) plus multi-normal model (Model 3). The results reveal that (1) the simulations derived from Bayesian modularization method are more accurate with the highest Nash-Sutcliffe efficiency value, and (2) the Bayesian modularization method performs best in uncertainty estimates of entire flows and in terms of the application and computational efficiency. The study thus introduces a new approach for reducing the extreme flow's effect on the discharge uncertainty assessment of hydrological models via Bayesian. Keywords: extreme flow, uncertainty assessment, Bayesian modularization, hydrological model, WASMOD

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

La Russa, D

Purpose: The purpose of this project is to develop a robust method of parameter estimation for a Poisson-based TCP model using Bayesian inference. Methods: Bayesian inference was performed using the PyMC3 probabilistic programming framework written in Python. A Poisson-based TCP regression model that accounts for clonogen proliferation was fit to observed rates of local relapse as a function of equivalent dose in 2 Gy fractions for a population of 623 stage-I non-small-cell lung cancer patients. The Slice Markov Chain Monte Carlo sampling algorithm was used to sample the posterior distributions, and was initiated using the maximum of the posterior distributionsmore » found by optimization. The calculation of TCP with each sample step required integration over the free parameter α, which was performed using an adaptive 24-point Gauss-Legendre quadrature. Convergence was verified via inspection of the trace plot and posterior distribution for each of the fit parameters, as well as with comparisons of the most probable parameter values with their respective maximum likelihood estimates. Results: Posterior distributions for α, the standard deviation of α (σ), the average tumour cell-doubling time (Td), and the repopulation delay time (Tk), were generated assuming α/β = 10 Gy, and a fixed clonogen density of 10{sup 7} cm−{sup 3}. Posterior predictive plots generated from samples from these posterior distributions are in excellent agreement with the observed rates of local relapse used in the Bayesian inference. The most probable values of the model parameters also agree well with maximum likelihood estimates. Conclusion: A robust method of performing Bayesian inference of TCP data using a complex TCP model has been established.« less

Uncertainty Quantification given Discontinuous Climate Model Response and a Limited Number of Model Runs

NASA Astrophysics Data System (ADS)

Sargsyan, K.; Safta, C.; Debusschere, B.; Najm, H.

2010-12-01

Uncertainty quantification in complex climate models is challenged by the sparsity of available climate model predictions due to the high computational cost of model runs. Another feature that prevents classical uncertainty analysis from being readily applicable is bifurcative behavior in climate model response with respect to certain input parameters. A typical example is the Atlantic Meridional Overturning Circulation. The predicted maximum overturning stream function exhibits discontinuity across a curve in the space of two uncertain parameters, namely climate sensitivity and CO2 forcing. We outline a methodology for uncertainty quantification given discontinuous model response and a limited number of model runs. Our approach is two-fold. First we detect the discontinuity with Bayesian inference, thus obtaining a probabilistic representation of the discontinuity curve shape and location for arbitrarily distributed input parameter values. Then, we construct spectral representations of uncertainty, using Polynomial Chaos (PC) expansions on either side of the discontinuity curve, leading to an averaged-PC representation of the forward model that allows efficient uncertainty quantification. The approach is enabled by a Rosenblatt transformation that maps each side of the discontinuity to regular domains where desirable orthogonality properties for the spectral bases hold. We obtain PC modes by either orthogonal projection or Bayesian inference, and argue for a hybrid approach that targets a balance between the accuracy provided by the orthogonal projection and the flexibility provided by the Bayesian inference - where the latter allows obtaining reasonable expansions without extra forward model runs. The model output, and its associated uncertainty at specific design points, are then computed by taking an ensemble average over PC expansions corresponding to possible realizations of the discontinuity curve. The methodology is tested on synthetic examples of discontinuous model data with adjustable sharpness and structure. This work was supported by the Sandia National Laboratories Seniors’ Council LDRD (Laboratory Directed Research and Development) program. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Company, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

Wind power application research on the fusion of the determination and ensemble prediction

NASA Astrophysics Data System (ADS)

Lan, Shi; Lina, Xu; Yuzhu, Hao

2017-07-01

The fused product of wind speed for the wind farm is designed through the use of wind speed products of ensemble prediction from the European Centre for Medium-Range Weather Forecasts (ECMWF) and professional numerical model products on wind power based on Mesoscale Model5 (MM5) and Beijing Rapid Update Cycle (BJ-RUC), which are suitable for short-term wind power forecasting and electric dispatch. The single-valued forecast is formed by calculating the different ensemble statistics of the Bayesian probabilistic forecasting representing the uncertainty of ECMWF ensemble prediction. Using autoregressive integrated moving average (ARIMA) model to improve the time resolution of the single-valued forecast, and based on the Bayesian model averaging (BMA) and the deterministic numerical model prediction, the optimal wind speed forecasting curve and the confidence interval are provided. The result shows that the fusion forecast has made obvious improvement to the accuracy relative to the existing numerical forecasting products. Compared with the 0-24 h existing deterministic forecast in the validation period, the mean absolute error (MAE) is decreased by 24.3 % and the correlation coefficient (R) is increased by 12.5 %. In comparison with the ECMWF ensemble forecast, the MAE is reduced by 11.7 %, and R is increased 14.5 %. Additionally, MAE did not increase with the prolongation of the forecast ahead.

Structural equation modeling of the inflammatory response to traffic air pollution

PubMed Central

Baja, Emmanuel S.; Schwartz, Joel D.; Coull, Brent A.; Wellenius, Gregory A.; Vokonas, Pantel S.; Suh, Helen H.

2015-01-01

Several epidemiological studies have reported conflicting results on the effect of traffic-related pollutants on markers of inflammation. In a Bayesian framework, we examined the effect of traffic pollution on inflammation using structural equation models (SEMs). We studied measurements of C-reactive protein (CRP), soluble vascular cell adhesion molecule-1 (sVCAM-1), and soluble intracellular adhesion molecule-1 (sICAM-1) for 749 elderly men from the Normative Aging Study. Using repeated measures SEMs, we fit a latent variable for traffic pollution that is reflected by levels of black carbon, carbon monoxide, nitrogen monoxide and nitrogen dioxide to estimate its effect on a latent variable for inflammation that included sICAM-1, sVCAM-1 and CRP. Exposure periods were assessed using 1-, 2-, 3-, 7-, 14- and 30-day moving averages previsit. We compared our findings using SEMs with those obtained using linear mixed models. Traffic pollution was related to increased inflammation for 3-, 7-, 14- and 30-day exposure periods. An inter-quartile range increase in traffic pollution was associated with a 2.3% (95% posterior interval (PI): 0.0–4.7%) increase in inflammation for the 3-day moving average, with the most significant association observed for the 30-day moving average (23.9%; 95% PI: 13.9–36.7%). Traffic pollution adversely impacts inflammation in the elderly. SEMs in a Bayesian framework can comprehensively incorporate multiple pollutants and health outcomes simultaneously in air pollution–cardiovascular epidemiological studies. PMID:23232970

Incorporating measurement error in n = 1 psychological autoregressive modeling.

PubMed

Schuurman, Noémi K; Houtveen, Jan H; Hamaker, Ellen L

2015-01-01

Measurement error is omnipresent in psychological data. However, the vast majority of applications of autoregressive time series analyses in psychology do not take measurement error into account. Disregarding measurement error when it is present in the data results in a bias of the autoregressive parameters. We discuss two models that take measurement error into account: An autoregressive model with a white noise term (AR+WN), and an autoregressive moving average (ARMA) model. In a simulation study we compare the parameter recovery performance of these models, and compare this performance for both a Bayesian and frequentist approach. We find that overall, the AR+WN model performs better. Furthermore, we find that for realistic (i.e., small) sample sizes, psychological research would benefit from a Bayesian approach in fitting these models. Finally, we illustrate the effect of disregarding measurement error in an AR(1) model by means of an empirical application on mood data in women. We find that, depending on the person, approximately 30-50% of the total variance was due to measurement error, and that disregarding this measurement error results in a substantial underestimation of the autoregressive parameters.

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.

A Bayesian Nonparametric Approach to Test Equating

ERIC Educational Resources Information Center

Karabatsos, George; Walker, Stephen G.

2009-01-01

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are…

Model Diagnostics for Bayesian Networks

ERIC Educational Resources Information Center

Sinharay, Sandip

2006-01-01

Bayesian networks are frequently used in educational assessments primarily for learning about students' knowledge and skills. There is a lack of works on assessing fit of Bayesian networks. This article employs the posterior predictive model checking method, a popular Bayesian model checking tool, to assess fit of simple Bayesian networks. A…

ModelTest Server: a web-based tool for the statistical selection of models of nucleotide substitution online

PubMed Central

Posada, David

2006-01-01

ModelTest server is a web-based application for the selection of models of nucleotide substitution using the program ModelTest. The server takes as input a text file with likelihood scores for the set of candidate models. Models can be selected with hierarchical likelihood ratio tests, or with the Akaike or Bayesian information criteria. The output includes several statistics for the assessment of model selection uncertainty, for model averaging or to estimate the relative importance of model parameters. The server can be accessed at . PMID:16845102

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.

Bayesian source term estimation of atmospheric releases in urban areas using LES approach.

PubMed

Xue, Fei; Kikumoto, Hideki; Li, Xiaofeng; Ooka, Ryozo

2018-05-05

The estimation of source information from limited measurements of a sensor network is a challenging inverse problem, which can be viewed as an assimilation process of the observed concentration data and the predicted concentration data. When dealing with releases in built-up areas, the predicted data are generally obtained by the Reynolds-averaged Navier-Stokes (RANS) equations, which yields building-resolving results; however, RANS-based models are outperformed by large-eddy simulation (LES) in the predictions of both airflow and dispersion. Therefore, it is important to explore the possibility of improving the estimation of the source parameters by using the LES approach. In this paper, a novel source term estimation method is proposed based on LES approach using Bayesian inference. The source-receptor relationship is obtained by solving the adjoint equations constructed using the time-averaged flow field simulated by the LES approach based on the gradient diffusion hypothesis. A wind tunnel experiment with a constant point source downwind of a single building model is used to evaluate the performance of the proposed method, which is compared with that of the existing method using a RANS model. The results show that the proposed method reduces the errors of source location and releasing strength by 77% and 28%, respectively. Copyright © 2018 Elsevier B.V. All rights reserved.

Multiple organ definition in CT using a Bayesian approach for 3D model fitting

NASA Astrophysics Data System (ADS)

Boes, Jennifer L.; Weymouth, Terry E.; Meyer, Charles R.

1995-08-01

Organ definition in computed tomography (CT) is of interest for treatment planning and response monitoring. We present a method for organ definition using a priori information about shape encoded in a set of biometric organ models--specifically for the liver and kidney-- that accurately represents patient population shape information. Each model is generated by averaging surfaces from a learning set of organ shapes previously registered into a standard space defined by a small set of landmarks. The model is placed in a specific patient's data set by identifying these landmarks and using them as the basis for model deformation; this preliminary representation is then iteratively fit to the patient's data based on a Bayesian formulation of the model's priors and CT edge information, yielding a complete organ surface. We demonstrate this technique using a set of fifteen abdominal CT data sets for liver surface definition both before and after the addition of a kidney model to the fitting; we demonstrate the effectiveness of this tool for organ surface definition in this low-contrast domain.

A Bayesian random effects discrete-choice model for resource selection: Population-level selection inference

USGS Publications Warehouse

Thomas, D.L.; Johnson, D.; Griffith, B.

2006-01-01

Modeling the probability of use of land units characterized by discrete and continuous measures, we present a Bayesian random-effects model to assess resource selection. This model provides simultaneous estimation of both individual- and population-level selection. Deviance information criterion (DIC), a Bayesian alternative to AIC that is sample-size specific, is used for model selection. Aerial radiolocation data from 76 adult female caribou (Rangifer tarandus) and calf pairs during 1 year on an Arctic coastal plain calving ground were used to illustrate models and assess population-level selection of landscape attributes, as well as individual heterogeneity of selection. Landscape attributes included elevation, NDVI (a measure of forage greenness), and land cover-type classification. Results from the first of a 2-stage model-selection procedure indicated that there is substantial heterogeneity among cow-calf pairs with respect to selection of the landscape attributes. In the second stage, selection of models with heterogeneity included indicated that at the population-level, NDVI and land cover class were significant attributes for selection of different landscapes by pairs on the calving ground. Population-level selection coefficients indicate that the pairs generally select landscapes with higher levels of NDVI, but the relationship is quadratic. The highest rate of selection occurs at values of NDVI less than the maximum observed. Results for land cover-class selections coefficients indicate that wet sedge, moist sedge, herbaceous tussock tundra, and shrub tussock tundra are selected at approximately the same rate, while alpine and sparsely vegetated landscapes are selected at a lower rate. Furthermore, the variability in selection by individual caribou for moist sedge and sparsely vegetated landscapes is large relative to the variability in selection of other land cover types. The example analysis illustrates that, while sometimes computationally intense, a Bayesian hierarchical discrete-choice model for resource selection can provide managers with 2 components of population-level inference: average population selection and variability of selection. Both components are necessary to make sound management decisions based on animal selection.

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.

Incorporation of GRACE Data into a Bayesian Model for Groundwater Drought Monitoring

NASA Astrophysics Data System (ADS)

Slinski, K.; Hogue, T. S.; McCray, J. E.; Porter, A.

2015-12-01

Groundwater drought, defined as the sustained occurrence of below average availability of groundwater, is marked by below average water levels in aquifers and reduced flows to groundwater-fed rivers and wetlands. The impact of groundwater drought on ecosystems, agriculture, municipal water supply, and the energy sector is an increasingly important global issue. However, current drought monitors heavily rely on precipitation and vegetative stress indices to characterize the timing, duration, and severity of drought events. The paucity of in situ observations of aquifer levels is a substantial obstacle to the development of systems to monitor groundwater drought in drought-prone areas, particularly in developing countries. Observations from the NASA/German Space Agency's Gravity Recovery and Climate Experiment (GRACE) have been used to estimate changes in groundwater storage over areas with sparse point measurements. This study incorporates GRACE total water storage observations into a Bayesian framework to assess the performance of a probabilistic model for monitoring groundwater drought based on remote sensing data. Overall, it is hoped that these methods will improve global drought preparedness and risk reduction by providing information on groundwater drought necessary to manage its impacts on ecosystems, as well as on the agricultural, municipal, and energy sectors.

Quantification of model uncertainty in aerosol optical thickness retrieval from Ozone Monitoring Instrument (OMI) measurements

NASA Astrophysics Data System (ADS)

Määttä, A.; Laine, M.; Tamminen, J.; Veefkind, J. P.

2013-09-01

We study uncertainty quantification in remote sensing of aerosols in the atmosphere with top of the atmosphere reflectance measurements from the nadir-viewing Ozone Monitoring Instrument (OMI). Focus is on the uncertainty in aerosol model selection of pre-calculated aerosol models and on the statistical modelling of the model inadequacies. The aim is to apply statistical methodologies that improve the uncertainty estimates of the aerosol optical thickness (AOT) retrieval by propagating model selection and model error related uncertainties more realistically. We utilise Bayesian model selection and model averaging methods for the model selection problem and use Gaussian processes to model the smooth systematic discrepancies from the modelled to observed reflectance. The systematic model error is learned from an ensemble of operational retrievals. The operational OMI multi-wavelength aerosol retrieval algorithm OMAERO is used for cloud free, over land pixels of the OMI instrument with the additional Bayesian model selection and model discrepancy techniques. The method is demonstrated with four examples with different aerosol properties: weakly absorbing aerosols, forest fires over Greece and Russia, and Sahara dessert dust. The presented statistical methodology is general; it is not restricted to this particular satellite retrieval application.

A Bayesian approach to estimate evoked potentials.

PubMed

Sparacino, Giovanni; Milani, Stefano; Arslan, Edoardo; Cobelli, Claudio

2002-06-01

Several approaches, based on different assumptions and with various degree of theoretical sophistication and implementation complexity, have been developed for improving the measurement of evoked potentials (EP) performed by conventional averaging (CA). In many of these methods, one of the major challenges is the exploitation of a priori knowledge. In this paper, we present a new method where the 2nd-order statistical information on the background EEG and on the unknown EP, necessary for the optimal filtering of each sweep in a Bayesian estimation framework, is, respectively, estimated from pre-stimulus data and obtained through a multiple integration of a white noise process model. The latter model is flexible (i.e. it can be employed for a large class of EP) and simple enough to be easily identifiable from the post-stimulus data thanks to a smoothing criterion. The mean EP is determined as the weighted average of the filtered sweeps, where each weight is inversely proportional to the expected value of the norm of the correspondent filter error, a quantity determinable thanks to the employment of the Bayesian approach. The performance of the new approach is shown on both simulated and real auditory EP. A signal-to-noise ratio enhancement is obtained that can allow the (possibly automatic) identification of peak latencies and amplitudes with less sweeps than those required by CA. For cochlear EP, the method also allows the audiology investigator to gather new and clinically important information. The possibility of handling single-sweep analysis with further development of the method is also addressed.

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.

An ensemble-based dynamic Bayesian averaging approach for discharge simulations using multiple global precipitation products and hydrological models

NASA Astrophysics Data System (ADS)

Qi, Wei; Liu, Junguo; Yang, Hong; Sweetapple, Chris

2018-03-01

Global precipitation products are very important datasets in flow simulations, especially in poorly gauged regions. Uncertainties resulting from precipitation products, hydrological models and their combinations vary with time and data magnitude, and undermine their application to flow simulations. However, previous studies have not quantified these uncertainties individually and explicitly. This study developed an ensemble-based dynamic Bayesian averaging approach (e-Bay) for deterministic discharge simulations using multiple global precipitation products and hydrological models. In this approach, the joint probability of precipitation products and hydrological models being correct is quantified based on uncertainties in maximum and mean estimation, posterior probability is quantified as functions of the magnitude and timing of discharges, and the law of total probability is implemented to calculate expected discharges. Six global fine-resolution precipitation products and two hydrological models of different complexities are included in an illustrative application. e-Bay can effectively quantify uncertainties and therefore generate better deterministic discharges than traditional approaches (weighted average methods with equal and varying weights and maximum likelihood approach). The mean Nash-Sutcliffe Efficiency values of e-Bay are up to 0.97 and 0.85 in training and validation periods respectively, which are at least 0.06 and 0.13 higher than traditional approaches. In addition, with increased training data, assessment criteria values of e-Bay show smaller fluctuations than traditional approaches and its performance becomes outstanding. The proposed e-Bay approach bridges the gap between global precipitation products and their pragmatic applications to discharge simulations, and is beneficial to water resources management in ungauged or poorly gauged regions across the world.

Bayesian calibration of the Community Land Model using surrogates

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

Ray, Jaideep; Hou, Zhangshuan; Huang, Maoyi

2014-02-01

We present results from the Bayesian calibration of hydrological parameters of the Community Land Model (CLM), which is often used in climate simulations and Earth system models. A statistical inverse problem is formulated for three hydrological parameters, conditional on observations of latent heat surface fluxes over 48 months. Our calibration method uses polynomial and Gaussian process surrogates of the CLM, and solves the parameter estimation problem using a Markov chain Monte Carlo sampler. Posterior probability densities for the parameters are developed for two sites with different soil and vegetation covers. Our method also allows us to examine the structural errormore » in CLM under two error models. We find that surrogate models can be created for CLM in most cases. The posterior distributions are more predictive than the default parameter values in CLM. Climatologically averaging the observations does not modify the parameters' distributions significantly. The structural error model reveals a correlation time-scale which can be used to identify the physical process that could be contributing to it. While the calibrated CLM has a higher predictive skill, the calibration is under-dispersive.« less

Quantitative trait nucleotide analysis using Bayesian model selection.

PubMed

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

2005-10-01

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

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.

A Bayesian modelling framework for tornado occurrences in North America

NASA Astrophysics Data System (ADS)

Cheng, Vincent Y. S.; Arhonditsis, George B.; Sills, David M. L.; Gough, William A.; Auld, Heather

2015-03-01

Tornadoes represent one of nature’s most hazardous phenomena that have been responsible for significant destruction and devastating fatalities. Here we present a Bayesian modelling approach for elucidating the spatiotemporal patterns of tornado activity in North America. Our analysis shows a significant increase in the Canadian Prairies and the Northern Great Plains during the summer, indicating a clear transition of tornado activity from the United States to Canada. The linkage between monthly-averaged atmospheric variables and likelihood of tornado events is characterized by distinct seasonality; the convective available potential energy is the predominant factor in the summer; vertical wind shear appears to have a strong signature primarily in the winter and secondarily in the summer; and storm relative environmental helicity is most influential in the spring. The present probabilistic mapping can be used to draw inference on the likelihood of tornado occurrence in any location in North America within a selected time period of the year.

A Bayesian modelling framework for tornado occurrences in North America.

PubMed

Cheng, Vincent Y S; Arhonditsis, George B; Sills, David M L; Gough, William A; Auld, Heather

2015-03-25

Tornadoes represent one of nature's most hazardous phenomena that have been responsible for significant destruction and devastating fatalities. Here we present a Bayesian modelling approach for elucidating the spatiotemporal patterns of tornado activity in North America. Our analysis shows a significant increase in the Canadian Prairies and the Northern Great Plains during the summer, indicating a clear transition of tornado activity from the United States to Canada. The linkage between monthly-averaged atmospheric variables and likelihood of tornado events is characterized by distinct seasonality; the convective available potential energy is the predominant factor in the summer; vertical wind shear appears to have a strong signature primarily in the winter and secondarily in the summer; and storm relative environmental helicity is most influential in the spring. The present probabilistic mapping can be used to draw inference on the likelihood of tornado occurrence in any location in North America within a selected time period of the year.

Bayesian inversion of refraction seismic traveltime data

NASA Astrophysics Data System (ADS)

Ryberg, T.; Haberland, Ch

2018-03-01

We apply a Bayesian Markov chain Monte Carlo (McMC) formalism to the inversion of refraction seismic, traveltime data sets to derive 2-D velocity models below linear arrays (i.e. profiles) of sources and seismic receivers. Typical refraction data sets, especially when using the far-offset observations, are known as having experimental geometries which are very poor, highly ill-posed and far from being ideal. As a consequence, the structural resolution quickly degrades with depth. Conventional inversion techniques, based on regularization, potentially suffer from the choice of appropriate inversion parameters (i.e. number and distribution of cells, starting velocity models, damping and smoothing constraints, data noise level, etc.) and only local model space exploration. McMC techniques are used for exhaustive sampling of the model space without the need of prior knowledge (or assumptions) of inversion parameters, resulting in a large number of models fitting the observations. Statistical analysis of these models allows to derive an average (reference) solution and its standard deviation, thus providing uncertainty estimates of the inversion result. The highly non-linear character of the inversion problem, mainly caused by the experiment geometry, does not allow to derive a reference solution and error map by a simply averaging procedure. We present a modified averaging technique, which excludes parts of the prior distribution in the posterior values due to poor ray coverage, thus providing reliable estimates of inversion model properties even in those parts of the models. The model is discretized by a set of Voronoi polygons (with constant slowness cells) or a triangulated mesh (with interpolation within the triangles). Forward traveltime calculations are performed by a fast, finite-difference-based eikonal solver. The method is applied to a data set from a refraction seismic survey from Northern Namibia and compared to conventional tomography. An inversion test for a synthetic data set from a known model is also presented.

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 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

An introduction to using Bayesian linear regression with clinical data.

PubMed

Baldwin, Scott A; Larson, Michael J

2017-11-01

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

A Bayesian partition modelling approach to resolve spatial variability in climate records from borehole temperature inversion

NASA Astrophysics Data System (ADS)

Hopcroft, Peter O.; Gallagher, Kerry; Pain, Christopher C.

2009-08-01

Collections of suitably chosen borehole profiles can be used to infer large-scale trends in ground-surface temperature (GST) histories for the past few hundred years. These reconstructions are based on a large database of carefully selected borehole temperature measurements from around the globe. Since non-climatic thermal influences are difficult to identify, representative temperature histories are derived by averaging individual reconstructions to minimize the influence of these perturbing factors. This may lead to three potentially important drawbacks: the net signal of non-climatic factors may not be zero, meaning that the average does not reflect the best estimate of past climate; the averaging over large areas restricts the useful amount of more local climate change information available; and the inversion methods used to reconstruct the past temperatures at each site must be mathematically identical and are therefore not necessarily best suited to all data sets. In this work, we avoid these issues by using a Bayesian partition model (BPM), which is computed using a trans-dimensional form of a Markov chain Monte Carlo algorithm. This then allows the number and spatial distribution of different GST histories to be inferred from a given set of borehole data by partitioning the geographical area into discrete partitions. Profiles that are heavily influenced by non-climatic factors will be partitioned separately. Conversely, profiles with climatic information, which is consistent with neighbouring profiles, will then be inferred to lie in the same partition. The geographical extent of these partitions then leads to information on the regional extent of the climatic signal. In this study, three case studies are described using synthetic and real data. The first demonstrates that the Bayesian partition model method is able to correctly partition a suite of synthetic profiles according to the inferred GST history. In the second, more realistic case, a series of temperature profiles are calculated using surface air temperatures of a global climate model simulation. In the final case, 23 real boreholes from the United Kingdom, previously used for climatic reconstructions, are examined and the results compared with a local instrumental temperature series and the previous estimate derived from the same borehole data. The results indicate that the majority (17) of the 23 boreholes are unsuitable for climatic reconstruction purposes, at least without including other thermal processes in the forward model.

Translating Uncertain Sea Level Projections Into Infrastructure Impacts Using a Bayesian Framework

NASA Astrophysics Data System (ADS)

Moftakhari, Hamed; AghaKouchak, Amir; Sanders, Brett F.; Matthew, Richard A.; Mazdiyasni, Omid

2017-12-01

Climate change may affect ocean-driven coastal flooding regimes by both raising the mean sea level (msl) and altering ocean-atmosphere interactions. For reliable projections of coastal flood risk, information provided by different climate models must be considered in addition to associated uncertainties. In this paper, we propose a framework to project future coastal water levels and quantify the resulting flooding hazard to infrastructure. We use Bayesian Model Averaging to generate a weighted ensemble of storm surge predictions from eight climate models for two coastal counties in California. The resulting ensembles combined with msl projections, and predicted astronomical tides are then used to quantify changes in the likelihood of road flooding under representative concentration pathways 4.5 and 8.5 in the near-future (1998-2063) and mid-future (2018-2083). The results show that road flooding rates will be significantly higher in the near-future and mid-future compared to the recent past (1950-2015) if adaptation measures are not implemented.

Spatial cluster detection using dynamic programming.

PubMed

Sverchkov, Yuriy; Jiang, Xia; Cooper, Gregory F

2012-03-25

The task of spatial cluster detection involves finding spatial regions where some property deviates from the norm or the expected value. In a probabilistic setting this task can be expressed as finding a region where some event is significantly more likely than usual. Spatial cluster detection is of interest in fields such as biosurveillance, mining of astronomical data, military surveillance, and analysis of fMRI images. In almost all such applications we are interested both in the question of whether a cluster exists in the data, and if it exists, we are interested in finding the most accurate characterization of the cluster. We present a general dynamic programming algorithm for grid-based spatial cluster detection. The algorithm can be used for both Bayesian maximum a-posteriori (MAP) estimation of the most likely spatial distribution of clusters and Bayesian model averaging over a large space of spatial cluster distributions to compute the posterior probability of an unusual spatial clustering. The algorithm is explained and evaluated in the context of a biosurveillance application, specifically the detection and identification of Influenza outbreaks based on emergency department visits. A relatively simple underlying model is constructed for the purpose of evaluating the algorithm, and the algorithm is evaluated using the model and semi-synthetic test data. When compared to baseline methods, tests indicate that the new algorithm can improve MAP estimates under certain conditions: the greedy algorithm we compared our method to was found to be more sensitive to smaller outbreaks, while as the size of the outbreaks increases, in terms of area affected and proportion of individuals affected, our method overtakes the greedy algorithm in spatial precision and recall. The new algorithm performs on-par with baseline methods in the task of Bayesian model averaging. We conclude that the dynamic programming algorithm performs on-par with other available methods for spatial cluster detection and point to its low computational cost and extendability as advantages in favor of further research and use of the algorithm.

Spatial cluster detection using dynamic programming

PubMed Central

2012-01-01

Background The task of spatial cluster detection involves finding spatial regions where some property deviates from the norm or the expected value. In a probabilistic setting this task can be expressed as finding a region where some event is significantly more likely than usual. Spatial cluster detection is of interest in fields such as biosurveillance, mining of astronomical data, military surveillance, and analysis of fMRI images. In almost all such applications we are interested both in the question of whether a cluster exists in the data, and if it exists, we are interested in finding the most accurate characterization of the cluster. Methods We present a general dynamic programming algorithm for grid-based spatial cluster detection. The algorithm can be used for both Bayesian maximum a-posteriori (MAP) estimation of the most likely spatial distribution of clusters and Bayesian model averaging over a large space of spatial cluster distributions to compute the posterior probability of an unusual spatial clustering. The algorithm is explained and evaluated in the context of a biosurveillance application, specifically the detection and identification of Influenza outbreaks based on emergency department visits. A relatively simple underlying model is constructed for the purpose of evaluating the algorithm, and the algorithm is evaluated using the model and semi-synthetic test data. Results When compared to baseline methods, tests indicate that the new algorithm can improve MAP estimates under certain conditions: the greedy algorithm we compared our method to was found to be more sensitive to smaller outbreaks, while as the size of the outbreaks increases, in terms of area affected and proportion of individuals affected, our method overtakes the greedy algorithm in spatial precision and recall. The new algorithm performs on-par with baseline methods in the task of Bayesian model averaging. Conclusions We conclude that the dynamic programming algorithm performs on-par with other available methods for spatial cluster detection and point to its low computational cost and extendability as advantages in favor of further research and use of the algorithm. PMID:22443103

Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods

DOE PAGES

Liu, Peigui; Elshall, Ahmed S.; Ye, Ming; ...

2016-02-05

Evaluating marginal likelihood is the most critical and computationally expensive task, when conducting Bayesian model averaging to quantify parametric and model uncertainties. The evaluation is commonly done by using Laplace approximations to evaluate semianalytical expressions of the marginal likelihood or by using Monte Carlo (MC) methods to evaluate arithmetic or harmonic mean of a joint likelihood function. This study introduces a new MC method, i.e., thermodynamic integration, which has not been attempted in environmental modeling. Instead of using samples only from prior parameter space (as in arithmetic mean evaluation) or posterior parameter space (as in harmonic mean evaluation), the thermodynamicmore » integration method uses samples generated gradually from the prior to posterior parameter space. This is done through a path sampling that conducts Markov chain Monte Carlo simulation with different power coefficient values applied to the joint likelihood function. The thermodynamic integration method is evaluated using three analytical functions by comparing the method with two variants of the Laplace approximation method and three MC methods, including the nested sampling method that is recently introduced into environmental modeling. The thermodynamic integration method outperforms the other methods in terms of their accuracy, convergence, and consistency. The thermodynamic integration method is also applied to a synthetic case of groundwater modeling with four alternative models. The application shows that model probabilities obtained using the thermodynamic integration method improves predictive performance of Bayesian model averaging. As a result, the thermodynamic integration method is mathematically rigorous, and its MC implementation is computationally general for a wide range of environmental problems.« less

[Determination of wine original regions using information fusion of NIR and MIR spectroscopy].

PubMed

Xiang, Ling-Li; Li, Meng-Hua; Li, Jing-Mingz; Li, Jun-Hui; Zhang, Lu-Da; Zhao, Long-Lian

2014-10-01

Geographical origins of wine grapes are significant factors affecting wine quality and wine prices. Tasters' evaluation is a good method but has some limitations. It is important to discriminate different wine original regions quickly and accurately. The present paper proposed a method to determine wine original regions based on Bayesian information fusion that fused near-infrared (NIR) transmission spectra information and mid-infrared (MIR) ATR spectra information of wines. This method improved the determination results by expanding the sources of analysis information. NIR spectra and MIR spectra of 153 wine samples from four different regions of grape growing were collected by near-infrared and mid-infrared Fourier transform spe trometer separately. These four different regions are Huailai, Yantai, Gansu and Changli, which areall typical geographical originals for Chinese wines. NIR and MIR discriminant models for wine regions were established using partial least squares discriminant analysis (PLS-DA) based on NIR spectra and MIR spectra separately. In PLS-DA, the regions of wine samples are presented in group of binary code. There are four wine regions in this paper, thereby using four nodes standing for categorical variables. The output nodes values for each sample in NIR and MIR models were normalized first. These values stand for the probabilities of each sample belonging to each category. They seemed as the input to the Bayesian discriminant formula as a priori probability value. The probabilities were substituteed into the Bayesian formula to get posterior probabilities, by which we can judge the new class characteristics of these samples. Considering the stability of PLS-DA models, all the wine samples were divided into calibration sets and validation sets randomly for ten times. The results of NIR and MIR discriminant models of four wine regions were as follows: the average accuracy rates of calibration sets were 78.21% (NIR) and 82.57% (MIR), and the average accuracy rates of validation sets were 82.50% (NIR) and 81.98% (MIR). After using the method proposed in this paper, the accuracy rates of calibration and validation changed to 87.11% and 90.87% separately, which all achieved better results of determination than individual spectroscopy. These results suggest that Bayesian information fusion of NIR and MIR spectra is feasible for fast identification of wine original regions.

Development and comparison in uncertainty assessment based Bayesian modularization method in hydrological modeling

NASA Astrophysics Data System (ADS)

Li, Lu; Xu, Chong-Yu; Engeland, Kolbjørn

2013-04-01

SummaryWith respect to model calibration, parameter estimation and analysis of uncertainty sources, various regression and probabilistic approaches are used in hydrological modeling. A family of Bayesian methods, which incorporates different sources of information into a single analysis through Bayes' theorem, is widely used for uncertainty assessment. However, none of these approaches can well treat the impact of high flows in hydrological modeling. This study proposes a Bayesian modularization uncertainty assessment approach in which the highest streamflow observations are treated as suspect information that should not influence the inference of the main bulk of the model parameters. This study includes a comprehensive comparison and evaluation of uncertainty assessments by our new Bayesian modularization method and standard Bayesian methods using the Metropolis-Hastings (MH) algorithm with the daily hydrological model WASMOD. Three likelihood functions were used in combination with standard Bayesian method: the AR(1) plus Normal model independent of time (Model 1), the AR(1) plus Normal model dependent on time (Model 2) and the AR(1) plus Multi-normal model (Model 3). The results reveal that the Bayesian modularization method provides the most accurate streamflow estimates measured by the Nash-Sutcliffe efficiency and provide the best in uncertainty estimates for low, medium and entire flows compared to standard Bayesian methods. The study thus provides a new approach for reducing the impact of high flows on the discharge uncertainty assessment of hydrological models via Bayesian method.

Bayesian models: A statistical primer for ecologists

USGS Publications Warehouse

Hobbs, N. Thompson; Hooten, Mevin B.

2015-01-01

Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods—in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach.Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals.This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management.Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticiansCovers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and moreDeemphasizes computer coding in favor of basic principlesExplains how to write out properly factored statistical expressions representing Bayesian models

Forecasting mortality of road traffic injuries in China using seasonal autoregressive integrated moving average model.

PubMed

Zhang, Xujun; Pang, Yuanyuan; Cui, Mengjing; Stallones, Lorann; Xiang, Huiyun

2015-02-01

Road traffic injuries have become a major public health problem in China. This study aimed to develop statistical models for predicting road traffic deaths and to analyze seasonality of deaths in China. A seasonal autoregressive integrated moving average (SARIMA) model was used to fit the data from 2000 to 2011. Akaike Information Criterion, Bayesian Information Criterion, and mean absolute percentage error were used to evaluate the constructed models. Autocorrelation function and partial autocorrelation function of residuals and Ljung-Box test were used to compare the goodness-of-fit between the different models. The SARIMA model was used to forecast monthly road traffic deaths in 2012. The seasonal pattern of road traffic mortality data was statistically significant in China. SARIMA (1, 1, 1) (0, 1, 1)12 model was the best fitting model among various candidate models; the Akaike Information Criterion, Bayesian Information Criterion, and mean absolute percentage error were -483.679, -475.053, and 4.937, respectively. Goodness-of-fit testing showed nonautocorrelations in the residuals of the model (Ljung-Box test, Q = 4.86, P = .993). The fitted deaths using the SARIMA (1, 1, 1) (0, 1, 1)12 model for years 2000 to 2011 closely followed the observed number of road traffic deaths for the same years. The predicted and observed deaths were also very close for 2012. This study suggests that accurate forecasting of road traffic death incidence is possible using SARIMA model. The SARIMA model applied to historical road traffic deaths data could provide important evidence of burden of road traffic injuries in China. Copyright © 2015 Elsevier Inc. All rights reserved.

Incorporating measurement error in n = 1 psychological autoregressive modeling

PubMed Central

Schuurman, Noémi K.; Houtveen, Jan H.; Hamaker, Ellen L.

2015-01-01

Measurement error is omnipresent in psychological data. However, the vast majority of applications of autoregressive time series analyses in psychology do not take measurement error into account. Disregarding measurement error when it is present in the data results in a bias of the autoregressive parameters. We discuss two models that take measurement error into account: An autoregressive model with a white noise term (AR+WN), and an autoregressive moving average (ARMA) model. In a simulation study we compare the parameter recovery performance of these models, and compare this performance for both a Bayesian and frequentist approach. We find that overall, the AR+WN model performs better. Furthermore, we find that for realistic (i.e., small) sample sizes, psychological research would benefit from a Bayesian approach in fitting these models. Finally, we illustrate the effect of disregarding measurement error in an AR(1) model by means of an empirical application on mood data in women. We find that, depending on the person, approximately 30–50% of the total variance was due to measurement error, and that disregarding this measurement error results in a substantial underestimation of the autoregressive parameters. PMID:26283988

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.

Association of climate drivers with rainfall in New South Wales, Australia, using Bayesian Model Averaging

NASA Astrophysics Data System (ADS)

Duc, Hiep Nguyen; Rivett, Kelly; MacSween, Katrina; Le-Anh, Linh

2017-01-01

Rainfall in New South Wales (NSW), located in the southeast of the Australian continent, is known to be influenced by four major climate drivers: the El Niño/Southern Oscillation (ENSO), the Interdecadal Pacific Oscillation (IPO), the Southern Annular Mode (SAM) and the Indian Ocean Dipole (IOD). Many studies have shown the influences of ENSO, IPO modulation, SAM and IOD on rainfall in Australia and on southeast Australia in particular. However, only limited work has been undertaken using a multiple regression framework to examine the extent of the combined effect of these climate drivers on rainfall. This paper analysed the role of these combined climate drivers and their interaction on the rainfall in NSW using Bayesian Model Averaging (BMA) to account for model uncertainty by considering each of the linear models across the whole model space which is equal to the set of all possible combinations of predictors to find the model posterior probabilities and their expected predictor coefficients. Using BMA for linear regression models, we are able to corroborate and confirm the results from many previous studies. In addition, the method gives the ranking order of importance and the probability of the association of each of the climate drivers and their interaction on the rainfall at a site. The ability to quantify the relative contribution of the climate drivers offers the key to understand the complex interaction of drivers on rainfall, or lack of rainfall in a region, such as the three big droughts in southeastern Australia which have been the subject of discussion and debate recently on their causes.

A study of finite mixture model: Bayesian approach on financial time series data

NASA Astrophysics Data System (ADS)

Phoong, Seuk-Yen; Ismail, Mohd Tahir

2014-07-01

Recently, statistician have emphasized on the fitting finite mixture model by using Bayesian method. Finite mixture model is a mixture of distributions in modeling a statistical distribution meanwhile Bayesian method is a statistical method that use to fit the mixture model. Bayesian method is being used widely because it has asymptotic properties which provide remarkable result. In addition, Bayesian method also shows consistency characteristic which means the parameter estimates are close to the predictive distributions. In the present paper, the number of components for mixture model is studied by using Bayesian Information Criterion. Identify the number of component is important because it may lead to an invalid result. Later, the Bayesian method is utilized to fit the k-component mixture model in order to explore the relationship between rubber price and stock market price for Malaysia, Thailand, Philippines and Indonesia. Lastly, the results showed that there is a negative effect among rubber price and stock market price for all selected countries.

Hydraulic Conductivity Estimation using Bayesian Model Averaging and Generalized Parameterization

NASA Astrophysics Data System (ADS)

Tsai, F. T.; Li, X.

2006-12-01

Non-uniqueness in parameterization scheme is an inherent problem in groundwater inverse modeling due to limited data. To cope with the non-uniqueness problem of parameterization, we introduce a Bayesian Model Averaging (BMA) method to integrate a set of selected parameterization methods. The estimation uncertainty in BMA includes the uncertainty in individual parameterization methods as the within-parameterization variance and the uncertainty from using different parameterization methods as the between-parameterization variance. Moreover, the generalized parameterization (GP) method is considered in the geostatistical framework in this study. The GP method aims at increasing the flexibility of parameterization through the combination of a zonation structure and an interpolation method. The use of BMP with GP avoids over-confidence in a single parameterization method. A normalized least-squares estimation (NLSE) is adopted to calculate the posterior probability for each GP. We employee the adjoint state method for the sensitivity analysis on the weighting coefficients in the GP method. The adjoint state method is also applied to the NLSE problem. The proposed methodology is implemented to the Alamitos Barrier Project (ABP) in California, where the spatially distributed hydraulic conductivity is estimated. The optimal weighting coefficients embedded in GP are identified through the maximum likelihood estimation (MLE) where the misfits between the observed and calculated groundwater heads are minimized. The conditional mean and conditional variance of the estimated hydraulic conductivity distribution using BMA are obtained to assess the estimation uncertainty.

Bayesian Data-Model Fit Assessment for Structural Equation Modeling

ERIC Educational Resources Information Center

Levy, Roy

2011-01-01

Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes…

Statistical Surrogate Models for Estimating Probability of High-Consequence Climate Change

NASA Astrophysics Data System (ADS)

Field, R.; Constantine, P.; Boslough, M.

2011-12-01

We have posed the climate change problem in a framework similar to that used in safety engineering, by acknowledging that probabilistic risk assessments focused on low-probability, high-consequence climate events are perhaps more appropriate than studies focused simply on best estimates. To properly explore the tails of the distribution requires extensive sampling, which is not possible with existing coupled atmospheric models due to the high computational cost of each simulation. We have developed specialized statistical surrogate models (SSMs) that can be used to make predictions about the tails of the associated probability distributions. A SSM is different than a deterministic surrogate model in that it represents each climate variable of interest as a space/time random field, that is, a random variable for every fixed location in the atmosphere at all times. The SSM can be calibrated to available spatial and temporal data from existing climate databases, or to a collection of outputs from general circulation models. Because of its reduced size and complexity, the realization of a large number of independent model outputs from a SSM becomes computationally straightforward, so that quantifying the risk associated with low-probability, high-consequence climate events becomes feasible. A Bayesian framework was also developed to provide quantitative measures of confidence, via Bayesian credible intervals, to assess these risks. To illustrate the use of the SSM, we considered two collections of NCAR CCSM 3.0 output data. The first collection corresponds to average December surface temperature for years 1990-1999 based on a collection of 8 different model runs obtained from the Program for Climate Model Diagnosis and Intercomparison (PCMDI). We calibrated the surrogate model to the available model data and make various point predictions. We also analyzed average precipitation rate in June, July, and August over a 54-year period assuming a cyclic Y2K ocean model. We applied the calibrated surrogate model to study the probability that the precipitation rate falls below certain thresholds and utilized the Bayesian approach to quantify our confidence in these predictions. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000.

Bayesian averaging over Decision Tree models for trauma severity scoring.

PubMed

Schetinin, V; Jakaite, L; Krzanowski, W

2018-01-01

Health care practitioners analyse possible risks of misleading decisions and need to estimate and quantify uncertainty in predictions. We have examined the "gold" standard of screening a patient's conditions for predicting survival probability, based on logistic regression modelling, which is used in trauma care for clinical purposes and quality audit. This methodology is based on theoretical assumptions about data and uncertainties. Models induced within such an approach have exposed a number of problems, providing unexplained fluctuation of predicted survival and low accuracy of estimating uncertainty intervals within which predictions are made. Bayesian method, which in theory is capable of providing accurate predictions and uncertainty estimates, has been adopted in our study using Decision Tree models. Our approach has been tested on a large set of patients registered in the US National Trauma Data Bank and has outperformed the standard method in terms of prediction accuracy, thereby providing practitioners with accurate estimates of the predictive posterior densities of interest that are required for making risk-aware decisions. Copyright © 2017 Elsevier B.V. All rights reserved.

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.

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 guide to Bayesian model selection for ecologists

USGS Publications Warehouse

Hooten, Mevin B.; Hobbs, N.T.

2015-01-01

The steady upward trend in the use of model selection and Bayesian methods in ecological research has made it clear that both approaches to inference are important for modern analysis of models and data. However, in teaching Bayesian methods and in working with our research colleagues, we have noticed a general dissatisfaction with the available literature on Bayesian model selection and multimodel inference. Students and researchers new to Bayesian methods quickly find that the published advice on model selection is often preferential in its treatment of options for analysis, frequently advocating one particular method above others. The recent appearance of many articles and textbooks on Bayesian modeling has provided welcome background on relevant approaches to model selection in the Bayesian framework, but most of these are either very narrowly focused in scope or inaccessible to ecologists. Moreover, the methodological details of Bayesian model selection approaches are spread thinly throughout the literature, appearing in journals from many different fields. Our aim with this guide is to condense the large body of literature on Bayesian approaches to model selection and multimodel inference and present it specifically for quantitative ecologists as neutrally as possible. We also bring to light a few important and fundamental concepts relating directly to model selection that seem to have gone unnoticed in the ecological literature. Throughout, we provide only a minimal discussion of philosophy, preferring instead to examine the breadth of approaches as well as their practical advantages and disadvantages. This guide serves as a reference for ecologists using Bayesian methods, so that they can better understand their options and can make an informed choice that is best aligned with their goals for inference.

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…

Geographical mapping and Bayesian spatial modeling of malaria incidence in Sistan and Baluchistan province, Iran.

PubMed

Zayeri, Farid; Salehi, Masoud; Pirhosseini, Hasan

2011-12-01

To present the geographical map of malaria and identify some of the important environmental factors of this disease in Sistan and Baluchistan province, Iran. We used the registered malaria data to compute the standard incidence rates (SIRs) of malaria in different areas of Sistan and Baluchistan province for a nine-year period (from 2001 to 2009). Statistical analyses consisted of two different parts: geographical mapping of malaria incidence rates, and modeling the environmental factors. The empirical Bayesian estimates of malaria SIRs were utilized for geographical mapping of malaria and a Poisson random effects model was used for assessing the effect of environmental factors on malaria SIRs. In general, 64,926 new cases of malaria were registered in Sistan and Baluchistan Province from 2001 to 2009. Among them, 42,695 patients (65.8%) were male and 22,231 patients (34.2%) were female. Modeling the environmental factors showed that malaria incidence rates had positive relationship with humidity, elevation, average minimum temperature and average maximum temperature, while rainfall had negative effect on malaria SIRs in this province. The results of the present study reveals that malaria is still a serious health problem in Sistan and Baluchistan province, Iran. Geographical map and related environmental factors of malaria can help the health policy makers to intervene in high risk areas more efficiently and allocate the resources in a proper manner. Copyright © 2011 Hainan Medical College. Published by Elsevier B.V. All rights reserved.

Uncertainty aggregation and reduction in structure-material performance prediction

NASA Astrophysics Data System (ADS)

Hu, Zhen; Mahadevan, Sankaran; Ao, Dan

2018-02-01

An uncertainty aggregation and reduction framework is presented for structure-material performance prediction. Different types of uncertainty sources, structural analysis model, and material performance prediction model are connected through a Bayesian network for systematic uncertainty aggregation analysis. To reduce the uncertainty in the computational structure-material performance prediction model, Bayesian updating using experimental observation data is investigated based on the Bayesian network. It is observed that the Bayesian updating results will have large error if the model cannot accurately represent the actual physics, and that this error will be propagated to the predicted performance distribution. To address this issue, this paper proposes a novel uncertainty reduction method by integrating Bayesian calibration with model validation adaptively. The observation domain of the quantity of interest is first discretized into multiple segments. An adaptive algorithm is then developed to perform model validation and Bayesian updating over these observation segments sequentially. Only information from observation segments where the model prediction is highly reliable is used for Bayesian updating; this is found to increase the effectiveness and efficiency of uncertainty reduction. A composite rotorcraft hub component fatigue life prediction model, which combines a finite element structural analysis model and a material damage model, is used to demonstrate the proposed method.

Bayesian selection of misspecified models is overconfident and may cause spurious posterior probabilities for phylogenetic trees.

PubMed

Yang, Ziheng; Zhu, Tianqi

2018-02-20

The Bayesian method is noted to produce spuriously high posterior probabilities for phylogenetic trees in analysis of large datasets, but the precise reasons for this overconfidence are unknown. In general, the performance of Bayesian selection of misspecified models is poorly understood, even though this is of great scientific interest since models are never true in real data analysis. Here we characterize the asymptotic behavior of Bayesian model selection and show that when the competing models are equally wrong, Bayesian model selection exhibits surprising and polarized behaviors in large datasets, supporting one model with full force while rejecting the others. If one model is slightly less wrong than the other, the less wrong model will eventually win when the amount of data increases, but the method may become overconfident before it becomes reliable. We suggest that this extreme behavior may be a major factor for the spuriously high posterior probabilities for evolutionary trees. The philosophical implications of our results to the application of Bayesian model selection to evaluate opposing scientific hypotheses are yet to be explored, as are the behaviors of non-Bayesian methods in similar situations.

Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs

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

Karagiannis, Georgios, E-mail: georgios.karagiannis@pnnl.gov; Lin, Guang, E-mail: guang.lin@pnnl.gov

2014-02-15

Generalized polynomial chaos (gPC) expansions allow us to represent the solution of a stochastic system using a series of polynomial chaos basis functions. The number of gPC terms increases dramatically as the dimension of the random input variables increases. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs when the corresponding deterministic solver is computationally expensive, evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solutions, in both spatial and random domains, bymore » coupling Bayesian model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spatial points, via (1) the Bayesian model average (BMA) or (2) the median probability model, and their construction as spatial functions on the spatial domain via spline interpolation. The former accounts for the model uncertainty and provides Bayes-optimal predictions; while the latter provides a sparse representation of the stochastic solutions by evaluating the expansion on a subset of dominating gPC bases. Moreover, the proposed methods quantify the importance of the gPC bases in the probabilistic sense through inclusion probabilities. We design a Markov chain Monte Carlo (MCMC) sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed methods are suitable for, but not restricted to, problems whose stochastic solutions are sparse in the stochastic space with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the accuracy and performance of the proposed methods and make comparisons with other approaches on solving elliptic SPDEs with 1-, 14- and 40-random dimensions.« less

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.

Bayesian Fundamentalism or Enlightenment? On the explanatory status and theoretical contributions of Bayesian models of cognition.

PubMed

Jones, Matt; Love, Bradley C

2011-08-01

The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology - namely, Behaviorism and evolutionary psychology - that set aside mechanistic explanations or make use of optimality assumptions. Through these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls that have plagued previous theoretical movements.

How the Bayesians Got Their Beliefs (and What Those Beliefs Actually Are): Comment on Bowers and Davis (2012)

ERIC Educational Resources Information Center

Griffiths, Thomas L.; Chater, Nick; Norris, Dennis; Pouget, Alexandre

2012-01-01

Bowers and Davis (2012) criticize Bayesian modelers for telling "just so" stories about cognition and neuroscience. Their criticisms are weakened by not giving an accurate characterization of the motivation behind Bayesian modeling or the ways in which Bayesian models are used and by not evaluating this theoretical framework against specific…

Bayesian Regression with Network Prior: Optimal Bayesian Filtering Perspective

PubMed Central

Qian, Xiaoning; Dougherty, Edward R.

2017-01-01

The recently introduced intrinsically Bayesian robust filter (IBRF) provides fully optimal filtering relative to a prior distribution over an uncertainty class ofjoint random process models, whereas formerly the theory was limited to model-constrained Bayesian robust filters, for which optimization was limited to the filters that are optimal for models in the uncertainty class. This paper extends the IBRF theory to the situation where there are both a prior on the uncertainty class and sample data. The result is optimal Bayesian filtering (OBF), where optimality is relative to the posterior distribution derived from the prior and the data. The IBRF theories for effective characteristics and canonical expansions extend to the OBF setting. A salient focus of the present work is to demonstrate the advantages of Bayesian regression within the OBF setting over the classical Bayesian approach in the context otlinear Gaussian models. PMID:28824268

Modeling Diagnostic Assessments with Bayesian Networks

ERIC Educational Resources Information Center

Almond, Russell G.; DiBello, Louis V.; Moulder, Brad; Zapata-Rivera, Juan-Diego

2007-01-01

This paper defines Bayesian network models and examines their applications to IRT-based cognitive diagnostic modeling. These models are especially suited to building inference engines designed to be synchronous with the finer grained student models that arise in skills diagnostic assessment. Aspects of the theory and use of Bayesian network models…

Estimation of genetic parameters for milk yield in Murrah buffaloes by Bayesian inference.

PubMed

Breda, F C; Albuquerque, L G; Euclydes, R F; Bignardi, A B; Baldi, F; Torres, R A; Barbosa, L; Tonhati, H

2010-02-01

Random regression models were used to estimate genetic parameters for test-day milk yield in Murrah buffaloes using Bayesian inference. Data comprised 17,935 test-day milk records from 1,433 buffaloes. Twelve models were tested using different combinations of third-, fourth-, fifth-, sixth-, and seventh-order orthogonal polynomials of weeks of lactation for additive genetic and permanent environmental effects. All models included the fixed effects of contemporary group, number of daily milkings and age of cow at calving as covariate (linear and quadratic effect). In addition, residual variances were considered to be heterogeneous with 6 classes of variance. Models were selected based on the residual mean square error, weighted average of residual variance estimates, and estimates of variance components, heritabilities, correlations, eigenvalues, and eigenfunctions. Results indicated that changes in the order of fit for additive genetic and permanent environmental random effects influenced the estimation of genetic parameters. Heritability estimates ranged from 0.19 to 0.31. Genetic correlation estimates were close to unity between adjacent test-day records, but decreased gradually as the interval between test-days increased. Results from mean squared error and weighted averages of residual variance estimates suggested that a model considering sixth- and seventh-order Legendre polynomials for additive and permanent environmental effects, respectively, and 6 classes for residual variances, provided the best fit. Nevertheless, this model presented the largest degree of complexity. A more parsimonious model, with fourth- and sixth-order polynomials, respectively, for these same effects, yielded very similar genetic parameter estimates. Therefore, this last model is recommended for routine applications. Copyright 2010 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Wheeler, David C.; Waller, Lance A.

2009-03-01

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

Philosophy and the practice of Bayesian statistics

PubMed Central

Gelman, Andrew; Shalizi, Cosma Rohilla

2015-01-01

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework. PMID:22364575

Philosophy and the practice of Bayesian statistics.

PubMed

Gelman, Andrew; Shalizi, Cosma Rohilla

2013-02-01

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework. © 2012 The British Psychological Society.

Visual feature extraction from voxel-weighted averaging of stimulus images in 2 fMRI studies.

PubMed

Hart, Corey B; Rose, William J

2013-11-01

Multiple studies have provided evidence for distributed object representation in the brain, with several recent experiments leveraging basis function estimates for partial image reconstruction from fMRI data. Using a novel combination of statistical decomposition, generalized linear models, and stimulus averaging on previously examined image sets and Bayesian regression of recorded fMRI activity during presentation of these data sets, we identify a subset of relevant voxels that appear to code for covarying object features. Using a technique we term "voxel-weighted averaging," we isolate image filters that these voxels appear to implement. The results, though very cursory, appear to have significant implications for hierarchical and deep-learning-type approaches toward the understanding of neural coding and representation.

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

Prediction-error variance in Bayesian model updating: a comparative study

NASA Astrophysics Data System (ADS)

Asadollahi, Parisa; Li, Jian; Huang, Yong

2017-04-01

In Bayesian model updating, the likelihood function is commonly formulated by stochastic embedding in which the maximum information entropy probability model of prediction error variances plays an important role and it is Gaussian distribution subject to the first two moments as constraints. The selection of prediction error variances can be formulated as a model class selection problem, which automatically involves a trade-off between the average data-fit of the model class and the information it extracts from the data. Therefore, it is critical for the robustness in the updating of the structural model especially in the presence of modeling errors. To date, three ways of considering prediction error variances have been seem in the literature: 1) setting constant values empirically, 2) estimating them based on the goodness-of-fit of the measured data, and 3) updating them as uncertain parameters by applying Bayes' Theorem at the model class level. In this paper, the effect of different strategies to deal with the prediction error variances on the model updating performance is investigated explicitly. A six-story shear building model with six uncertain stiffness parameters is employed as an illustrative example. Transitional Markov Chain Monte Carlo is used to draw samples of the posterior probability density function of the structure model parameters as well as the uncertain prediction variances. The different levels of modeling uncertainty and complexity are modeled through three FE models, including a true model, a model with more complexity, and a model with modeling error. Bayesian updating is performed for the three FE models considering the three aforementioned treatments of the prediction error variances. The effect of number of measurements on the model updating performance is also examined in the study. The results are compared based on model class assessment and indicate that updating the prediction error variances as uncertain parameters at the model class level produces more robust results especially when the number of measurement is small.

Performance of Optimally Merged Multisatellite Precipitation Products Using the Dynamic Bayesian Model Averaging Scheme Over the Tibetan Plateau

NASA Astrophysics Data System (ADS)

Ma, Yingzhao; Hong, Yang; Chen, Yang; Yang, Yuan; Tang, Guoqiang; Yao, Yunjun; Long, Di; Li, Changmin; Han, Zhongying; Liu, Ronghua

2018-01-01

Accurate estimation of precipitation from satellites at high spatiotemporal scales over the Tibetan Plateau (TP) remains a challenge. In this study, we proposed a general framework for blending multiple satellite precipitation data using the dynamic Bayesian model averaging (BMA) algorithm. The blended experiment was performed at a daily 0.25° grid scale for 2007-2012 among Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA) 3B42RT and 3B42V7, Climate Prediction Center MORPHing technique (CMORPH), and Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks-Climate Data Record (PERSIANN-CDR). First, the BMA weights were optimized using the expectation-maximization (EM) method for each member on each day at 200 calibrated sites and then interpolated to the entire plateau using the ordinary kriging (OK) approach. Thus, the merging data were produced by weighted sums of the individuals over the plateau. The dynamic BMA approach showed better performance with a smaller root-mean-square error (RMSE) of 6.77 mm/day, higher correlation coefficient of 0.592, and closer Euclid value of 0.833, compared to the individuals at 15 validated sites. Moreover, BMA has proven to be more robust in terms of seasonality, topography, and other parameters than traditional ensemble methods including simple model averaging (SMA) and one-outlier removed (OOR). Error analysis between BMA and the state-of-the-art IMERG in the summer of 2014 further proved that the performance of BMA was superior with respect to multisatellite precipitation data merging. This study demonstrates that BMA provides a new solution for blending multiple satellite data in regions with limited gauges.

Bayesian inference based on dual generalized order statistics from the exponentiated Weibull model

NASA Astrophysics Data System (ADS)

Al Sobhi, Mashail M.

2015-02-01

Bayesian estimation for the two parameters and the reliability function of the exponentiated Weibull model are obtained based on dual generalized order statistics (DGOS). Also, Bayesian prediction bounds for future DGOS from exponentiated Weibull model are obtained. The symmetric and asymmetric loss functions are considered for Bayesian computations. The Markov chain Monte Carlo (MCMC) methods are used for computing the Bayes estimates and prediction bounds. The results have been specialized to the lower record values. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation.

Fundamentals and Recent Developments in Approximate Bayesian Computation

PubMed Central

Lintusaari, Jarno; Gutmann, Michael U.; Dutta, Ritabrata; Kaski, Samuel; Corander, Jukka

2017-01-01

Abstract Bayesian inference plays an important role in phylogenetics, evolutionary biology, and in many other branches of science. It provides a principled framework for dealing with uncertainty and quantifying how it changes in the light of new evidence. For many complex models and inference problems, however, only approximate quantitative answers are obtainable. Approximate Bayesian computation (ABC) refers to a family of algorithms for approximate inference that makes a minimal set of assumptions by only requiring that sampling from a model is possible. We explain here the fundamentals of ABC, review the classical algorithms, and highlight recent developments. [ABC; approximate Bayesian computation; Bayesian inference; likelihood-free inference; phylogenetics; simulator-based models; stochastic simulation models; tree-based models.] PMID:28175922

Improving timing sensitivity in the microhertz frequency regime: limits from PSR J1713+0747 on gravitational waves produced by supermassive black hole binaries

NASA Astrophysics Data System (ADS)

Perera, B. B. P.; Stappers, B. W.; Babak, S.; Keith, M. J.; Antoniadis, J.; Bassa, C. G.; Caballero, R. N.; Champion, D. J.; Cognard, I.; Desvignes, G.; Graikou, E.; Guillemot, L.; Janssen, G. H.; Karuppusamy, R.; Kramer, M.; Lazarus, P.; Lentati, L.; Liu, K.; Lyne, A. G.; McKee, J. W.; Osłowski, S.; Perrodin, D.; Sanidas, S. A.; Sesana, A.; Shaifullah, G.; Theureau, G.; Verbiest, J. P. W.; Taylor, S. R.

2018-07-01

We search for continuous gravitational waves (CGWs) produced by individual supermassive black hole binaries in circular orbits using high-cadence timing observations of PSR J1713+0747. We observe this millisecond pulsar using the telescopes in the European Pulsar Timing Array with an average cadence of approximately 1.6 d over the period between 2011 April and 2015 July, including an approximately daily average between 2013 February and 2014 April. The high-cadence observations are used to improve the pulsar timing sensitivity across the gravitational wave frequency range of 0.008-5μHz. We use two algorithms in the analysis, including a spectral fitting method and a Bayesian approach. For an independent comparison, we also use a previously published Bayesian algorithm. We find that the Bayesian approaches provide optimal results and the timing observations of the pulsar place a 95 per cent upper limit on the sky-averaged strain amplitude of CGWs to be ≲3.5 × 10-13 at a reference frequency of 1 μHz. We also find a 95 per cent upper limit on the sky-averaged strain amplitude of low-frequency CGWs to be ≲1.4 × 10-14 at a reference frequency of 20 nHz.

Improving timing sensitivity in the microhertz frequency regime: limits from PSR J1713+0747 on gravitational waves produced by super-massive black-hole binaries

NASA Astrophysics Data System (ADS)

Perera, B. B. P.; Stappers, B. W.; Babak, S.; Keith, M. J.; Antoniadis, J.; Bassa, C. G.; Caballero, R. N.; Champion, D. J.; Cognard, I.; Desvignes, G.; Graikou, E.; Guillemot, L.; Janssen, G. H.; Karuppusamy, R.; Kramer, M.; Lazarus, P.; Lentati, L.; Liu, K.; Lyne, A. G.; McKee, J. W.; Osłowski, S.; Perrodin, D.; Sanidas, S. A.; Sesana, A.; Shaifullah, G.; Theureau, G.; Verbiest, J. P. W.; Taylor, S. R.

2018-05-01

We search for continuous gravitational waves (CGWs) produced by individual super-massive black-hole binaries (SMBHBs) in circular orbits using high-cadence timing observations of PSR J1713+0747. We observe this millisecond pulsar using the telescopes in the European Pulsar Timing Array (EPTA) with an average cadence of approximately 1.6 days over the period between April 2011 and July 2015, including an approximately daily average between February 2013 and April 2014. The high-cadence observations are used to improve the pulsar timing sensitivity across the GW frequency range of 0.008 - 5 μHz. We use two algorithms in the analysis, including a spectral fitting method and a Bayesian approach. For an independent comparison, we also use a previously published Bayesian algorithm. We find that the Bayesian approaches provide optimal results and the timing observations of the pulsar place a 95 per cent upper limit on the sky-averaged strain amplitude of CGWs to be ≲ 3.5 × 10-13 at a reference frequency of 1 μHz. We also find a 95 per cent upper limit on the sky-averaged strain amplitude of low-frequency CGWs to be ≲ 1.4 × 10-14 at a reference frequency of 20 nHz.

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.

An objective Bayesian analysis of a crossover design via model selection and model averaging.

PubMed

Li, Dandan; Sivaganesan, Siva

2016-11-10

Inference about the treatment effect in a crossover design has received much attention over time owing to the uncertainty in the existence of the carryover effect and its impact on the estimation of the treatment effect. Adding to this uncertainty is that the existence of the carryover effect and its size may depend on the presence of the treatment effect and its size. We consider estimation and testing hypothesis about the treatment effect in a two-period crossover design, assuming normally distributed response variable, and use an objective Bayesian approach to test the hypothesis about the treatment effect and to estimate its size when it exists while accounting for the uncertainty about the presence of the carryover effect as well as the treatment and period effects. We evaluate and compare the performance of the proposed approach with a standard frequentist approach using simulated data, and real data. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Inverse Modeling of Hydrologic Parameters Using Surface Flux and Runoff Observations in the Community Land Model

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

Sun, Yu; Hou, Zhangshuan; Huang, Maoyi

2013-12-10

This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Two inversion strategies, the deterministic least-square fitting and stochastic Markov-Chain Monte-Carlo (MCMC) - Bayesian inversion approaches, are evaluated by applying them to CLM4 at selected sites. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find thatmore » using model parameters calibrated by the least-square fitting provides little improvements in the model simulations but the sampling-based stochastic inversion approaches are consistent - as more information comes in, the predictive intervals of the calibrated parameters become narrower and the misfits between the calculated and observed responses decrease. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to the different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.« less

Inverse modeling of hydrologic parameters using surface flux and runoff observations in the Community Land Model

NASA Astrophysics Data System (ADS)

Sun, Y.; Hou, Z.; Huang, M.; Tian, F.; Leung, L. Ruby

2013-12-01

This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Both deterministic least-square fitting and stochastic Markov-chain Monte Carlo (MCMC)-Bayesian inversion approaches are evaluated by applying them to CLM4 at selected sites with different climate and soil conditions. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find that using model parameters calibrated by the sampling-based stochastic inversion approaches provides significant improvements in the model simulations compared to using default CLM4 parameter values, and that as more information comes in, the predictive intervals (ranges of posterior distributions) of the calibrated parameters become narrower. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.

Sizing Up the Milky Way: A Bayesian Mixture Model Meta-analysis of Photometric Scale Length Measurements

NASA Astrophysics Data System (ADS)

Licquia, Timothy C.; Newman, Jeffrey A.

2016-11-01

The exponential scale length (L d ) of the Milky Way’s (MW’s) disk is a critical parameter for describing the global physical size of our Galaxy, important both for interpreting other Galactic measurements and helping us to understand how our Galaxy fits into extragalactic contexts. Unfortunately, current estimates span a wide range of values and are often statistically incompatible with one another. Here, we perform a Bayesian meta-analysis to determine an improved, aggregate estimate for L d , utilizing a mixture-model approach to account for the possibility that any one measurement has not properly accounted for all statistical or systematic errors. Within this machinery, we explore a variety of ways of modeling the nature of problematic measurements, and then employ a Bayesian model averaging technique to derive net posterior distributions that incorporate any model-selection uncertainty. Our meta-analysis combines 29 different (15 visible and 14 infrared) photometric measurements of L d available in the literature; these involve a broad assortment of observational data sets, MW models and assumptions, and methodologies, all tabulated herein. Analyzing the visible and infrared measurements separately yields estimates for L d of {2.71}-0.20+0.22 kpc and {2.51}-0.13+0.15 kpc, respectively, whereas considering them all combined yields 2.64 ± 0.13 kpc. The ratio between the visible and infrared scale lengths determined here is very similar to that measured in external spiral galaxies. We use these results to update the model of the Galactic disk from our previous work, constraining its stellar mass to be {4.8}-1.1+1.5× {10}10 M ⊙, and the MW’s total stellar mass to be {5.7}-1.1+1.5× {10}10 M ⊙.

Improving Computational Efficiency of Prediction in Model-based Prognostics Using the Unscented Transform

DTIC Science & Technology

2010-10-01

bodies becomes greater as surface as- perities wear down (Hutchings, 1992). We characterize friction damage by a change in the friction coefficient...points are such a set, and satisfy an additional constraint in which the skew ( third moment) is minimized, which reduces the average error for a...On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, 10, 197–208. Hutchings, I. M. (1992). Tribology : friction

Potential uncertainty reduction in model-averaged benchmark dose estimates informed by an additional dose study.

PubMed

Shao, Kan; Small, Mitchell J

2011-10-01

A methodology is presented for assessing the information value of an additional dosage experiment in existing bioassay studies. The analysis demonstrates the potential reduction in the uncertainty of toxicity metrics derived from expanded studies, providing insights for future studies. Bayesian methods are used to fit alternative dose-response models using Markov chain Monte Carlo (MCMC) simulation for parameter estimation and Bayesian model averaging (BMA) is used to compare and combine the alternative models. BMA predictions for benchmark dose (BMD) are developed, with uncertainty in these predictions used to derive the lower bound BMDL. The MCMC and BMA results provide a basis for a subsequent Monte Carlo analysis that backcasts the dosage where an additional test group would have been most beneficial in reducing the uncertainty in the BMD prediction, along with the magnitude of the expected uncertainty reduction. Uncertainty reductions are measured in terms of reduced interval widths of predicted BMD values and increases in BMDL values that occur as a result of this reduced uncertainty. The methodology is illustrated using two existing data sets for TCDD carcinogenicity, fitted with two alternative dose-response models (logistic and quantal-linear). The example shows that an additional dose at a relatively high value would have been most effective for reducing the uncertainty in BMA BMD estimates, with predicted reductions in the widths of uncertainty intervals of approximately 30%, and expected increases in BMDL values of 5-10%. The results demonstrate that dose selection for studies that subsequently inform dose-response models can benefit from consideration of how these models will be fit, combined, and interpreted. © 2011 Society for Risk Analysis.

Bayesian random local clocks, or one rate to rule them all

PubMed Central

2010-01-01

Background Relaxed molecular clock models allow divergence time dating and "relaxed phylogenetic" inference, in which a time tree is estimated in the face of unequal rates across lineages. We present a new method for relaxing the assumption of a strict molecular clock using Markov chain Monte Carlo to implement Bayesian modeling averaging over random local molecular clocks. The new method approaches the problem of rate variation among lineages by proposing a series of local molecular clocks, each extending over a subregion of the full phylogeny. Each branch in a phylogeny (subtending a clade) is a possible location for a change of rate from one local clock to a new one. Thus, including both the global molecular clock and the unconstrained model results, there are a total of 22n-2 possible rate models available for averaging with 1, 2, ..., 2n - 2 different rate categories. Results We propose an efficient method to sample this model space while simultaneously estimating the phylogeny. The new method conveniently allows a direct test of the strict molecular clock, in which one rate rules them all, against a large array of alternative local molecular clock models. We illustrate the method's utility on three example data sets involving mammal, primate and influenza evolution. Finally, we explore methods to visualize the complex posterior distribution that results from inference under such models. Conclusions The examples suggest that large sequence datasets may only require a small number of local molecular clocks to reconcile their branch lengths with a time scale. All of the analyses described here are implemented in the open access software package BEAST 1.5.4 (http://beast-mcmc.googlecode.com/). PMID:20807414

A Bayesian approach for estimating under-reported dengue incidence with a focus on non-linear associations between climate and dengue in Dhaka, Bangladesh.

PubMed

Sharmin, Sifat; Glass, Kathryn; Viennet, Elvina; Harley, David

2018-04-01

Determining the relation between climate and dengue incidence is challenging due to under-reporting of disease and consequent biased incidence estimates. Non-linear associations between climate and incidence compound this. Here, we introduce a modelling framework to estimate dengue incidence from passive surveillance data while incorporating non-linear climate effects. We estimated the true number of cases per month using a Bayesian generalised linear model, developed in stages to adjust for under-reporting. A semi-parametric thin-plate spline approach was used to quantify non-linear climate effects. The approach was applied to data collected from the national dengue surveillance system of Bangladesh. The model estimated that only 2.8% (95% credible interval 2.7-2.8) of all cases in the capital Dhaka were reported through passive case reporting. The optimal mean monthly temperature for dengue transmission is 29℃ and average monthly rainfall above 15 mm decreases transmission. Our approach provides an estimate of true incidence and an understanding of the effects of temperature and rainfall on dengue transmission in Dhaka, Bangladesh.

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.

Bayesian networks for maritime traffic accident prevention: benefits and challenges.

PubMed

Hänninen, Maria

2014-12-01

Bayesian networks are quantitative modeling tools whose applications to the maritime traffic safety context are becoming more popular. This paper discusses the utilization of Bayesian networks in maritime safety modeling. Based on literature and the author's own experiences, the paper studies what Bayesian networks can offer to maritime accident prevention and safety modeling and discusses a few challenges in their application to this context. It is argued that the capability of representing rather complex, not necessarily causal but uncertain relationships makes Bayesian networks an attractive modeling tool for the maritime safety and accidents. Furthermore, as the maritime accident and safety data is still rather scarce and has some quality problems, the possibility to combine data with expert knowledge and the easy way of updating the model after acquiring more evidence further enhance their feasibility. However, eliciting the probabilities from the maritime experts might be challenging and the model validation can be tricky. It is concluded that with the utilization of several data sources, Bayesian updating, dynamic modeling, and hidden nodes for latent variables, Bayesian networks are rather well-suited tools for the maritime safety management and decision-making. Copyright © 2014 Elsevier Ltd. All rights reserved.

Regional patterns of future runoff changes from Earth system models constrained by observation

NASA Astrophysics Data System (ADS)

Yang, Hui; Zhou, Feng; Piao, Shilong; Huang, Mengtian; Chen, Anping; Ciais, Philippe; Li, Yue; Lian, Xu; Peng, Shushi; Zeng, Zhenzhong

2017-06-01

In the recent Intergovernmental Panel on Climate Change assessment, multimodel ensembles (arithmetic model averaging, AMA) were constructed with equal weights given to Earth system models, without considering the performance of each model at reproducing current conditions. Here we use Bayesian model averaging (BMA) to construct a weighted model ensemble for runoff projections. Higher weights are given to models with better performance in estimating historical decadal mean runoff. Using the BMA method, we find that by the end of this century, the increase of global runoff (9.8 ± 1.5%) under Representative Concentration Pathway 8.5 is significantly lower than estimated from AMA (12.2 ± 1.3%). BMA presents a less severe runoff increase than AMA at northern high latitudes and a more severe decrease in Amazonia. Runoff decrease in Amazonia is stronger than the intermodel difference. The intermodel difference in runoff changes is mainly caused not only by precipitation differences among models, but also by evapotranspiration differences at the high northern latitudes.

Bootstrap-after-bootstrap model averaging for reducing model uncertainty in model selection for air pollution mortality studies.

PubMed

Roberts, Steven; Martin, Michael A

2010-01-01

Concerns have been raised about findings of associations between particulate matter (PM) air pollution and mortality that have been based on a single "best" model arising from a model selection procedure, because such a strategy may ignore model uncertainty inherently involved in searching through a set of candidate models to find the best model. Model averaging has been proposed as a method of allowing for model uncertainty in this context. To propose an extension (double BOOT) to a previously described bootstrap model-averaging procedure (BOOT) for use in time series studies of the association between PM and mortality. We compared double BOOT and BOOT with Bayesian model averaging (BMA) and a standard method of model selection [standard Akaike's information criterion (AIC)]. Actual time series data from the United States are used to conduct a simulation study to compare and contrast the performance of double BOOT, BOOT, BMA, and standard AIC. Double BOOT produced estimates of the effect of PM on mortality that have had smaller root mean squared error than did those produced by BOOT, BMA, and standard AIC. This performance boost resulted from estimates produced by double BOOT having smaller variance than those produced by BOOT and BMA. Double BOOT is a viable alternative to BOOT and BMA for producing estimates of the mortality effect of PM.

Bayesian Framework for Water Quality Model Uncertainty Estimation and Risk Management

EPA Science Inventory

A formal Bayesian methodology is presented for integrated model calibration and risk-based water quality management using Bayesian Monte Carlo simulation and maximum likelihood estimation (BMCML). The primary focus is on lucid integration of model calibration with risk-based wat...

Rapid recipe formulation for plasma etching of new materials

NASA Astrophysics Data System (ADS)

Chopra, Meghali; Zhang, Zizhuo; Ekerdt, John; Bonnecaze, Roger T.

2016-03-01

A fast and inexpensive scheme for etch rate prediction using flexible continuum models and Bayesian statistics is demonstrated. Bulk etch rates of MgO are predicted using a steady-state model with volume-averaged plasma parameters and classical Langmuir surface kinetics. Plasma particle and surface kinetics are modeled within a global plasma framework using single component Metropolis Hastings methods and limited data. The accuracy of these predictions is evaluated with synthetic and experimental etch rate data for magnesium oxide in an ICP-RIE system. This approach is compared and superior to factorial models generated from JMP, a software package frequently employed for recipe creation and optimization.

A Comparison of General Diagnostic Models (GDM) and Bayesian Networks Using a Middle School Mathematics Test

ERIC Educational Resources Information Center

Wu, Haiyan

2013-01-01

General diagnostic models (GDMs) and Bayesian networks are mathematical frameworks that cover a wide variety of psychometric models. Both extend latent class models, and while GDMs also extend item response theory (IRT) models, Bayesian networks can be parameterized using discretized IRT. The purpose of this study is to examine similarities and…

Perceptual decision making: drift-diffusion model is equivalent to a Bayesian model

PubMed Central

Bitzer, Sebastian; Park, Hame; Blankenburg, Felix; Kiebel, Stefan J.

2014-01-01

Behavioral data obtained with perceptual decision making experiments are typically analyzed with the drift-diffusion model. This parsimonious model accumulates noisy pieces of evidence toward a decision bound to explain the accuracy and reaction times of subjects. Recently, Bayesian models have been proposed to explain how the brain extracts information from noisy input as typically presented in perceptual decision making tasks. It has long been known that the drift-diffusion model is tightly linked with such functional Bayesian models but the precise relationship of the two mechanisms was never made explicit. Using a Bayesian model, we derived the equations which relate parameter values between these models. In practice we show that this equivalence is useful when fitting multi-subject data. We further show that the Bayesian model suggests different decision variables which all predict equal responses and discuss how these may be discriminated based on neural correlates of accumulated evidence. In addition, we discuss extensions to the Bayesian model which would be difficult to derive for the drift-diffusion model. We suggest that these and other extensions may be highly useful for deriving new experiments which test novel hypotheses. PMID:24616689

Applications of Bayesian Procrustes shape analysis to ensemble radar reflectivity nowcast verification

NASA Astrophysics Data System (ADS)

Fox, Neil I.; Micheas, Athanasios C.; Peng, Yuqiang

2016-07-01

This paper introduces the use of Bayesian full Procrustes shape analysis in object-oriented meteorological applications. In particular, the Procrustes methodology is used to generate mean forecast precipitation fields from a set of ensemble forecasts. This approach has advantages over other ensemble averaging techniques in that it can produce a forecast that retains the morphological features of the precipitation structures and present the range of forecast outcomes represented by the ensemble. The production of the ensemble mean avoids the problems of smoothing that result from simple pixel or cell averaging, while producing credible sets that retain information on ensemble spread. Also in this paper, the full Bayesian Procrustes scheme is used as an object verification tool for precipitation forecasts. This is an extension of a previously presented Procrustes shape analysis based verification approach into a full Bayesian format designed to handle the verification of precipitation forecasts that match objects from an ensemble of forecast fields to a single truth image. The methodology is tested on radar reflectivity nowcasts produced in the Warning Decision Support System - Integrated Information (WDSS-II) by varying parameters in the K-means cluster tracking scheme.

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

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.

Estimating virus occurrence using Bayesian modeling in multiple drinking water systems of the United States

USGS Publications Warehouse

Varughese, Eunice A.; Brinkman, Nichole E; Anneken, Emily M; Cashdollar, Jennifer S; Fout, G. Shay; Furlong, Edward T.; Kolpin, Dana W.; Glassmeyer, Susan T.; Keely, Scott P

2017-01-01

incorporated into a Bayesian model to more accurately determine viral load in both source and treated water. Results of the Bayesian model indicated that viruses are present in source water and treated water. By using a Bayesian framework that incorporates inhibition, as well as many other parameters that affect viral detection, this study offers an approach for more accurately estimating the occurrence of viral pathogens in environmental waters.

A local approach for focussed Bayesian fusion

NASA Astrophysics Data System (ADS)

Sander, Jennifer; Heizmann, Michael; Goussev, Igor; Beyerer, Jürgen

2009-04-01

Local Bayesian fusion approaches aim to reduce high storage and computational costs of Bayesian fusion which is separated from fixed modeling assumptions. Using the small world formalism, we argue why this proceeding is conform with Bayesian theory. Then, we concentrate on the realization of local Bayesian fusion by focussing the fusion process solely on local regions that are task relevant with a high probability. The resulting local models correspond then to restricted versions of the original one. In a previous publication, we used bounds for the probability of misleading evidence to show the validity of the pre-evaluation of task specific knowledge and prior information which we perform to build local models. In this paper, we prove the validity of this proceeding using information theoretic arguments. For additional efficiency, local Bayesian fusion can be realized in a distributed manner. Here, several local Bayesian fusion tasks are evaluated and unified after the actual fusion process. For the practical realization of distributed local Bayesian fusion, software agents are predestinated. There is a natural analogy between the resulting agent based architecture and criminal investigations in real life. We show how this analogy can be used to improve the efficiency of distributed local Bayesian fusion additionally. Using a landscape model, we present an experimental study of distributed local Bayesian fusion in the field of reconnaissance, which highlights its high potential.

Bayesian Model Averaging with Change Points to Assess the Impact of Vaccination and Public Health Interventions

PubMed Central

Warren, Joshua L.; Schuck-Paim, Cynthia; Lustig, Roger; Lewnard, Joseph A.; Fuentes, Rodrigo; Bruhn, Christian A. W.; Taylor, Robert J.; Simonsen, Lone; Weinberger, Daniel M.

2017-01-01

Background: Pneumococcal conjugate vaccines (PCVs) prevent invasive pneumococcal disease and pneumonia. However, some low-and middle-income countries have yet to introduce PCV into their immunization programs due, in part, to lack of certainty about the potential impact. Assessing PCV benefits is challenging because specific data on pneumococcal disease are often lacking, and it can be difficult to separate the effects of factors other than the vaccine that could also affect pneumococcal disease rates. Methods: We assess PCV impact by combining Bayesian model averaging with change-point models to estimate the timing and magnitude of vaccine-associated changes, while controlling for seasonality and other covariates. We applied our approach to monthly time series of age-stratified hospitalizations related to pneumococcal infection in children younger 5 years of age in the United States, Brazil, and Chile. Results: Our method accurately detected changes in data in which we knew true and noteworthy changes occurred, i.e., in simulated data and for invasive pneumococcal disease. Moreover, 24 months after the vaccine introduction, we detected reductions of 14%, 9%, and 9% in the United States, Brazil, and Chile, respectively, in all-cause pneumonia (ACP) hospitalizations for age group 0 to <1 years of age. Conclusions: Our approach provides a flexible and sensitive method to detect changes in disease incidence that occur after the introduction of a vaccine or other intervention, while avoiding biases that exist in current approaches to time-trend analyses. PMID:28767518

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

NASA Astrophysics Data System (ADS)

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

2012-02-01

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

A Variational Bayes Genomic-Enabled Prediction Model with Genotype × Environment Interaction

PubMed Central

Montesinos-López, Osval A.; Montesinos-López, Abelardo; Crossa, José; Montesinos-López, José Cricelio; Luna-Vázquez, Francisco Javier; Salinas-Ruiz, Josafhat; Herrera-Morales, José R.; Buenrostro-Mariscal, Raymundo

2017-01-01

There are Bayesian and non-Bayesian genomic models that take into account G×E interactions. However, the computational cost of implementing Bayesian models is high, and becomes almost impossible when the number of genotypes, environments, and traits is very large, while, in non-Bayesian models, there are often important and unsolved convergence problems. The variational Bayes method is popular in machine learning, and, by approximating the probability distributions through optimization, it tends to be faster than Markov Chain Monte Carlo methods. For this reason, in this paper, we propose a new genomic variational Bayes version of the Bayesian genomic model with G×E using half-t priors on each standard deviation (SD) term to guarantee highly noninformative and posterior inferences that are not sensitive to the choice of hyper-parameters. We show the complete theoretical derivation of the full conditional and the variational posterior distributions, and their implementations. We used eight experimental genomic maize and wheat data sets to illustrate the new proposed variational Bayes approximation, and compared its predictions and implementation time with a standard Bayesian genomic model with G×E. Results indicated that prediction accuracies are slightly higher in the standard Bayesian model with G×E than in its variational counterpart, but, in terms of computation time, the variational Bayes genomic model with G×E is, in general, 10 times faster than the conventional Bayesian genomic model with G×E. For this reason, the proposed model may be a useful tool for researchers who need to predict and select genotypes in several environments. PMID:28391241

A Variational Bayes Genomic-Enabled Prediction Model with Genotype × Environment Interaction.

PubMed

Montesinos-López, Osval A; Montesinos-López, Abelardo; Crossa, José; Montesinos-López, José Cricelio; Luna-Vázquez, Francisco Javier; Salinas-Ruiz, Josafhat; Herrera-Morales, José R; Buenrostro-Mariscal, Raymundo

2017-06-07

There are Bayesian and non-Bayesian genomic models that take into account G×E interactions. However, the computational cost of implementing Bayesian models is high, and becomes almost impossible when the number of genotypes, environments, and traits is very large, while, in non-Bayesian models, there are often important and unsolved convergence problems. The variational Bayes method is popular in machine learning, and, by approximating the probability distributions through optimization, it tends to be faster than Markov Chain Monte Carlo methods. For this reason, in this paper, we propose a new genomic variational Bayes version of the Bayesian genomic model with G×E using half-t priors on each standard deviation (SD) term to guarantee highly noninformative and posterior inferences that are not sensitive to the choice of hyper-parameters. We show the complete theoretical derivation of the full conditional and the variational posterior distributions, and their implementations. We used eight experimental genomic maize and wheat data sets to illustrate the new proposed variational Bayes approximation, and compared its predictions and implementation time with a standard Bayesian genomic model with G×E. Results indicated that prediction accuracies are slightly higher in the standard Bayesian model with G×E than in its variational counterpart, but, in terms of computation time, the variational Bayes genomic model with G×E is, in general, 10 times faster than the conventional Bayesian genomic model with G×E. For this reason, the proposed model may be a useful tool for researchers who need to predict and select genotypes in several environments. Copyright © 2017 Montesinos-López et al.

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.

The Type Ia Supernova Color-Magnitude Relation and Host Galaxy Dust: A Simple Hierarchical Bayesian Model

NASA Astrophysics Data System (ADS)

Mandel, Kaisey S.; Scolnic, Daniel M.; Shariff, Hikmatali; Foley, Ryan J.; Kirshner, Robert P.

2017-06-01

Conventional Type Ia supernova (SN Ia) cosmology analyses currently use a simplistic linear regression of magnitude versus color and light curve shape, which does not model intrinsic SN Ia variations and host galaxy dust as physically distinct effects, resulting in low color-magnitude slopes. We construct a probabilistic generative model for the dusty distribution of extinguished absolute magnitudes and apparent colors as the convolution of an intrinsic SN Ia color-magnitude distribution and a host galaxy dust reddening-extinction distribution. If the intrinsic color-magnitude (M B versus B - V) slope {β }{int} differs from the host galaxy dust law R B , this convolution results in a specific curve of mean extinguished absolute magnitude versus apparent color. The derivative of this curve smoothly transitions from {β }{int} in the blue tail to R B in the red tail of the apparent color distribution. The conventional linear fit approximates this effective curve near the average apparent color, resulting in an apparent slope {β }{app} between {β }{int} and R B . We incorporate these effects into a hierarchical Bayesian statistical model for SN Ia light curve measurements, and analyze a data set of SALT2 optical light curve fits of 248 nearby SNe Ia at z< 0.10. The conventional linear fit gives {β }{app}≈ 3. Our model finds {β }{int}=2.3+/- 0.3 and a distinct dust law of {R}B=3.8+/- 0.3, consistent with the average for Milky Way dust, while correcting a systematic distance bias of ˜0.10 mag in the tails of the apparent color distribution. Finally, we extend our model to examine the SN Ia luminosity-host mass dependence in terms of intrinsic and dust components.

Bayesian convolutional neural network based MRI brain extraction on nonhuman primates.

PubMed

Zhao, Gengyan; Liu, Fang; Oler, Jonathan A; Meyerand, Mary E; Kalin, Ned H; Birn, Rasmus M

2018-07-15

Brain extraction or skull stripping of magnetic resonance images (MRI) is an essential step in neuroimaging studies, the accuracy of which can severely affect subsequent image processing procedures. Current automatic brain extraction methods demonstrate good results on human brains, but are often far from satisfactory on nonhuman primates, which are a necessary part of neuroscience research. To overcome the challenges of brain extraction in nonhuman primates, we propose a fully-automated brain extraction pipeline combining deep Bayesian convolutional neural network (CNN) and fully connected three-dimensional (3D) conditional random field (CRF). The deep Bayesian CNN, Bayesian SegNet, is used as the core segmentation engine. As a probabilistic network, it is not only able to perform accurate high-resolution pixel-wise brain segmentation, but also capable of measuring the model uncertainty by Monte Carlo sampling with dropout in the testing stage. Then, fully connected 3D CRF is used to refine the probability result from Bayesian SegNet in the whole 3D context of the brain volume. The proposed method was evaluated with a manually brain-extracted dataset comprising T1w images of 100 nonhuman primates. Our method outperforms six popular publicly available brain extraction packages and three well-established deep learning based methods with a mean Dice coefficient of 0.985 and a mean average symmetric surface distance of 0.220 mm. A better performance against all the compared methods was verified by statistical tests (all p-values < 10 -4 , two-sided, Bonferroni corrected). The maximum uncertainty of the model on nonhuman primate brain extraction has a mean value of 0.116 across all the 100 subjects. The behavior of the uncertainty was also studied, which shows the uncertainty increases as the training set size decreases, the number of inconsistent labels in the training set increases, or the inconsistency between the training set and the testing set increases. Copyright © 2018 Elsevier Inc. All rights reserved.

Inference in the Wild: A Framework for Human Situation Assessment and a Case Study of Air Combat.

PubMed

McAnally, Ken; Davey, Catherine; White, Daniel; Stimson, Murray; Mascaro, Steven; Korb, Kevin

2018-06-24

Situation awareness is a key construct in human factors and arises from a process of situation assessment (SA). SA comprises the perception of information, its integration with existing knowledge, the search for new information, and the prediction of the future state of the world, including the consequences of planned actions. Causal models implemented as Bayesian networks (BNs) are attractive for modeling all of these processes within a single, unified framework. We elicited declarative knowledge from two Royal Australian Air Force (RAAF) fighter pilots about the information sources used in the identification (ID) of airborne entities and the causal relationships between these sources. This knowledge was represented in a BN (the declarative model) that was evaluated against the performance of 19 RAAF fighter pilots in a low-fidelity simulation. Pilot behavior was well predicted by a simple associative model (the behavioral model) with only three attributes of ID. Search for information by pilots was largely compensatory and was near-optimal with respect to the behavioral model. The average revision of beliefs in response to evidence was close to Bayesian, but there was substantial variability. Together, these results demonstrate the value of BNs for modeling human SA. Copyright © 2018 Cognitive Science Society, Inc.

Effects of error covariance structure on estimation of model averaging weights and predictive performance

USGS Publications Warehouse

Lu, Dan; Ye, Ming; Meyer, Philip D.; Curtis, Gary P.; Shi, Xiaoqing; Niu, Xu-Feng; Yabusaki, Steve B.

2013-01-01

When conducting model averaging for assessing groundwater conceptual model uncertainty, the averaging weights are often evaluated using model selection criteria such as AIC, AICc, BIC, and KIC (Akaike Information Criterion, Corrected Akaike Information Criterion, Bayesian Information Criterion, and Kashyap Information Criterion, respectively). However, this method often leads to an unrealistic situation in which the best model receives overwhelmingly large averaging weight (close to 100%), which cannot be justified by available data and knowledge. It was found in this study that this problem was caused by using the covariance matrix, CE, of measurement errors for estimating the negative log likelihood function common to all the model selection criteria. This problem can be resolved by using the covariance matrix, Cek, of total errors (including model errors and measurement errors) to account for the correlation between the total errors. An iterative two-stage method was developed in the context of maximum likelihood inverse modeling to iteratively infer the unknown Cek from the residuals during model calibration. The inferred Cek was then used in the evaluation of model selection criteria and model averaging weights. While this method was limited to serial data using time series techniques in this study, it can be extended to spatial data using geostatistical techniques. The method was first evaluated in a synthetic study and then applied to an experimental study, in which alternative surface complexation models were developed to simulate column experiments of uranium reactive transport. It was found that the total errors of the alternative models were temporally correlated due to the model errors. The iterative two-stage method using Cekresolved the problem that the best model receives 100% model averaging weight, and the resulting model averaging weights were supported by the calibration results and physical understanding of the alternative models. Using Cek obtained from the iterative two-stage method also improved predictive performance of the individual models and model averaging in both synthetic and experimental studies.

Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data

ERIC Educational Resources Information Center

Lee, Sik-Yum

2006-01-01

A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm is used to produce the joint Bayesian estimates of…

Dynamic Bayesian Network Modeling of Game Based Diagnostic Assessments. CRESST Report 837

ERIC Educational Resources Information Center

Levy, Roy

2014-01-01

Digital games offer an appealing environment for assessing student proficiencies, including skills and misconceptions in a diagnostic setting. This paper proposes a dynamic Bayesian network modeling approach for observations of student performance from an educational video game. A Bayesian approach to model construction, calibration, and use in…

Bayesian techniques for analyzing group differences in the Iowa Gambling Task: A case study of intuitive and deliberate decision-makers.

PubMed

Steingroever, Helen; Pachur, Thorsten; Šmíra, Martin; Lee, Michael D

2018-06-01

The Iowa Gambling Task (IGT) is one of the most popular experimental paradigms for comparing complex decision-making across groups. Most commonly, IGT behavior is analyzed using frequentist tests to compare performance across groups, and to compare inferred parameters of cognitive models developed for the IGT. Here, we present a Bayesian alternative based on Bayesian repeated-measures ANOVA for comparing performance, and a suite of three complementary model-based methods for assessing the cognitive processes underlying IGT performance. The three model-based methods involve Bayesian hierarchical parameter estimation, Bayes factor model comparison, and Bayesian latent-mixture modeling. We illustrate these Bayesian methods by applying them to test the extent to which differences in intuitive versus deliberate decision style are associated with differences in IGT performance. The results show that intuitive and deliberate decision-makers behave similarly on the IGT, and the modeling analyses consistently suggest that both groups of decision-makers rely on similar cognitive processes. Our results challenge the notion that individual differences in intuitive and deliberate decision styles have a broad impact on decision-making. They also highlight the advantages of Bayesian methods, especially their ability to quantify evidence in favor of the null hypothesis, and that they allow model-based analyses to incorporate hierarchical and latent-mixture structures.

Invited commentary: Lost in estimation--searching for alternatives to markov chains to fit complex Bayesian models.

PubMed

Molitor, John

2012-03-01

Bayesian methods have seen an increase in popularity in a wide variety of scientific fields, including epidemiology. One of the main reasons for their widespread application is the power of the Markov chain Monte Carlo (MCMC) techniques generally used to fit these models. As a result, researchers often implicitly associate Bayesian models with MCMC estimation procedures. However, Bayesian models do not always require Markov-chain-based methods for parameter estimation. This is important, as MCMC estimation methods, while generally quite powerful, are complex and computationally expensive and suffer from convergence problems related to the manner in which they generate correlated samples used to estimate probability distributions for parameters of interest. In this issue of the Journal, Cole et al. (Am J Epidemiol. 2012;175(5):368-375) present an interesting paper that discusses non-Markov-chain-based approaches to fitting Bayesian models. These methods, though limited, can overcome some of the problems associated with MCMC techniques and promise to provide simpler approaches to fitting Bayesian models. Applied researchers will find these estimation approaches intuitively appealing and will gain a deeper understanding of Bayesian models through their use. However, readers should be aware that other non-Markov-chain-based methods are currently in active development and have been widely published in other fields.

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

PubMed

Norris, Dennis

2006-04-01

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

Implementation of bayesian model averaging on the weather data forecasting applications utilizing open weather map

NASA Astrophysics Data System (ADS)

Rahmat, R. F.; Nasution, F. R.; Seniman; Syahputra, M. F.; Sitompul, O. S.

2018-02-01

Weather is condition of air in a certain region at a relatively short period of time, measured with various parameters such as; temperature, air preasure, wind velocity, humidity and another phenomenons in the atmosphere. In fact, extreme weather due to global warming would lead to drought, flood, hurricane and other forms of weather occasion, which directly affects social andeconomic activities. Hence, a forecasting technique is to predict weather with distinctive output, particullary mapping process based on GIS with information about current weather status in certain cordinates of each region with capability to forecast for seven days afterward. Data used in this research are retrieved in real time from the server openweathermap and BMKG. In order to obtain a low error rate and high accuracy of forecasting, the authors use Bayesian Model Averaging (BMA) method. The result shows that the BMA method has good accuracy. Forecasting error value is calculated by mean square error shows (MSE). The error value emerges at minumum temperature rated at 0.28 and maximum temperature rated at 0.15. Meanwhile, the error value of minimum humidity rates at 0.38 and the error value of maximum humidity rates at 0.04. Afterall, the forecasting error rate of wind speed is at 0.076. The lower the forecasting error rate, the more optimized the accuracy is.

Data-driven confounder selection via Markov and Bayesian networks.

PubMed

Häggström, Jenny

2018-06-01

To unbiasedly estimate a causal effect on an outcome unconfoundedness is often assumed. If there is sufficient knowledge on the underlying causal structure then existing confounder selection criteria can be used to select subsets of the observed pretreatment covariates, X, sufficient for unconfoundedness, if such subsets exist. Here, estimation of these target subsets is considered when the underlying causal structure is unknown. The proposed method is to model the causal structure by a probabilistic graphical model, for example, a Markov or Bayesian network, estimate this graph from observed data and select the target subsets given the estimated graph. The approach is evaluated by simulation both in a high-dimensional setting where unconfoundedness holds given X and in a setting where unconfoundedness only holds given subsets of X. Several common target subsets are investigated and the selected subsets are compared with respect to accuracy in estimating the average causal effect. The proposed method is implemented with existing software that can easily handle high-dimensional data, in terms of large samples and large number of covariates. The results from the simulation study show that, if unconfoundedness holds given X, this approach is very successful in selecting the target subsets, outperforming alternative approaches based on random forests and LASSO, and that the subset estimating the target subset containing all causes of outcome yields smallest MSE in the average causal effect estimation. © 2017, The International Biometric Society.

Spatiotemporal Modeling of Ozone Levels in Quebec (Canada): A Comparison of Kriging, Land-Use Regression (LUR), and Combined Bayesian Maximum Entropy–LUR Approaches

PubMed Central

Adam-Poupart, Ariane; Brand, Allan; Fournier, Michel; Jerrett, Michael

2014-01-01

Background: Ambient air ozone (O3) is a pulmonary irritant that has been associated with respiratory health effects including increased lung inflammation and permeability, airway hyperreactivity, respiratory symptoms, and decreased lung function. Estimation of O3 exposure is a complex task because the pollutant exhibits complex spatiotemporal patterns. To refine the quality of exposure estimation, various spatiotemporal methods have been developed worldwide. Objectives: We sought to compare the accuracy of three spatiotemporal models to predict summer ground-level O3 in Quebec, Canada. Methods: We developed a land-use mixed-effects regression (LUR) model based on readily available data (air quality and meteorological monitoring data, road networks information, latitude), a Bayesian maximum entropy (BME) model incorporating both O3 monitoring station data and the land-use mixed model outputs (BME-LUR), and a kriging method model based only on available O3 monitoring station data (BME kriging). We performed leave-one-station-out cross-validation and visually assessed the predictive capability of each model by examining the mean temporal and spatial distributions of the average estimated errors. Results: The BME-LUR was the best predictive model (R2 = 0.653) with the lowest root mean-square error (RMSE ;7.06 ppb), followed by the LUR model (R2 = 0.466, RMSE = 8.747) and the BME kriging model (R2 = 0.414, RMSE = 9.164). Conclusions: Our findings suggest that errors of estimation in the interpolation of O3 concentrations with BME can be greatly reduced by incorporating outputs from a LUR model developed with readily available data. Citation: Adam-Poupart A, Brand A, Fournier M, Jerrett M, Smargiassi A. 2014. Spatiotemporal modeling of ozone levels in Quebec (Canada): a comparison of kriging, land-use regression (LUR), and combined Bayesian maximum entropy–LUR approaches. Environ Health Perspect 122:970–976; http://dx.doi.org/10.1289/ehp.1306566 PMID:24879650

Stochastic modelling of the monthly average maximum and minimum temperature patterns in India 1981-2015

NASA Astrophysics Data System (ADS)

Narasimha Murthy, K. V.; Saravana, R.; Vijaya Kumar, K.

2018-04-01

The paper investigates the stochastic modelling and forecasting of monthly average maximum and minimum temperature patterns through suitable seasonal auto regressive integrated moving average (SARIMA) model for the period 1981-2015 in India. The variations and distributions of monthly maximum and minimum temperatures are analyzed through Box plots and cumulative distribution functions. The time series plot indicates that the maximum temperature series contain sharp peaks in almost all the years, while it is not true for the minimum temperature series, so both the series are modelled separately. The possible SARIMA model has been chosen based on observing autocorrelation function (ACF), partial autocorrelation function (PACF), and inverse autocorrelation function (IACF) of the logarithmic transformed temperature series. The SARIMA (1, 0, 0) × (0, 1, 1)12 model is selected for monthly average maximum and minimum temperature series based on minimum Bayesian information criteria. The model parameters are obtained using maximum-likelihood method with the help of standard error of residuals. The adequacy of the selected model is determined using correlation diagnostic checking through ACF, PACF, IACF, and p values of Ljung-Box test statistic of residuals and using normal diagnostic checking through the kernel and normal density curves of histogram and Q-Q plot. Finally, the forecasting of monthly maximum and minimum temperature patterns of India for the next 3 years has been noticed with the help of selected model.

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 modeling of flexible cognitive control

PubMed Central

Jiang, Jiefeng; Heller, Katherine; Egner, Tobias

2014-01-01

“Cognitive control” describes endogenous guidance of behavior in situations where routine stimulus-response associations are suboptimal for achieving a desired goal. The computational and neural mechanisms underlying this capacity remain poorly understood. We examine recent advances stemming from the application of a Bayesian learner perspective that provides optimal prediction for control processes. In reviewing the application of Bayesian models to cognitive control, we note that an important limitation in current models is a lack of a plausible mechanism for the flexible adjustment of control over conflict levels changing at varying temporal scales. We then show that flexible cognitive control can be achieved by a Bayesian model with a volatility-driven learning mechanism that modulates dynamically the relative dependence on recent and remote experiences in its prediction of future control demand. We conclude that the emergent Bayesian perspective on computational mechanisms of cognitive control holds considerable promise, especially if future studies can identify neural substrates of the variables encoded by these models, and determine the nature (Bayesian or otherwise) of their neural implementation. PMID:24929218

Bayesian generalized linear mixed modeling of Tuberculosis using informative priors.

PubMed

Ojo, Oluwatobi Blessing; Lougue, Siaka; Woldegerima, Woldegebriel Assefa

2017-01-01

TB is rated as one of the world's deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014.

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.

Bayesian Parameter Inference and Model Selection by Population Annealing in Systems Biology

PubMed Central

Murakami, Yohei

2014-01-01

Parameter inference and model selection are very important for mathematical modeling in systems biology. Bayesian statistics can be used to conduct both parameter inference and model selection. Especially, the framework named approximate Bayesian computation is often used for parameter inference and model selection in systems biology. However, Monte Carlo methods needs to be used to compute Bayesian posterior distributions. In addition, the posterior distributions of parameters are sometimes almost uniform or very similar to their prior distributions. In such cases, it is difficult to choose one specific value of parameter with high credibility as the representative value of the distribution. To overcome the problems, we introduced one of the population Monte Carlo algorithms, population annealing. Although population annealing is usually used in statistical mechanics, we showed that population annealing can be used to compute Bayesian posterior distributions in the approximate Bayesian computation framework. To deal with un-identifiability of the representative values of parameters, we proposed to run the simulations with the parameter ensemble sampled from the posterior distribution, named “posterior parameter ensemble”. We showed that population annealing is an efficient and convenient algorithm to generate posterior parameter ensemble. We also showed that the simulations with the posterior parameter ensemble can, not only reproduce the data used for parameter inference, but also capture and predict the data which was not used for parameter inference. Lastly, we introduced the marginal likelihood in the approximate Bayesian computation framework for Bayesian model selection. We showed that population annealing enables us to compute the marginal likelihood in the approximate Bayesian computation framework and conduct model selection depending on the Bayes factor. PMID:25089832

Evaluation of Oceanic Transport Statistics By Use of Transient Tracers and Bayesian Methods

NASA Astrophysics Data System (ADS)

Trossman, D. S.; Thompson, L.; Mecking, S.; Bryan, F.; Peacock, S.

2013-12-01

Key variables that quantify the time scales over which atmospheric signals penetrate into the oceanic interior and their uncertainties are computed using Bayesian methods and transient tracers from both models and observations. First, the mean residence times, subduction rates, and formation rates of Subtropical Mode Water (STMW) and Subpolar Mode Water (SPMW) in the North Atlantic and Subantarctic Mode Water (SAMW) in the Southern Ocean are estimated by combining a model and observations of chlorofluorocarbon-11 (CFC-11) via Bayesian Model Averaging (BMA), statistical technique that weights model estimates according to how close they agree with observations. Second, a Bayesian method is presented to find two oceanic transport parameters associated with the age distribution of ocean waters, the transit-time distribution (TTD), by combining an eddying global ocean model's estimate of the TTD with hydrographic observations of CFC-11, temperature, and salinity. Uncertainties associated with objectively mapping irregularly spaced bottle data are quantified by making use of a thin-plate spline and then propagated via the two Bayesian techniques. It is found that the subduction of STMW, SPMW, and SAMW is mostly an advective process, but up to about one-third of STMW subduction likely owes to non-advective processes. Also, while the formation of STMW is mostly due to subduction, the formation of SPMW is mostly due to other processes. About half of the formation of SAMW is due to subduction and half is due to other processes. A combination of air-sea flux, acting on relatively short time scales, and turbulent mixing, acting on a wide range of time scales, is likely the dominant SPMW erosion mechanism. Air-sea flux is likely responsible for most STMW erosion, and turbulent mixing is likely responsible for most SAMW erosion. Two oceanic transport parameters, the mean age of a water parcel and the half-variance associated with the TTD, estimated using the model's tracers as data (BayesPOP) and those estimated using tracer observations as data (BayesObs) provide information about the sources of model biases, and give a more nuanced picture than can be found by comparing the simulated CFC-11 concentrations with observed CFC-11 concentrations. Using the differences between the two oceanic transport parameters from BayesObs and those from BayesPOP with and without a constant Peclet number assumption along each of the hydrographic cross-sections considered here, it is found that the model's diffusivity tensor biases lead to larger model errors than the model's mean advection time biases. However, it is also found that mean advection time biases in the model are statistically significant at the 95% level where mode water is found.

Comparison of two non-convex mixed-integer nonlinear programming algorithms applied to autoregressive moving average model structure and parameter estimation

NASA Astrophysics Data System (ADS)

Uilhoorn, F. E.

2016-10-01

In this article, the stochastic modelling approach proposed by Box and Jenkins is treated as a mixed-integer nonlinear programming (MINLP) problem solved with a mesh adaptive direct search and a real-coded genetic class of algorithms. The aim is to estimate the real-valued parameters and non-negative integer, correlated structure of stationary autoregressive moving average (ARMA) processes. The maximum likelihood function of the stationary ARMA process is embedded in Akaike's information criterion and the Bayesian information criterion, whereas the estimation procedure is based on Kalman filter recursions. The constraints imposed on the objective function enforce stability and invertibility. The best ARMA model is regarded as the global minimum of the non-convex MINLP problem. The robustness and computational performance of the MINLP solvers are compared with brute-force enumeration. Numerical experiments are done for existing time series and one new data set.

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.

Stochastic analog neutron transport with TRIPOLI-4 and FREYA: Bayesian uncertainty quantification for neutron multiplicity counting

DOE PAGES

Verbeke, J. M.; Petit, O.

2016-06-01

From nuclear safeguards to homeland security applications, the need for the better modeling of nuclear interactions has grown over the past decades. Current Monte Carlo radiation transport codes compute average quantities with great accuracy and performance; however, performance and averaging come at the price of limited interaction-by-interaction modeling. These codes often lack the capability of modeling interactions exactly: for a given collision, energy is not conserved, energies of emitted particles are uncorrelated, and multiplicities of prompt fission neutrons and photons are uncorrelated. Many modern applications require more exclusive quantities than averages, such as the fluctuations in certain observables (e.g., themore » neutron multiplicity) and correlations between neutrons and photons. In an effort to meet this need, the radiation transport Monte Carlo code TRIPOLI-4® was modified to provide a specific mode that models nuclear interactions in a full analog way, replicating as much as possible the underlying physical process. Furthermore, the computational model FREYA (Fission Reaction Event Yield Algorithm) was coupled with TRIPOLI-4 to model complete fission events. As a result, FREYA automatically includes fluctuations as well as correlations resulting from conservation of energy and momentum.« less

Large ensemble modeling of the last deglacial retreat of the West Antarctic Ice Sheet: comparison of simple and advanced statistical techniques

NASA Astrophysics Data System (ADS)

Pollard, David; Chang, Won; Haran, Murali; Applegate, Patrick; DeConto, Robert

2016-05-01

A 3-D hybrid ice-sheet model is applied to the last deglacial retreat of the West Antarctic Ice Sheet over the last ˜ 20 000 yr. A large ensemble of 625 model runs is used to calibrate the model to modern and geologic data, including reconstructed grounding lines, relative sea-level records, elevation-age data and uplift rates, with an aggregate score computed for each run that measures overall model-data misfit. Two types of statistical methods are used to analyze the large-ensemble results: simple averaging weighted by the aggregate score, and more advanced Bayesian techniques involving Gaussian process-based emulation and calibration, and Markov chain Monte Carlo. The analyses provide sea-level-rise envelopes with well-defined parametric uncertainty bounds, but the simple averaging method only provides robust results with full-factorial parameter sampling in the large ensemble. Results for best-fit parameter ranges and envelopes of equivalent sea-level rise with the simple averaging method agree well with the more advanced techniques. Best-fit parameter ranges confirm earlier values expected from prior model tuning, including large basal sliding coefficients on modern ocean beds.

A comparative analysis of 9 multi-model averaging approaches in hydrological continuous streamflow simulation

NASA Astrophysics Data System (ADS)

Arsenault, Richard; Gatien, Philippe; Renaud, Benoit; Brissette, François; Martel, Jean-Luc

2015-10-01

This study aims to test whether a weighted combination of several hydrological models can simulate flows more accurately than the models taken individually. In addition, the project attempts to identify the most efficient model averaging method and the optimal number of models to include in the weighting scheme. In order to address the first objective, streamflow was simulated using four lumped hydrological models (HSAMI, HMETS, MOHYSE and GR4J-6), each of which were calibrated with three different objective functions on 429 watersheds. The resulting 12 hydrographs (4 models × 3 metrics) were weighted and combined with the help of 9 averaging methods which are the simple arithmetic mean (SAM), Akaike information criterion (AICA), Bates-Granger (BGA), Bayes information criterion (BICA), Bayesian model averaging (BMA), Granger-Ramanathan average variant A, B and C (GRA, GRB and GRC) and the average by SCE-UA optimization (SCA). The same weights were then applied to the hydrographs in validation mode, and the Nash-Sutcliffe Efficiency metric was measured between the averaged and observed hydrographs. Statistical analyses were performed to compare the accuracy of weighted methods to that of individual models. A Kruskal-Wallis test and a multi-objective optimization algorithm were then used to identify the most efficient weighted method and the optimal number of models to integrate. Results suggest that the GRA, GRB, GRC and SCA weighted methods perform better than the individual members. Model averaging from these four methods were superior to the best of the individual members in 76% of the cases. Optimal combinations on all watersheds included at least one of each of the four hydrological models. None of the optimal combinations included all members of the ensemble of 12 hydrographs. The Granger-Ramanathan average variant C (GRC) is recommended as the best compromise between accuracy, speed of execution, and simplicity.

A Bayesian-based multilevel factorial analysis method for analyzing parameter uncertainty of hydrological model

NASA Astrophysics Data System (ADS)

Liu, Y. R.; Li, Y. P.; Huang, G. H.; Zhang, J. L.; Fan, Y. R.

2017-10-01

In this study, a Bayesian-based multilevel factorial analysis (BMFA) method is developed to assess parameter uncertainties and their effects on hydrological model responses. In BMFA, Differential Evolution Adaptive Metropolis (DREAM) algorithm is employed to approximate the posterior distributions of model parameters with Bayesian inference; factorial analysis (FA) technique is used for measuring the specific variations of hydrological responses in terms of posterior distributions to investigate the individual and interactive effects of parameters on model outputs. BMFA is then applied to a case study of the Jinghe River watershed in the Loess Plateau of China to display its validity and applicability. The uncertainties of four sensitive parameters, including soil conservation service runoff curve number to moisture condition II (CN2), soil hydraulic conductivity (SOL_K), plant available water capacity (SOL_AWC), and soil depth (SOL_Z), are investigated. Results reveal that (i) CN2 has positive effect on peak flow, implying that the concentrated rainfall during rainy season can cause infiltration-excess surface flow, which is an considerable contributor to peak flow in this watershed; (ii) SOL_K has positive effect on average flow, implying that the widely distributed cambisols can lead to medium percolation capacity; (iii) the interaction between SOL_AWC and SOL_Z has noticeable effect on the peak flow and their effects are dependent upon each other, which discloses that soil depth can significant influence the processes of plant uptake of soil water in this watershed. Based on the above findings, the significant parameters and the relationship among uncertain parameters can be specified, such that hydrological model's capability for simulating/predicting water resources of the Jinghe River watershed can be improved.

Selection of Polynomial Chaos Bases via Bayesian Model Uncertainty Methods with Applications to Sparse Approximation of PDEs with Stochastic Inputs

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

Karagiannis, Georgios; Lin, Guang

2014-02-15

Generalized polynomial chaos (gPC) expansions allow the representation of the solution of a stochastic system as a series of polynomial terms. The number of gPC terms increases dramatically with the dimension of the random input variables. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs if the evaluations of the system are expensive, the evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solution, both in spacial and random domains, by coupling Bayesianmore » model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spacial points via (1) Bayesian model average or (2) medial probability model, and their construction as functions on the spacial domain via spline interpolation. The former accounts the model uncertainty and provides Bayes-optimal predictions; while the latter, additionally, provides a sparse representation of the solution by evaluating the expansion on a subset of dominating gPC bases when represented as a gPC expansion. Moreover, the method quantifies the importance of the gPC bases through inclusion probabilities. We design an MCMC sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed method is suitable for, but not restricted to, problems whose stochastic solution is sparse at the stochastic level with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the good performance of the proposed method and make comparisons with others on 1D, 14D and 40D in random space elliptic stochastic partial differential equations.« less

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

NASA Astrophysics Data System (ADS)

Nomura, Shunichi; Ogata, Yosihiko

2016-04-01

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

A Hierarchical Multivariate Bayesian Approach to Ensemble Model output Statistics in Atmospheric Prediction

DTIC Science & Technology

2017-09-01

efficacy of statistical post-processing methods downstream of these dynamical model components with a hierarchical multivariate Bayesian approach to...Bayesian hierarchical modeling, Markov chain Monte Carlo methods , Metropolis algorithm, machine learning, atmospheric prediction 15. NUMBER OF PAGES...scale processes. However, this dissertation explores the efficacy of statistical post-processing methods downstream of these dynamical model components

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 Analysis of Longitudinal Data Using Growth Curve Models

ERIC Educational Resources Information Center

Zhang, Zhiyong; Hamagami, Fumiaki; Wang, Lijuan Lijuan; Nesselroade, John R.; Grimm, Kevin J.

2007-01-01

Bayesian methods for analyzing longitudinal data in social and behavioral research are recommended for their ability to incorporate prior information in estimating simple and complex models. We first summarize the basics of Bayesian methods before presenting an empirical example in which we fit a latent basis growth curve model to achievement data…

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

PubMed

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

2017-01-01

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

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

PubMed Central

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

2017-01-01

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

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.

Using statistical anomaly detection models to find clinical decision support malfunctions.

PubMed

Ray, Soumi; McEvoy, Dustin S; Aaron, Skye; Hickman, Thu-Trang; Wright, Adam

2018-05-11

Malfunctions in Clinical Decision Support (CDS) systems occur due to a multitude of reasons, and often go unnoticed, leading to potentially poor outcomes. Our goal was to identify malfunctions within CDS systems. We evaluated 6 anomaly detection models: (1) Poisson Changepoint Model, (2) Autoregressive Integrated Moving Average (ARIMA) Model, (3) Hierarchical Divisive Changepoint (HDC) Model, (4) Bayesian Changepoint Model, (5) Seasonal Hybrid Extreme Studentized Deviate (SHESD) Model, and (6) E-Divisive with Median (EDM) Model and characterized their ability to find known anomalies. We analyzed 4 CDS alerts with known malfunctions from the Longitudinal Medical Record (LMR) and Epic® (Epic Systems Corporation, Madison, WI, USA) at Brigham and Women's Hospital, Boston, MA. The 4 rules recommend lead testing in children, aspirin therapy in patients with coronary artery disease, pneumococcal vaccination in immunocompromised adults and thyroid testing in patients taking amiodarone. Poisson changepoint, ARIMA, HDC, Bayesian changepoint and the SHESD model were able to detect anomalies in an alert for lead screening in children and in an alert for pneumococcal conjugate vaccine in immunocompromised adults. EDM was able to detect anomalies in an alert for monitoring thyroid function in patients on amiodarone. Malfunctions/anomalies occur frequently in CDS alert systems. It is important to be able to detect such anomalies promptly. Anomaly detection models are useful tools to aid such detections.

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.

Comparison Between Linear and Non-parametric Regression Models for Genome-Enabled Prediction in Wheat

PubMed Central

Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne

2012-01-01

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models. PMID:23275882

Comparison between linear and non-parametric regression models for genome-enabled prediction in wheat.

PubMed

Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne

2012-12-01

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models.

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

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

PubMed

Kärkkäinen, Hanni P; Sillanpää, Mikko J

2013-09-04

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

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

PubMed Central

Kärkkäinen, Hanni P.; Sillanpää, Mikko J.

2013-01-01

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

APPLICATION OF BAYESIAN MONTE CARLO ANALYSIS TO A LAGRANGIAN PHOTOCHEMICAL AIR QUALITY MODEL. (R824792)

EPA Science Inventory

Uncertainties in ozone concentrations predicted with a Lagrangian photochemical air quality model have been estimated using Bayesian Monte Carlo (BMC) analysis. Bayesian Monte Carlo analysis provides a means of combining subjective "prior" uncertainty estimates developed ...

A SEMIPARAMETRIC BAYESIAN MODEL FOR CIRCULAR-LINEAR REGRESSION

EPA Science Inventory

We present a Bayesian approach to regress a circular variable on a linear predictor. The regression coefficients are assumed to have a nonparametric distribution with a Dirichlet process prior. The semiparametric Bayesian approach gives added flexibility to the model and is usefu...

A Bayesian alternative for multi-objective ecohydrological model specification

NASA Astrophysics Data System (ADS)

Tang, Yating; Marshall, Lucy; Sharma, Ashish; Ajami, Hoori

2018-01-01

Recent studies have identified the importance of vegetation processes in terrestrial hydrologic systems. Process-based ecohydrological models combine hydrological, physical, biochemical and ecological processes of the catchments, and as such are generally more complex and parametric than conceptual hydrological models. Thus, appropriate calibration objectives and model uncertainty analysis are essential for ecohydrological modeling. In recent years, Bayesian inference has become one of the most popular tools for quantifying the uncertainties in hydrological modeling with the development of Markov chain Monte Carlo (MCMC) techniques. The Bayesian approach offers an appealing alternative to traditional multi-objective hydrologic model calibrations by defining proper prior distributions that can be considered analogous to the ad-hoc weighting often prescribed in multi-objective calibration. Our study aims to develop appropriate prior distributions and likelihood functions that minimize the model uncertainties and bias within a Bayesian ecohydrological modeling framework based on a traditional Pareto-based model calibration technique. In our study, a Pareto-based multi-objective optimization and a formal Bayesian framework are implemented in a conceptual ecohydrological model that combines a hydrological model (HYMOD) and a modified Bucket Grassland Model (BGM). Simulations focused on one objective (streamflow/LAI) and multiple objectives (streamflow and LAI) with different emphasis defined via the prior distribution of the model error parameters. Results show more reliable outputs for both predicted streamflow and LAI using Bayesian multi-objective calibration with specified prior distributions for error parameters based on results from the Pareto front in the ecohydrological modeling. The methodology implemented here provides insight into the usefulness of multiobjective Bayesian calibration for ecohydrologic systems and the importance of appropriate prior distributions in such approaches.

Diagnostic accuracy of a bayesian latent group analysis for the detection of malingering-related poor effort.

PubMed

Ortega, Alonso; Labrenz, Stephan; Markowitsch, Hans J; Piefke, Martina

2013-01-01

In the last decade, different statistical techniques have been introduced to improve assessment of malingering-related poor effort. In this context, we have recently shown preliminary evidence that a Bayesian latent group model may help to optimize classification accuracy using a simulation research design. In the present study, we conducted two analyses. Firstly, we evaluated how accurately this Bayesian approach can distinguish between participants answering in an honest way (honest response group) and participants feigning cognitive impairment (experimental malingering group). Secondly, we tested the accuracy of our model in the differentiation between patients who had real cognitive deficits (cognitively impaired group) and participants who belonged to the experimental malingering group. All Bayesian analyses were conducted using the raw scores of a visual recognition forced-choice task (2AFC), the Test of Memory Malingering (TOMM, Trial 2), and the Word Memory Test (WMT, primary effort subtests). The first analysis showed 100% accuracy for the Bayesian model in distinguishing participants of both groups with all effort measures. The second analysis showed outstanding overall accuracy of the Bayesian model when estimates were obtained from the 2AFC and the TOMM raw scores. Diagnostic accuracy of the Bayesian model diminished when using the WMT total raw scores. Despite, overall diagnostic accuracy can still be considered excellent. The most plausible explanation for this decrement is the low performance in verbal recognition and fluency tasks of some patients of the cognitively impaired group. Additionally, the Bayesian model provides individual estimates, p(zi |D), of examinees' effort levels. In conclusion, both high classification accuracy levels and Bayesian individual estimates of effort may be very useful for clinicians when assessing for effort in medico-legal settings.

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

Estimating Tree Height-Diameter Models with the Bayesian Method

PubMed Central

Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the “best” model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2. PMID:24711733

Estimating tree height-diameter models with the Bayesian method.

PubMed

Zhang, Xiongqing; Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the "best" model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2.

Bayesian inversion of a CRN depth profile to infer Quaternary erosion of the northwestern Campine Plateau (NE Belgium)

NASA Astrophysics Data System (ADS)

Laloy, Eric; Beerten, Koen; Vanacker, Veerle; Christl, Marcus; Rogiers, Bart; Wouters, Laurent

2017-07-01

The rate at which low-lying sandy areas in temperate regions, such as the Campine Plateau (NE Belgium), have been eroding during the Quaternary is a matter of debate. Current knowledge on the average pace of landscape evolution in the Campine area is largely based on geological inferences and modern analogies. We performed a Bayesian inversion of an in situ-produced 10Be concentration depth profile to infer the average long-term erosion rate together with two other parameters: the surface exposure age and the inherited 10Be concentration. Compared to the latest advances in probabilistic inversion of cosmogenic radionuclide (CRN) data, our approach has the following two innovative components: it (1) uses Markov chain Monte Carlo (MCMC) sampling and (2) accounts (under certain assumptions) for the contribution of model errors to posterior uncertainty. To investigate to what extent our approach differs from the state of the art in practice, a comparison against the Bayesian inversion method implemented in the CRONUScalc program is made. Both approaches identify similar maximum a posteriori (MAP) parameter values, but posterior parameter and predictive uncertainty derived using the method taken in CRONUScalc is moderately underestimated. A simple way for producing more consistent uncertainty estimates with the CRONUScalc-like method in the presence of model errors is therefore suggested. Our inferred erosion rate of 39 ± 8. 9 mm kyr-1 (1σ) is relatively large in comparison with landforms that erode under comparable (paleo-)climates elsewhere in the world. We evaluate this value in the light of the erodibility of the substrate and sudden base level lowering during the Middle Pleistocene. A denser sampling scheme of a two-nuclide concentration depth profile would allow for better inferred erosion rate resolution, and including more uncertain parameters in the MCMC inversion.

Accurate Biomass Estimation via Bayesian Adaptive Sampling

NASA Technical Reports Server (NTRS)

Wheeler, Kevin R.; Knuth, Kevin H.; Castle, Joseph P.; Lvov, Nikolay

2005-01-01

The following concepts were introduced: a) Bayesian adaptive sampling for solving biomass estimation; b) Characterization of MISR Rahman model parameters conditioned upon MODIS landcover. c) Rigorous non-parametric Bayesian approach to analytic mixture model determination. d) Unique U.S. asset for science product validation and verification.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Neonatal heart rate prediction.

PubMed

Abdel-Rahman, Yumna; Jeremic, Aleksander; Tan, Kenneth

2009-01-01

Technological advances have caused a decrease in the number of infant deaths. Pre-term infants now have a substantially increased chance of survival. One of the mechanisms that is vital to saving the lives of these infants is continuous monitoring and early diagnosis. With continuous monitoring huge amounts of data are collected with so much information embedded in them. By using statistical analysis this information can be extracted and used to aid diagnosis and to understand development. In this study we have a large dataset containing over 180 pre-term infants whose heart rates were recorded over the length of their stay in the Neonatal Intensive Care Unit (NICU). We test two types of models, empirical bayesian and autoregressive moving average. We then attempt to predict future values. The autoregressive moving average model showed better results but required more computation.

Load Balancing Using Time Series Analysis for Soft Real Time Systems with Statistically Periodic Loads

NASA Technical Reports Server (NTRS)

Hailperin, Max

1993-01-01

This thesis provides design and analysis of techniques for global load balancing on ensemble architectures running soft-real-time object-oriented applications with statistically periodic loads. It focuses on estimating the instantaneous average load over all the processing elements. The major contribution is the use of explicit stochastic process models for both the loading and the averaging itself. These models are exploited via statistical time-series analysis and Bayesian inference to provide improved average load estimates, and thus to facilitate global load balancing. This thesis explains the distributed algorithms used and provides some optimality results. It also describes the algorithms' implementation and gives performance results from simulation. These results show that our techniques allow more accurate estimation of the global system load ing, resulting in fewer object migration than local methods. Our method is shown to provide superior performance, relative not only to static load-balancing schemes but also to many adaptive methods.

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

Bayesian generalized linear mixed modeling of Tuberculosis using informative priors

PubMed Central

Woldegerima, Woldegebriel Assefa

2017-01-01

TB is rated as one of the world’s deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014. PMID:28257437

SOMBI: Bayesian identification of parameter relations in unstructured cosmological data

NASA Astrophysics Data System (ADS)

Frank, Philipp; Jasche, Jens; Enßlin, Torsten A.

2016-11-01

This work describes the implementation and application of a correlation determination method based on self organizing maps and Bayesian inference (SOMBI). SOMBI aims to automatically identify relations between different observed parameters in unstructured cosmological or astrophysical surveys by automatically identifying data clusters in high-dimensional datasets via the self organizing map neural network algorithm. Parameter relations are then revealed by means of a Bayesian inference within respective identified data clusters. Specifically such relations are assumed to be parametrized as a polynomial of unknown order. The Bayesian approach results in a posterior probability distribution function for respective polynomial coefficients. To decide which polynomial order suffices to describe correlation structures in data, we include a method for model selection, the Bayesian information criterion, to the analysis. The performance of the SOMBI algorithm is tested with mock data. As illustration we also provide applications of our method to cosmological data. In particular, we present results of a correlation analysis between galaxy and active galactic nucleus (AGN) properties provided by the SDSS catalog with the cosmic large-scale-structure (LSS). The results indicate that the combined galaxy and LSS dataset indeed is clustered into several sub-samples of data with different average properties (for example different stellar masses or web-type classifications). The majority of data clusters appear to have a similar correlation structure between galaxy properties and the LSS. In particular we revealed a positive and linear dependency between the stellar mass, the absolute magnitude and the color of a galaxy with the corresponding cosmic density field. A remaining subset of data shows inverted correlations, which might be an artifact of non-linear redshift distortions.

A Fast Surrogate-facilitated Data-driven Bayesian Approach to Uncertainty Quantification of a Regional Groundwater Flow Model with Structural Error

NASA Astrophysics Data System (ADS)

Xu, T.; Valocchi, A. J.; Ye, M.; Liang, F.

2016-12-01

Due to simplification and/or misrepresentation of the real aquifer system, numerical groundwater flow and solute transport models are usually subject to model structural error. During model calibration, the hydrogeological parameters may be overly adjusted to compensate for unknown structural error. This may result in biased predictions when models are used to forecast aquifer response to new forcing. In this study, we extend a fully Bayesian method [Xu and Valocchi, 2015] to calibrate a real-world, regional groundwater flow model. The method uses a data-driven error model to describe model structural error and jointly infers model parameters and structural error. In this study, Bayesian inference is facilitated using high performance computing and fast surrogate models. The surrogate models are constructed using machine learning techniques to emulate the response simulated by the computationally expensive groundwater model. We demonstrate in the real-world case study that explicitly accounting for model structural error yields parameter posterior distributions that are substantially different from those derived by the classical Bayesian calibration that does not account for model structural error. In addition, the Bayesian with error model method gives significantly more accurate prediction along with reasonable credible intervals.

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…

Lateralization is predicted by reduced coupling from the left to right prefrontal cortex during semantic decisions on written words.

PubMed

Seghier, Mohamed L; Josse, Goulven; Leff, Alexander P; Price, Cathy J

2011-07-01

Over 90% of people activate the left hemisphere more than the right hemisphere for language processing. Here, we show that the degree to which language is left lateralized is inversely related to the degree to which left frontal regions drive activity in homotopic right frontal regions. Lateralization was assessed in 60 subjects using functional magnetic resonance imaging (fMRI) activation for semantic decisions on verbal (written words) and nonverbal (pictures of objects) stimuli. Regional interactions between left and right ventral and dorsal frontal regions were assessed using dynamic causal modeling (DCM), random-effects Bayesian model selection at the family level, and Bayesian model averaging at the connection level. We found that 1) semantic decisions on words and pictures modulated interhemispheric coupling between the left and right dorsal frontal regions, 2) activation was more left lateralized for words than pictures, and 3) for words only, left lateralization was greater when the coupling from the left to right dorsal frontal cortex was reduced. These results have theoretical implications for understanding how left and right hemispheres communicate with one another during the processing of lateralized functions.

Incorporating approximation error in surrogate based Bayesian inversion

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Intermediate-term forecasting of aftershocks from an early aftershock sequence: Bayesian and ensemble forecasting approaches

NASA Astrophysics Data System (ADS)

Omi, Takahiro; Ogata, Yosihiko; Hirata, Yoshito; Aihara, Kazuyuki

2015-04-01

Because aftershock occurrences can cause significant seismic risks for a considerable time after the main shock, prospective forecasting of the intermediate-term aftershock activity as soon as possible is important. The epidemic-type aftershock sequence (ETAS) model with the maximum likelihood estimate effectively reproduces general aftershock activity including secondary or higher-order aftershocks and can be employed for the forecasting. However, because we cannot always expect the accurate parameter estimation from incomplete early aftershock data where many events are missing, such forecasting using only a single estimated parameter set (plug-in forecasting) can frequently perform poorly. Therefore, we here propose Bayesian forecasting that combines the forecasts by the ETAS model with various probable parameter sets given the data. By conducting forecasting tests of 1 month period aftershocks based on the first 1 day data after the main shock as an example of the early intermediate-term forecasting, we show that the Bayesian forecasting performs better than the plug-in forecasting on average in terms of the log-likelihood score. Furthermore, to improve forecasting of large aftershocks, we apply a nonparametric (NP) model using magnitude data during the learning period and compare its forecasting performance with that of the Gutenberg-Richter (G-R) formula. We show that the NP forecast performs better than the G-R formula in some cases but worse in other cases. Therefore, robust forecasting can be obtained by employing an ensemble forecast that combines the two complementary forecasts. Our proposed method is useful for a stable unbiased intermediate-term assessment of aftershock probabilities.

Moving in Parallel Toward a Modern Modeling Epistemology: Bayes Factors and Frequentist Modeling Methods.

PubMed

Rodgers, Joseph Lee

2016-01-01

The Bayesian-frequentist debate typically portrays these statistical perspectives as opposing views. However, both Bayesian and frequentist statisticians have expanded their epistemological basis away from a singular focus on the null hypothesis, to a broader perspective involving the development and comparison of competing statistical/mathematical models. For frequentists, statistical developments such as structural equation modeling and multilevel modeling have facilitated this transition. For Bayesians, the Bayes factor has facilitated this transition. The Bayes factor is treated in articles within this issue of Multivariate Behavioral Research. The current presentation provides brief commentary on those articles and more extended discussion of the transition toward a modern modeling epistemology. In certain respects, Bayesians and frequentists share common goals.

A Bayesian Model of the Memory Colour Effect.

PubMed

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

2018-01-01

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

A Bayesian Model of the Memory Colour Effect

PubMed Central

Olkkonen, Maria; Gegenfurtner, Karl R.

2018-01-01

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

Prediction and repeatability of milk coagulation properties and curd-firming modeling parameters of ovine milk using Fourier-transform infrared spectroscopy and Bayesian models.

PubMed

Ferragina, A; Cipolat-Gotet, C; Cecchinato, A; Pazzola, M; Dettori, M L; Vacca, G M; Bittante, G

2017-05-01

The aim of this study was to apply Bayesian models to the Fourier-transform infrared spectroscopy spectra of individual sheep milk samples to derive calibration equations to predict traditional and modeled milk coagulation properties (MCP), and to assess the repeatability of MCP measures and their predictions. Data consisted of 1,002 individual milk samples collected from Sarda ewes reared in 22 farms in the region of Sardinia (Italy) for which MCP and modeled curd-firming parameters were available. Two milk samples were taken from 87 ewes and analyzed with the aim of estimating repeatability, whereas a single sample was taken from the other 915 ewes. Therefore, a total of 1,089 analyses were performed. For each sample, 2 spectra in the infrared region 5,011 to 925 cm -1 were available and averaged before data analysis. BayesB models were used to calibrate equations for each of the traits. Prediction accuracy was estimated for each trait and model using 20 replicates of a training-testing validation procedure. The repeatability of MCP measures and their predictions were also compared. The correlations between measured and predicted traits, in the external validation, were always higher than 0.5 (0.88 for rennet coagulation time). We confirmed that the most important element for finding the prediction accuracy is the repeatability of the gold standard analyses used for building calibration equations. Repeatability measures of the predicted traits were generally high (≥95%), even for those traits with moderate analytical repeatability. Our results show that Bayesian models applied to Fourier-transform infrared spectra are powerful tools for cheap and rapid prediction of important traits in ovine milk and, compared with other methods, could help in the interpretation of results. Copyright © 2017 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

A Web-Based System for Bayesian Benchmark Dose Estimation.

PubMed

Shao, Kan; Shapiro, Andrew J

2018-01-11

Benchmark dose (BMD) modeling is an important step in human health risk assessment and is used as the default approach to identify the point of departure for risk assessment. A probabilistic framework for dose-response assessment has been proposed and advocated by various institutions and organizations; therefore, a reliable tool is needed to provide distributional estimates for BMD and other important quantities in dose-response assessment. We developed an online system for Bayesian BMD (BBMD) estimation and compared results from this software with U.S. Environmental Protection Agency's (EPA's) Benchmark Dose Software (BMDS). The system is built on a Bayesian framework featuring the application of Markov chain Monte Carlo (MCMC) sampling for model parameter estimation and BMD calculation, which makes the BBMD system fundamentally different from the currently prevailing BMD software packages. In addition to estimating the traditional BMDs for dichotomous and continuous data, the developed system is also capable of computing model-averaged BMD estimates. A total of 518 dichotomous and 108 continuous data sets extracted from the U.S. EPA's Integrated Risk Information System (IRIS) database (and similar databases) were used as testing data to compare the estimates from the BBMD and BMDS programs. The results suggest that the BBMD system may outperform the BMDS program in a number of aspects, including fewer failed BMD and BMDL calculations and estimates. The BBMD system is a useful alternative tool for estimating BMD with additional functionalities for BMD analysis based on most recent research. Most importantly, the BBMD has the potential to incorporate prior information to make dose-response modeling more reliable and can provide distributional estimates for important quantities in dose-response assessment, which greatly facilitates the current trend for probabilistic risk assessment. https://doi.org/10.1289/EHP1289.

Using Bayesian Networks to Improve Knowledge Assessment

ERIC Educational Resources Information Center

Millan, Eva; Descalco, Luis; Castillo, Gladys; Oliveira, Paula; Diogo, Sandra

2013-01-01

In this paper, we describe the integration and evaluation of an existing generic Bayesian student model (GBSM) into an existing computerized testing system within the Mathematics Education Project (PmatE--Projecto Matematica Ensino) of the University of Aveiro. This generic Bayesian student model had been previously evaluated with simulated…

Bayesian Posterior Odds Ratios: Statistical Tools for Collaborative Evaluations

ERIC Educational Resources Information Center

Hicks, Tyler; Rodríguez-Campos, Liliana; Choi, Jeong Hoon

2018-01-01

To begin statistical analysis, Bayesians quantify their confidence in modeling hypotheses with priors. A prior describes the probability of a certain modeling hypothesis apart from the data. Bayesians should be able to defend their choice of prior to a skeptical audience. Collaboration between evaluators and stakeholders could make their choices…

BCM: toolkit for Bayesian analysis of Computational Models using samplers.

PubMed

Thijssen, Bram; Dijkstra, Tjeerd M H; Heskes, Tom; Wessels, Lodewyk F A

2016-10-21

Computational models in biology are characterized by a large degree of uncertainty. This uncertainty can be analyzed with Bayesian statistics, however, the sampling algorithms that are frequently used for calculating Bayesian statistical estimates are computationally demanding, and each algorithm has unique advantages and disadvantages. It is typically unclear, before starting an analysis, which algorithm will perform well on a given computational model. We present BCM, a toolkit for the Bayesian analysis of Computational Models using samplers. It provides efficient, multithreaded implementations of eleven algorithms for sampling from posterior probability distributions and for calculating marginal likelihoods. BCM includes tools to simplify the process of model specification and scripts for visualizing the results. The flexible architecture allows it to be used on diverse types of biological computational models. In an example inference task using a model of the cell cycle based on ordinary differential equations, BCM is significantly more efficient than existing software packages, allowing more challenging inference problems to be solved. BCM represents an efficient one-stop-shop for computational modelers wishing to use sampler-based Bayesian statistics.

Two Approaches to Calibration in Metrology

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

Campanelli, Mark

2014-04-01

Inferring mathematical relationships with quantified uncertainty from measurement data is common to computational science and metrology. Sufficient knowledge of measurement process noise enables Bayesian inference. Otherwise, an alternative approach is required, here termed compartmentalized inference, because collection of uncertain data and model inference occur independently. Bayesian parameterized model inference is compared to a Bayesian-compatible compartmentalized approach for ISO-GUM compliant calibration problems in renewable energy metrology. In either approach, model evidence can help reduce model discrepancy.

Bayesian data analysis in population ecology: motivations, methods, and benefits

USGS Publications Warehouse

Dorazio, Robert

2016-01-01

During the 20th century ecologists largely relied on the frequentist system of inference for the analysis of their data. However, in the past few decades ecologists have become increasingly interested in the use of Bayesian methods of data analysis. In this article I provide guidance to ecologists who would like to decide whether Bayesian methods can be used to improve their conclusions and predictions. I begin by providing a concise summary of Bayesian methods of analysis, including a comparison of differences between Bayesian and frequentist approaches to inference when using hierarchical models. Next I provide a list of problems where Bayesian methods of analysis may arguably be preferred over frequentist methods. These problems are usually encountered in analyses based on hierarchical models of data. I describe the essentials required for applying modern methods of Bayesian computation, and I use real-world examples to illustrate these methods. I conclude by summarizing what I perceive to be the main strengths and weaknesses of using Bayesian methods to solve ecological inference problems.

Blending Multiple Nitrogen Dioxide Data Sources for Neighborhood Estimates of Long-Term Exposure for Health Research.

PubMed

Hanigan, Ivan C; Williamson, Grant J; Knibbs, Luke D; Horsley, Joshua; Rolfe, Margaret I; Cope, Martin; Barnett, Adrian G; Cowie, Christine T; Heyworth, Jane S; Serre, Marc L; Jalaludin, Bin; Morgan, Geoffrey G

2017-11-07

Exposure to traffic related nitrogen dioxide (NO 2 ) air pollution is associated with adverse health outcomes. Average pollutant concentrations for fixed monitoring sites are often used to estimate exposures for health studies, however these can be imprecise due to difficulty and cost of spatial modeling at the resolution of neighborhoods (e.g., a scale of tens of meters) rather than at a coarse scale (around several kilometers). The objective of this study was to derive improved estimates of neighborhood NO 2 concentrations by blending measurements with modeled predictions in Sydney, Australia (a low pollution environment). We implemented the Bayesian maximum entropy approach to blend data with uncertainty defined using informative priors. We compiled NO 2 data from fixed-site monitors, chemical transport models, and satellite-based land use regression models to estimate neighborhood annual average NO 2 . The spatial model produced a posterior probability density function of estimated annual average concentrations that spanned an order of magnitude from 3 to 35 ppb. Validation using independent data showed improvement, with root mean squared error improvement of 6% compared with the land use regression model and 16% over the chemical transport model. These estimates will be used in studies of health effects and should minimize misclassification bias.

[Evaluation of estimation of prevalence ratio using bayesian log-binomial regression model].

PubMed

Gao, W L; Lin, H; Liu, X N; Ren, X W; Li, J S; Shen, X P; Zhu, S L

2017-03-10

To evaluate the estimation of prevalence ratio ( PR ) by using bayesian log-binomial regression model and its application, we estimated the PR of medical care-seeking prevalence to caregivers' recognition of risk signs of diarrhea in their infants by using bayesian log-binomial regression model in Openbugs software. The results showed that caregivers' recognition of infant' s risk signs of diarrhea was associated significantly with a 13% increase of medical care-seeking. Meanwhile, we compared the differences in PR 's point estimation and its interval estimation of medical care-seeking prevalence to caregivers' recognition of risk signs of diarrhea and convergence of three models (model 1: not adjusting for the covariates; model 2: adjusting for duration of caregivers' education, model 3: adjusting for distance between village and township and child month-age based on model 2) between bayesian log-binomial regression model and conventional log-binomial regression model. The results showed that all three bayesian log-binomial regression models were convergence and the estimated PRs were 1.130(95 %CI : 1.005-1.265), 1.128(95 %CI : 1.001-1.264) and 1.132(95 %CI : 1.004-1.267), respectively. Conventional log-binomial regression model 1 and model 2 were convergence and their PRs were 1.130(95 % CI : 1.055-1.206) and 1.126(95 % CI : 1.051-1.203), respectively, but the model 3 was misconvergence, so COPY method was used to estimate PR , which was 1.125 (95 %CI : 1.051-1.200). In addition, the point estimation and interval estimation of PRs from three bayesian log-binomial regression models differed slightly from those of PRs from conventional log-binomial regression model, but they had a good consistency in estimating PR . Therefore, bayesian log-binomial regression model can effectively estimate PR with less misconvergence and have more advantages in application compared with conventional log-binomial regression model.

Mortality atlas of the main causes of death in Switzerland, 2008-2012.

PubMed

Chammartin, Frédérique; Probst-Hensch, Nicole; Utzinger, Jürg; Vounatsou, Penelope

2016-01-01

Analysis of the spatial distribution of mortality data is important for identification of high-risk areas, which in turn might guide prevention, and modify behaviour and health resources allocation. This study aimed to update the Swiss mortality atlas by analysing recent data using Bayesian statistical methods. We present average pattern for the major causes of death in Switzerland. We analysed Swiss mortality data from death certificates for the period 2008-2012. Bayesian conditional autoregressive models were employed to smooth the standardised mortality rates and assess average patterns. Additionally, we developed models for age- and gender-specific sub-groups that account for urbanisation and linguistic areas in order to assess their effects on the different sub-groups. We describe the spatial pattern of the major causes of death that occurred in Switzerland between 2008 and 2012, namely 4 cardiovascular diseases, 10 different kinds of cancer, 2 external causes of death, as well as chronic respiratory diseases, Alzheimer's disease, diabetes, influenza and pneumonia, and liver diseases. In-depth analysis of age- and gender-specific mortality rates revealed significant disparities between urbanisation and linguistic areas. We provide a contemporary overview of the spatial distribution of the main causes of death in Switzerland. Our estimates and maps can help future research to deepen our understanding of the spatial variation of major causes of death in Switzerland, which in turn is crucial for targeting preventive measures, changing behaviours and a more cost-effective allocation of health resources.

Dynamic Bayesian network modeling for longitudinal brain morphometry

PubMed Central

Chen, Rong; Resnick, Susan M; Davatzikos, Christos; Herskovits, Edward H

2011-01-01

Identifying interactions among brain regions from structural magnetic-resonance images presents one of the major challenges in computational neuroanatomy. We propose a Bayesian data-mining approach to the detection of longitudinal morphological changes in the human brain. Our method uses a dynamic Bayesian network to represent evolving inter-regional dependencies. The major advantage of dynamic Bayesian network modeling is that it can represent complicated interactions among temporal processes. We validated our approach by analyzing a simulated atrophy study, and found that this approach requires only a small number of samples to detect the ground-truth temporal model. We further applied dynamic Bayesian network modeling to a longitudinal study of normal aging and mild cognitive impairment — the Baltimore Longitudinal Study of Aging. We found that interactions among regional volume-change rates for the mild cognitive impairment group are different from those for the normal-aging group. PMID:21963916

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.

Estimation of Groundwater Radon in North Carolina Using Land Use Regression and Bayesian Maximum Entropy.

PubMed

Messier, Kyle P; Campbell, Ted; Bradley, Philip J; Serre, Marc L

2015-08-18

Radon ((222)Rn) is a naturally occurring chemically inert, colorless, and odorless radioactive gas produced from the decay of uranium ((238)U), which is ubiquitous in rocks and soils worldwide. Exposure to (222)Rn is likely the second leading cause of lung cancer after cigarette smoking via inhalation; however, exposure through untreated groundwater is also a contributing factor to both inhalation and ingestion routes. A land use regression (LUR) model for groundwater (222)Rn with anisotropic geological and (238)U based explanatory variables is developed, which helps elucidate the factors contributing to elevated (222)Rn across North Carolina. The LUR is also integrated into the Bayesian Maximum Entropy (BME) geostatistical framework to increase accuracy and produce a point-level LUR-BME model of groundwater (222)Rn across North Carolina including prediction uncertainty. The LUR-BME model of groundwater (222)Rn results in a leave-one out cross-validation r(2) of 0.46 (Pearson correlation coefficient = 0.68), effectively predicting within the spatial covariance range. Modeled results of (222)Rn concentrations show variability among intrusive felsic geological formations likely due to average bedrock (238)U defined on the basis of overlying stream-sediment (238)U concentrations that is a widely distributed consistently analyzed point-source data.

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

NASA Astrophysics Data System (ADS)

Leube, Philipp; Geiges, Andreas; Nowak, Wolfgang

2010-05-01

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

On the use of Bayesian Monte-Carlo in evaluation of nuclear data

NASA Astrophysics Data System (ADS)

De Saint Jean, Cyrille; Archier, Pascal; Privas, Edwin; Noguere, Gilles

2017-09-01

As model parameters, necessary ingredients of theoretical models, are not always predicted by theory, a formal mathematical framework associated to the evaluation work is needed to obtain the best set of parameters (resonance parameters, optical models, fission barrier, average width, multigroup cross sections) with Bayesian statistical inference by comparing theory to experiment. The formal rule related to this methodology is to estimate the posterior density probability function of a set of parameters by solving an equation of the following type: pdf(posterior) ˜ pdf(prior) × a likelihood function. A fitting procedure can be seen as an estimation of the posterior density probability of a set of parameters (referred as x→?) knowing a prior information on these parameters and a likelihood which gives the probability density function of observing a data set knowing x→?. To solve this problem, two major paths could be taken: add approximations and hypothesis and obtain an equation to be solved numerically (minimum of a cost function or Generalized least Square method, referred as GLS) or use Monte-Carlo sampling of all prior distributions and estimate the final posterior distribution. Monte Carlo methods are natural solution for Bayesian inference problems. They avoid approximations (existing in traditional adjustment procedure based on chi-square minimization) and propose alternative in the choice of probability density distribution for priors and likelihoods. This paper will propose the use of what we are calling Bayesian Monte Carlo (referred as BMC in the rest of the manuscript) in the whole energy range from thermal, resonance and continuum range for all nuclear reaction models at these energies. Algorithms will be presented based on Monte-Carlo sampling and Markov chain. The objectives of BMC are to propose a reference calculation for validating the GLS calculations and approximations, to test probability density distributions effects and to provide the framework of finding global minimum if several local minimums exist. Application to resolved resonance, unresolved resonance and continuum evaluation as well as multigroup cross section data assimilation will be presented.

Classifying emotion in Twitter using Bayesian network

NASA Astrophysics Data System (ADS)

Surya Asriadie, Muhammad; Syahrul Mubarok, Mohamad; Adiwijaya

2018-03-01

Language is used to express not only facts, but also emotions. Emotions are noticeable from behavior up to the social media statuses written by a person. Analysis of emotions in a text is done in a variety of media such as Twitter. This paper studies classification of emotions on twitter using Bayesian network because of its ability to model uncertainty and relationships between features. The result is two models based on Bayesian network which are Full Bayesian Network (FBN) and Bayesian Network with Mood Indicator (BNM). FBN is a massive Bayesian network where each word is treated as a node. The study shows the method used to train FBN is not very effective to create the best model and performs worse compared to Naive Bayes. F1-score for FBN is 53.71%, while for Naive Bayes is 54.07%. BNM is proposed as an alternative method which is based on the improvement of Multinomial Naive Bayes and has much lower computational complexity compared to FBN. Even though it’s not better compared to FBN, the resulting model successfully improves the performance of Multinomial Naive Bayes. F1-Score for Multinomial Naive Bayes model is 51.49%, while for BNM is 52.14%.

Additive Genetic Variability and the Bayesian Alphabet

PubMed Central

Gianola, Daniel; de los Campos, Gustavo; Hill, William G.; Manfredi, Eduardo; Fernando, Rohan

2009-01-01

The use of all available molecular markers in statistical models for prediction of quantitative traits has led to what could be termed a genomic-assisted selection paradigm in animal and plant breeding. This article provides a critical review of some theoretical and statistical concepts in the context of genomic-assisted genetic evaluation of animals and crops. First, relationships between the (Bayesian) variance of marker effects in some regression models and additive genetic variance are examined under standard assumptions. Second, the connection between marker genotypes and resemblance between relatives is explored, and linkages between a marker-based model and the infinitesimal model are reviewed. Third, issues associated with the use of Bayesian models for marker-assisted selection, with a focus on the role of the priors, are examined from a theoretical angle. The sensitivity of a Bayesian specification that has been proposed (called “Bayes A”) with respect to priors is illustrated with a simulation. Methods that can solve potential shortcomings of some of these Bayesian regression procedures are discussed briefly. PMID:19620397

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Approximate Bayesian Computation Using Markov Chain Monte Carlo Simulation: Theory, Concepts, and Applications

NASA Astrophysics Data System (ADS)

Sadegh, M.; Vrugt, J. A.

2013-12-01

The ever increasing pace of computational power, along with continued advances in measurement technologies and improvements in process understanding has stimulated the development of increasingly complex hydrologic models that simulate soil moisture flow, groundwater recharge, surface runoff, root water uptake, and river discharge at increasingly finer spatial and temporal scales. Reconciling these system models with field and remote sensing data is a difficult task, particularly because average measures of model/data similarity inherently lack the power to provide a meaningful comparative evaluation of the consistency in model form and function. The very construction of the likelihood function - as a summary variable of the (usually averaged) properties of the error residuals - dilutes and mixes the available information into an index having little remaining correspondence to specific behaviors of the system (Gupta et al., 2008). The quest for a more powerful method for model evaluation has inspired Vrugt and Sadegh [2013] to introduce "likelihood-free" inference as vehicle for diagnostic model evaluation. This class of methods is also referred to as Approximate Bayesian Computation (ABC) and relaxes the need for an explicit likelihood function in favor of one or multiple different summary statistics rooted in hydrologic theory that together have a much stronger and compelling diagnostic power than some aggregated measure of the size of the error residuals. Here, we will introduce an efficient ABC sampling method that is orders of magnitude faster in exploring the posterior parameter distribution than commonly used rejection and Population Monte Carlo (PMC) samplers. Our methodology uses Markov Chain Monte Carlo simulation with DREAM, and takes advantage of a simple computational trick to resolve discontinuity problems with the application of set-theoretic summary statistics. We will also demonstrate a set of summary statistics that are rather insensitive to errors in the forcing data. This enhances prospects of detecting model structural deficiencies.

A comment on priors for Bayesian occupancy models.

PubMed

Northrup, Joseph M; Gerber, Brian D

2018-01-01

Understanding patterns of species occurrence and the processes underlying these patterns is fundamental to the study of ecology. One of the more commonly used approaches to investigate species occurrence patterns is occupancy modeling, which can account for imperfect detection of a species during surveys. In recent years, there has been a proliferation of Bayesian modeling in ecology, which includes fitting Bayesian occupancy models. The Bayesian framework is appealing to ecologists for many reasons, including the ability to incorporate prior information through the specification of prior distributions on parameters. While ecologists almost exclusively intend to choose priors so that they are "uninformative" or "vague", such priors can easily be unintentionally highly informative. Here we report on how the specification of a "vague" normally distributed (i.e., Gaussian) prior on coefficients in Bayesian occupancy models can unintentionally influence parameter estimation. Using both simulated data and empirical examples, we illustrate how this issue likely compromises inference about species-habitat relationships. While the extent to which these informative priors influence inference depends on the data set, researchers fitting Bayesian occupancy models should conduct sensitivity analyses to ensure intended inference, or employ less commonly used priors that are less informative (e.g., logistic or t prior distributions). We provide suggestions for addressing this issue in occupancy studies, and an online tool for exploring this issue under different contexts.

Final Report, DOE Early Career Award: Predictive modeling of complex physical systems: new tools for statistical inference, uncertainty quantification, and experimental design

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

Marzouk, Youssef

Predictive simulation of complex physical systems increasingly rests on the interplay of experimental observations with computational models. Key inputs, parameters, or structural aspects of models may be incomplete or unknown, and must be developed from indirect and limited observations. At the same time, quantified uncertainties are needed to qualify computational predictions in the support of design and decision-making. In this context, Bayesian statistics provides a foundation for inference from noisy and limited data, but at prohibitive computional expense. This project intends to make rigorous predictive modeling *feasible* in complex physical systems, via accelerated and scalable tools for uncertainty quantification, Bayesianmore » inference, and experimental design. Specific objectives are as follows: 1. Develop adaptive posterior approximations and dimensionality reduction approaches for Bayesian inference in high-dimensional nonlinear systems. 2. Extend accelerated Bayesian methodologies to large-scale {\\em sequential} data assimilation, fully treating nonlinear models and non-Gaussian state and parameter distributions. 3. Devise efficient surrogate-based methods for Bayesian model selection and the learning of model structure. 4. Develop scalable simulation/optimization approaches to nonlinear Bayesian experimental design, for both parameter inference and model selection. 5. Demonstrate these inferential tools on chemical kinetic models in reacting flow, constructing and refining thermochemical and electrochemical models from limited data. Demonstrate Bayesian filtering on canonical stochastic PDEs and in the dynamic estimation of inhomogeneous subsurface properties and flow fields.« less

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

NASA Astrophysics Data System (ADS)

Takiyama, Ken

2016-05-01

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

Inferring late-Holocene climate in the Ecuadorian Andes using a chironomid-based temperature inference model

NASA Astrophysics Data System (ADS)

Matthews-Bird, Frazer; Brooks, Stephen J.; Holden, Philip B.; Montoya, Encarni; Gosling, William D.

2016-06-01

Presented here is the first chironomid calibration data set for tropical South America. Surface sediments were collected from 59 lakes across Bolivia (15 lakes), Peru (32 lakes), and Ecuador (12 lakes) between 2004 and 2013 over an altitudinal gradient from 150 m above sea level (a.s.l) to 4655 m a.s.l, between 0-17° S and 64-78° W. The study sites cover a mean annual temperature (MAT) gradient of 25 °C. In total, 55 chironomid taxa were identified in the 59 calibration data set lakes. When used as a single explanatory variable, MAT explains 12.9 % of the variance (λ1/λ2 = 1.431). Two inference models were developed using weighted averaging (WA) and Bayesian methods. The best-performing model using conventional statistical methods was a WA (inverse) model (R2jack = 0.890; RMSEPjack = 2.404 °C, RMSEP - root mean squared error of prediction; mean biasjack = -0.017 °C; max biasjack = 4.665 °C). The Bayesian method produced a model with R2jack = 0.909, RMSEPjack = 2.373 °C, mean biasjack = 0.598 °C, and max biasjack = 3.158 °C. Both models were used to infer past temperatures from a ca. 3000-year record from the tropical Andes of Ecuador, Laguna Pindo. Inferred temperatures fluctuated around modern-day conditions but showed significant departures at certain intervals (ca. 1600 cal yr BP; ca. 3000-2500 cal yr BP). Both methods (WA and Bayesian) showed similar patterns of temperature variability; however, the magnitude of fluctuations differed. In general the WA method was more variable and often underestimated Holocene temperatures (by ca. -7 ± 2.5 °C relative to the modern period). The Bayesian method provided temperature anomaly estimates for cool periods that lay within the expected range of the Holocene (ca. -3 ± 3.4 °C). The error associated with both reconstructions is consistent with a constant temperature of 20 °C for the past 3000 years. We would caution, however, against an over-interpretation at this stage. The reconstruction can only currently be deemed qualitative and requires more research before quantitative estimates can be generated with confidence. Increasing the number, and spread, of lakes in the calibration data set would enable the detection of smaller climate signals.

Development of an Integrated Team Training Design and Assessment Architecture to Support Adaptability in Healthcare Teams

DTIC Science & Technology

2016-10-01

and implementation of embedded, adaptive feedback and performance assessment. The investigators also initiated work designing a Bayesian Belief ...training; Teamwork; Adaptive performance; Leadership; Simulation; Modeling; Bayesian belief networks (BBN) 16. SECURITY CLASSIFICATION OF: 17. LIMITATION...Trauma teams Team training Teamwork Adaptability Adaptive performance Leadership Simulation Modeling Bayesian belief networks (BBN) 6

A Bayesian Network Approach to Modeling Learning Progressions and Task Performance. CRESST Report 776

ERIC Educational Resources Information Center

West, Patti; Rutstein, Daisy Wise; Mislevy, Robert J.; Liu, Junhui; Choi, Younyoung; Levy, Roy; Crawford, Aaron; DiCerbo, Kristen E.; Chappel, Kristina; Behrens, John T.

2010-01-01

A major issue in the study of learning progressions (LPs) is linking student performance on assessment tasks to the progressions. This report describes the challenges faced in making this linkage using Bayesian networks to model LPs in the field of computer networking. The ideas are illustrated with exemplar Bayesian networks built on Cisco…

A Bayesian approach for temporally scaling climate for modeling ecological systems

USGS Publications Warehouse

Post van der Burg, Max; Anteau, Michael J.; McCauley, Lisa A.; Wiltermuth, Mark T.

2016-01-01

With climate change becoming more of concern, many ecologists are including climate variables in their system and statistical models. The Standardized Precipitation Evapotranspiration Index (SPEI) is a drought index that has potential advantages in modeling ecological response variables, including a flexible computation of the index over different timescales. However, little development has been made in terms of the choice of timescale for SPEI. We developed a Bayesian modeling approach for estimating the timescale for SPEI and demonstrated its use in modeling wetland hydrologic dynamics in two different eras (i.e., historical [pre-1970] and contemporary [post-2003]). Our goal was to determine whether differences in climate between the two eras could explain changes in the amount of water in wetlands. Our results showed that wetland water surface areas tended to be larger in wetter conditions, but also changed less in response to climate fluctuations in the contemporary era. We also found that the average timescale parameter was greater in the historical period, compared with the contemporary period. We were not able to determine whether this shift in timescale was due to a change in the timing of wet–dry periods or whether it was due to changes in the way wetlands responded to climate. Our results suggest that perhaps some interaction between climate and hydrologic response may be at work, and further analysis is needed to determine which has a stronger influence. Despite this, we suggest that our modeling approach enabled us to estimate the relevant timescale for SPEI and make inferences from those estimates. Likewise, our approach provides a mechanism for using prior information with future data to assess whether these patterns may continue over time. We suggest that ecologists consider using temporally scalable climate indices in conjunction with Bayesian analysis for assessing the role of climate in ecological systems.

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.

Nonparametric Bayesian Modeling for Automated Database Schema Matching

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

Ferragut, Erik M; Laska, Jason A

2015-01-01

The problem of merging databases arises in many government and commercial applications. Schema matching, a common first step, identifies equivalent fields between databases. We introduce a schema matching framework that builds nonparametric Bayesian models for each field and compares them by computing the probability that a single model could have generated both fields. Our experiments show that our method is more accurate and faster than the existing instance-based matching algorithms in part because of the use of nonparametric Bayesian models.

Development of dynamic Bayesian models for web application test management

NASA Astrophysics Data System (ADS)

Azarnova, T. V.; Polukhin, P. V.; Bondarenko, Yu V.; Kashirina, I. L.

2018-03-01

The mathematical apparatus of dynamic Bayesian networks is an effective and technically proven tool that can be used to model complex stochastic dynamic processes. According to the results of the research, mathematical models and methods of dynamic Bayesian networks provide a high coverage of stochastic tasks associated with error testing in multiuser software products operated in a dynamically changing environment. Formalized representation of the discrete test process as a dynamic Bayesian model allows us to organize the logical connection between individual test assets for multiple time slices. This approach gives an opportunity to present testing as a discrete process with set structural components responsible for the generation of test assets. Dynamic Bayesian network-based models allow us to combine in one management area individual units and testing components with different functionalities and a direct influence on each other in the process of comprehensive testing of various groups of computer bugs. The application of the proposed models provides an opportunity to use a consistent approach to formalize test principles and procedures, methods used to treat situational error signs, and methods used to produce analytical conclusions based on test results.

Trans-dimensional and hierarchical Bayesian approaches toward rigorous estimation of seismic sources and structures in the Northeast Asia

NASA Astrophysics Data System (ADS)

Kim, Seongryong; Tkalčić, Hrvoje; Mustać, Marija; Rhie, Junkee; Ford, Sean

2016-04-01

A framework is presented within which we provide rigorous estimations for seismic sources and structures in the Northeast Asia. We use Bayesian inversion methods, which enable statistical estimations of models and their uncertainties based on data information. Ambiguities in error statistics and model parameterizations are addressed by hierarchical and trans-dimensional (trans-D) techniques, which can be inherently implemented in the Bayesian inversions. Hence reliable estimation of model parameters and their uncertainties is possible, thus avoiding arbitrary regularizations and parameterizations. Hierarchical and trans-D inversions are performed to develop a three-dimensional velocity model using ambient noise data. To further improve the model, we perform joint inversions with receiver function data using a newly developed Bayesian method. For the source estimation, a novel moment tensor inversion method is presented and applied to regional waveform data of the North Korean nuclear explosion tests. By the combination of new Bayesian techniques and the structural model, coupled with meaningful uncertainties related to each of the processes, more quantitative monitoring and discrimination of seismic events is possible.

Bayesian Models Leveraging Bioactivity and Cytotoxicity Information for Drug Discovery

PubMed Central

Ekins, Sean; Reynolds, Robert C.; Kim, Hiyun; Koo, Mi-Sun; Ekonomidis, Marilyn; Talaue, Meliza; Paget, Steve D.; Woolhiser, Lisa K.; Lenaerts, Anne J.; Bunin, Barry A.; Connell, Nancy; Freundlich, Joel S.

2013-01-01

SUMMARY Identification of unique leads represents a significant challenge in drug discovery. This hurdle is magnified in neglected diseases such as tuberculosis. We have leveraged public high-throughput screening (HTS) data, to experimentally validate virtual screening approach employing Bayesian models built with bioactivity information (single-event model) as well as bioactivity and cytotoxicity information (dual-event model). We virtually screen a commercial library and experimentally confirm actives with hit rates exceeding typical HTS results by 1-2 orders of magnitude. The first dual-event Bayesian model identified compounds with antitubercular whole-cell activity and low mammalian cell cytotoxicity from a published set of antimalarials. The most potent hit exhibits the in vitro activity and in vitro/in vivo safety profile of a drug lead. These Bayesian models offer significant economies in time and cost to drug discovery. PMID:23521795

Bayesian data analysis for newcomers.

PubMed

Kruschke, John K; Liddell, Torrin M

2018-02-01

This article explains the foundational concepts of Bayesian data analysis using virtually no mathematical notation. Bayesian ideas already match your intuitions from everyday reasoning and from traditional data analysis. Simple examples of Bayesian data analysis are presented that illustrate how the information delivered by a Bayesian analysis can be directly interpreted. Bayesian approaches to null-value assessment are discussed. The article clarifies misconceptions about Bayesian methods that newcomers might have acquired elsewhere. We discuss prior distributions and explain how they are not a liability but an important asset. We discuss the relation of Bayesian data analysis to Bayesian models of mind, and we briefly discuss what methodological problems Bayesian data analysis is not meant to solve. After you have read this article, you should have a clear sense of how Bayesian data analysis works and the sort of information it delivers, and why that information is so intuitive and useful for drawing conclusions from data.

Evaluation of calibration efficacy under different levels of uncertainty

DOE PAGES

Heo, Yeonsook; Graziano, Diane J.; Guzowski, Leah; ...

2014-06-10

This study examines how calibration performs under different levels of uncertainty in model input data. It specifically assesses the efficacy of Bayesian calibration to enhance the reliability of EnergyPlus model predictions. A Bayesian approach can be used to update uncertain values of parameters, given measured energy-use data, and to quantify the associated uncertainty.We assess the efficacy of Bayesian calibration under a controlled virtual-reality setup, which enables rigorous validation of the accuracy of calibration results in terms of both calibrated parameter values and model predictions. Case studies demonstrate the performance of Bayesian calibration of base models developed from audit data withmore » differing levels of detail in building design, usage, and operation.« less

EFFICIENT MODEL-FITTING AND MODEL-COMPARISON FOR HIGH-DIMENSIONAL BAYESIAN GEOSTATISTICAL MODELS. (R826887)

EPA Science Inventory

Geostatistical models are appropriate for spatially distributed data measured at irregularly spaced locations. We propose an efficient Markov chain Monte Carlo (MCMC) algorithm for fitting Bayesian geostatistical models with substantial numbers of unknown parameters to sizable...

Universal Darwinism As a Process of Bayesian Inference.

PubMed

Campbell, John O

2016-01-01

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

Universal Darwinism As a Process of Bayesian Inference

PubMed Central

Campbell, John O.

2016-01-01

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

A Bayesian hierarchical diffusion model decomposition of performance in Approach–Avoidance Tasks

PubMed Central

Krypotos, Angelos-Miltiadis; Beckers, Tom; Kindt, Merel; Wagenmakers, Eric-Jan

2015-01-01

Common methods for analysing response time (RT) tasks, frequently used across different disciplines of psychology, suffer from a number of limitations such as the failure to directly measure the underlying latent processes of interest and the inability to take into account the uncertainty associated with each individual's point estimate of performance. Here, we discuss a Bayesian hierarchical diffusion model and apply it to RT data. This model allows researchers to decompose performance into meaningful psychological processes and to account optimally for individual differences and commonalities, even with relatively sparse data. We highlight the advantages of the Bayesian hierarchical diffusion model decomposition by applying it to performance on Approach–Avoidance Tasks, widely used in the emotion and psychopathology literature. Model fits for two experimental data-sets demonstrate that the model performs well. The Bayesian hierarchical diffusion model overcomes important limitations of current analysis procedures and provides deeper insight in latent psychological processes of interest. PMID:25491372

Multivariate Bayesian modeling of known and unknown causes of events--an application to biosurveillance.

PubMed

Shen, Yanna; Cooper, Gregory F

2012-09-01

This paper investigates Bayesian modeling of known and unknown causes of events in the context of disease-outbreak detection. We introduce a multivariate Bayesian approach that models multiple evidential features of every person in the population. This approach models and detects (1) known diseases (e.g., influenza and anthrax) by using informative prior probabilities and (2) unknown diseases (e.g., a new, highly contagious respiratory virus that has never been seen before) by using relatively non-informative prior probabilities. We report the results of simulation experiments which support that this modeling method can improve the detection of new disease outbreaks in a population. A contribution of this paper is that it introduces a multivariate Bayesian approach for jointly modeling both known and unknown causes of events. Such modeling has general applicability in domains where the space of known causes is incomplete. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.

Aerosol-type retrieval and uncertainty quantification from OMI data

NASA Astrophysics Data System (ADS)

Kauppi, Anu; Kolmonen, Pekka; Laine, Marko; Tamminen, Johanna

2017-11-01

We discuss uncertainty quantification for aerosol-type selection in satellite-based atmospheric aerosol retrieval. The retrieval procedure uses precalculated aerosol microphysical models stored in look-up tables (LUTs) and top-of-atmosphere (TOA) spectral reflectance measurements to solve the aerosol characteristics. The forward model approximations cause systematic differences between the modelled and observed reflectance. Acknowledging this model discrepancy as a source of uncertainty allows us to produce more realistic uncertainty estimates and assists the selection of the most appropriate LUTs for each individual retrieval.This paper focuses on the aerosol microphysical model selection and characterisation of uncertainty in the retrieved aerosol type and aerosol optical depth (AOD). The concept of model evidence is used as a tool for model comparison. The method is based on Bayesian inference approach, in which all uncertainties are described as a posterior probability distribution. When there is no single best-matching aerosol microphysical model, we use a statistical technique based on Bayesian model averaging to combine AOD posterior probability densities of the best-fitting models to obtain an averaged AOD estimate. We also determine the shared evidence of the best-matching models of a certain main aerosol type in order to quantify how plausible it is that it represents the underlying atmospheric aerosol conditions.The developed method is applied to Ozone Monitoring Instrument (OMI) measurements using a multiwavelength approach for retrieving the aerosol type and AOD estimate with uncertainty quantification for cloud-free over-land pixels. Several larger pixel set areas were studied in order to investigate the robustness of the developed method. We evaluated the retrieved AOD by comparison with ground-based measurements at example sites. We found that the uncertainty of AOD expressed by posterior probability distribution reflects the difficulty in model selection. The posterior probability distribution can provide a comprehensive characterisation of the uncertainty in this kind of problem for aerosol-type selection. As a result, the proposed method can account for the model error and also include the model selection uncertainty in the total uncertainty budget.

Model averaging in the presence of structural uncertainty about treatment effects: influence on treatment decision and expected value of information.

PubMed

Price, Malcolm J; Welton, Nicky J; Briggs, Andrew H; Ades, A E

2011-01-01

Standard approaches to estimation of Markov models with data from randomized controlled trials tend either to make a judgment about which transition(s) treatments act on, or they assume that treatment has a separate effect on every transition. An alternative is to fit a series of models that assume that treatment acts on specific transitions. Investigators can then choose among alternative models using goodness-of-fit statistics. However, structural uncertainty about any chosen parameterization will remain and this may have implications for the resulting decision and the need for further research. We describe a Bayesian approach to model estimation, and model selection. Structural uncertainty about which parameterization to use is accounted for using model averaging and we developed a formula for calculating the expected value of perfect information (EVPI) in averaged models. Marginal posterior distributions are generated for each of the cost-effectiveness parameters using Markov Chain Monte Carlo simulation in WinBUGS, or Monte-Carlo simulation in Excel (Microsoft Corp., Redmond, WA). We illustrate the approach with an example of treatments for asthma using aggregate-level data from a connected network of four treatments compared in three pair-wise randomized controlled trials. The standard errors of incremental net benefit using structured models is reduced by up to eight- or ninefold compared to the unstructured models, and the expected loss attaching to decision uncertainty by factors of several hundreds. Model averaging had considerable influence on the EVPI. Alternative structural assumptions can alter the treatment decision and have an overwhelming effect on model uncertainty and expected value of information. Structural uncertainty can be accounted for by model averaging, and the EVPI can be calculated for averaged models. Copyright © 2011 International Society for Pharmacoeconomics and Outcomes Research (ISPOR). Published by Elsevier Inc. All rights reserved.

ensembleBMA: An R Package for Probabilistic Forecasting using Ensembles and Bayesian Model Averaging

DTIC Science & Technology

2007-08-15

library is used to allow addition of the legend and map outline to the plot. > bluescale <- function(n) hsv (4/6, s = seq(from = 1 /8, to = 1 , length = n...v = 1 ) > plotBMAforecast( probFreeze290104, lon=srftGridData$lon, lat =srftGridData$ lat , type="image", col=bluescale(100)) > title("Probability of...probPrecip130103) # used to determine zlim in plots [ 1 ] 0.02832709 0.99534860 > plotBMAforecast( probPrecip130103[,Ŕ"], lon=prcpGridData$lon, lat

Investigation of hit-and-run crash occurrence and severity using real-time loop detector data and hierarchical Bayesian binary logit model with random effects.

PubMed

Xie, Meiquan; Cheng, Wen; Gill, Gurdiljot Singh; Zhou, Jiao; Jia, Xudong; Choi, Simon

2018-02-17

Most of the extensive research dedicated to identifying the influential factors of hit-and-run (HR) crashes has utilized typical maximum likelihood estimation binary logit models, and none have employed real-time traffic data. To fill this gap, this study focused on investigating factors contributing to HR crashes, as well as the severity levels of HR. This study analyzed 4-year crash and real-time loop detector data by employing hierarchical Bayesian models with random effects within a sequential logit structure. In addition to evaluation of the impact of random effects on model fitness and complexity, the prediction capability of the models was examined. Stepwise incremental sensitivity and specificity were calculated and receiver operating characteristic (ROC) curves were utilized to graphically illustrate the predictive performance of the model. Among the real-time flow variables, the average occupancy and speed from the upstream detector were observed to be positively correlated with HR crash possibility. The average upstream speed and speed difference between upstream and downstream speeds were correlated with the occurrence of severe HR crashes. In addition to real-time factors, other variables found influential for HR and severe HR crashes were length of segment, adverse weather conditions, dark lighting conditions with malfunctioning street lights, driving under the influence of alcohol, width of inner shoulder, and nighttime. This study suggests the potential traffic conditions of HR and severe HR occurrence, which refer to relatively congested upstream traffic conditions with high upstream speed and significant speed deviations on long segments. The above findings suggest that traffic enforcement should be directed toward mitigating risky driving under the aforementioned traffic conditions. Moreover, enforcement agencies may employ alcohol checkpoints to counter driving under the influence (DUI) at night. With regard to engineering improvements, wider inner shoulders may be constructed to potentially reduce HR cases and street lights should be installed and maintained in working condition to make roads less prone to such crashes.

Model Comparison of Bayesian Semiparametric and Parametric Structural Equation Models

ERIC Educational Resources Information Center

Song, Xin-Yuan; Xia, Ye-Mao; Pan, Jun-Hao; Lee, Sik-Yum

2011-01-01

Structural equation models have wide applications. One of the most important issues in analyzing structural equation models is model comparison. This article proposes a Bayesian model comparison statistic, namely the "L[subscript nu]"-measure for both semiparametric and parametric structural equation models. For illustration purposes, we consider…

Scale Mixture Models with Applications to Bayesian Inference

NASA Astrophysics Data System (ADS)

Qin, Zhaohui S.; Damien, Paul; Walker, Stephen

2003-11-01

Scale mixtures of uniform distributions are used to model non-normal data in time series and econometrics in a Bayesian framework. Heteroscedastic and skewed data models are also tackled using scale mixture of uniform distributions.

Rigorous Approach in Investigation of Seismic Structure and Source Characteristicsin Northeast Asia: Hierarchical and Trans-dimensional Bayesian Inversion

NASA Astrophysics Data System (ADS)

Mustac, M.; Kim, S.; Tkalcic, H.; Rhie, J.; Chen, Y.; Ford, S. R.; Sebastian, N.

2015-12-01

Conventional approaches to inverse problems suffer from non-linearity and non-uniqueness in estimations of seismic structures and source properties. Estimated results and associated uncertainties are often biased by applied regularizations and additional constraints, which are commonly introduced to solve such problems. Bayesian methods, however, provide statistically meaningful estimations of models and their uncertainties constrained by data information. In addition, hierarchical and trans-dimensional (trans-D) techniques are inherently implemented in the Bayesian framework to account for involved error statistics and model parameterizations, and, in turn, allow more rigorous estimations of the same. Here, we apply Bayesian methods throughout the entire inference process to estimate seismic structures and source properties in Northeast Asia including east China, the Korean peninsula, and the Japanese islands. Ambient noise analysis is first performed to obtain a base three-dimensional (3-D) heterogeneity model using continuous broadband waveforms from more than 300 stations. As for the tomography of surface wave group and phase velocities in the 5-70 s band, we adopt a hierarchical and trans-D Bayesian inversion method using Voronoi partition. The 3-D heterogeneity model is further improved by joint inversions of teleseismic receiver functions and dispersion data using a newly developed high-efficiency Bayesian technique. The obtained model is subsequently used to prepare 3-D structural Green's functions for the source characterization. A hierarchical Bayesian method for point source inversion using regional complete waveform data is applied to selected events from the region. The seismic structure and source characteristics with rigorously estimated uncertainties from the novel Bayesian methods provide enhanced monitoring and discrimination of seismic events in northeast Asia.

A Smoluchowski model of crystallization dynamics of small colloidal clusters

NASA Astrophysics Data System (ADS)

Beltran-Villegas, Daniel J.; Sehgal, Ray M.; Maroudas, Dimitrios; Ford, David M.; Bevan, Michael A.

2011-10-01

We investigate the dynamics of colloidal crystallization in a 32-particle system at a fixed value of interparticle depletion attraction that produces coexisting fluid and solid phases. Free energy landscapes (FELs) and diffusivity landscapes (DLs) are obtained as coefficients of 1D Smoluchowski equations using as order parameters either the radius of gyration or the average crystallinity. FELs and DLs are estimated by fitting the Smoluchowski equations to Brownian dynamics (BD) simulations using either linear fits to locally initiated trajectories or global fits to unbiased trajectories using Bayesian inference. The resulting FELs are compared to Monte Carlo Umbrella Sampling results. The accuracy of the FELs and DLs for modeling colloidal crystallization dynamics is evaluated by comparing mean first-passage times from BD simulations with analytical predictions using the FEL and DL models. While the 1D models accurately capture dynamics near the free energy minimum fluid and crystal configurations, predictions near the transition region are not quantitatively accurate. A preliminary investigation of ensemble averaged 2D order parameter trajectories suggests that 2D models are required to capture crystallization dynamics in the transition region.

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

PubMed

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

2016-03-01

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

Bayesian model aggregation for ensemble-based estimates of protein pKa values

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

Gosink, Luke J.; Hogan, Emilie A.; Pulsipher, Trenton C.

2014-03-01

This paper investigates an ensemble-based technique called Bayesian Model Averaging (BMA) to improve the performance of protein amino acid pmore » $$K_a$$ predictions. Structure-based p$$K_a$$ calculations play an important role in the mechanistic interpretation of protein structure and are also used to determine a wide range of protein properties. A diverse set of methods currently exist for p$$K_a$$ prediction, ranging from empirical statistical models to {\\it ab initio} quantum mechanical approaches. However, each of these methods are based on a set of assumptions that have inherent bias and sensitivities that can effect a model's accuracy and generalizability for p$$K_a$$ prediction in complicated biomolecular systems. We use BMA to combine eleven diverse prediction methods that each estimate pKa values of amino acids in staphylococcal nuclease. These methods are based on work conducted for the pKa Cooperative and the pKa measurements are based on experimental work conducted by the Garc{\\'i}a-Moreno lab. Our study demonstrates that the aggregated estimate obtained from BMA outperforms all individual prediction methods in our cross-validation study with improvements from 40-70\\% over other method classes. This work illustrates a new possible mechanism for improving the accuracy of p$$K_a$$ prediction and lays the foundation for future work on aggregate models that balance computational cost with prediction accuracy.« less

Semiparametric Thurstonian Models for Recurrent Choices: A Bayesian Analysis

ERIC Educational Resources Information Center

Ansari, Asim; Iyengar, Raghuram

2006-01-01

We develop semiparametric Bayesian Thurstonian models for analyzing repeated choice decisions involving multinomial, multivariate binary or multivariate ordinal data. Our modeling framework has multiple components that together yield considerable flexibility in modeling preference utilities, cross-sectional heterogeneity and parameter-driven…

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.

A Bayesian network based framework for real-time crash prediction on the basic freeway segments of urban expressways.

PubMed

Hossain, Moinul; Muromachi, Yasunori

2012-03-01

The concept of measuring the crash risk for a very short time window in near future is gaining more practicality due to the recent advancements in the fields of information systems and traffic sensor technology. Although some real-time crash prediction models have already been proposed, they are still primitive in nature and require substantial improvements to be implemented in real-life. This manuscript investigates the major shortcomings of the existing models and offers solutions to overcome them with an improved framework and modeling method. It employs random multinomial logit model to identify the most important predictors as well as the most suitable detector locations to acquire data to build such a model. Afterwards, it applies Bayesian belief net (BBN) to build the real-time crash prediction model. The model has been constructed using high resolution detector data collected from Shibuya 3 and Shinjuku 4 expressways under the jurisdiction of Tokyo Metropolitan Expressway Company Limited, Japan. It has been specifically built for the basic freeway segments and it predicts the chance of formation of a hazardous traffic condition within the next 4-9 min for a particular 250 meter long road section. The performance evaluation results reflect that at an average threshold value the model is able to successful classify 66% of the future crashes with a false alarm rate less than 20%. Copyright © 2011 Elsevier Ltd. All rights reserved.

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

ERIC Educational Resources Information Center

Rindskopf, David

2012-01-01

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

Careful with Those Priors: A Note on Bayesian Estimation in Two-Parameter Logistic Item Response Theory Models

ERIC Educational Resources Information Center

Marcoulides, Katerina M.

2018-01-01

This study examined the use of Bayesian analysis methods for the estimation of item parameters in a two-parameter logistic item response theory model. Using simulated data under various design conditions with both informative and non-informative priors, the parameter recovery of Bayesian analysis methods were examined. Overall results showed that…

A Bayesian Approach to Person Fit Analysis in Item Response Theory Models. Research Report.

ERIC Educational Resources Information Center

Glas, Cees A. W.; Meijer, Rob R.

A Bayesian approach to the evaluation of person fit in item response theory (IRT) models is presented. In a posterior predictive check, the observed value on a discrepancy variable is positioned in its posterior distribution. In a Bayesian framework, a Markov Chain Monte Carlo procedure can be used to generate samples of the posterior distribution…

A Tutorial Introduction to Bayesian Models of Cognitive Development

ERIC Educational Resources Information Center

Perfors, Amy; Tenenbaum, Joshua B.; Griffiths, Thomas L.; Xu, Fei

2011-01-01

We present an introduction to Bayesian inference as it is used in probabilistic models of cognitive development. Our goal is to provide an intuitive and accessible guide to the "what", the "how", and the "why" of the Bayesian approach: what sorts of problems and data the framework is most relevant for, and how and why it may be useful for…

A Simulation Study Comparison of Bayesian Estimation with Conventional Methods for Estimating Unknown Change Points

ERIC Educational Resources Information Center

Wang, Lijuan; McArdle, John J.

2008-01-01

The main purpose of this research is to evaluate the performance of a Bayesian approach for estimating unknown change points using Monte Carlo simulations. The univariate and bivariate unknown change point mixed models were presented and the basic idea of the Bayesian approach for estimating the models was discussed. The performance of Bayesian…

Estimation of parameter uncertainty for an activated sludge model using Bayesian inference: a comparison with the frequentist method.

PubMed

Zonta, Zivko J; Flotats, Xavier; Magrí, Albert

2014-08-01

The procedure commonly used for the assessment of the parameters included in activated sludge models (ASMs) relies on the estimation of their optimal value within a confidence region (i.e. frequentist inference). Once optimal values are estimated, parameter uncertainty is computed through the covariance matrix. However, alternative approaches based on the consideration of the model parameters as probability distributions (i.e. Bayesian inference), may be of interest. The aim of this work is to apply (and compare) both Bayesian and frequentist inference methods when assessing uncertainty for an ASM-type model, which considers intracellular storage and biomass growth, simultaneously. Practical identifiability was addressed exclusively considering respirometric profiles based on the oxygen uptake rate and with the aid of probabilistic global sensitivity analysis. Parameter uncertainty was thus estimated according to both the Bayesian and frequentist inferential procedures. Results were compared in order to evidence the strengths and weaknesses of both approaches. Since it was demonstrated that Bayesian inference could be reduced to a frequentist approach under particular hypotheses, the former can be considered as a more generalist methodology. Hence, the use of Bayesian inference is encouraged for tackling inferential issues in ASM environments.

Timing and effect of a safe routes to school program on child pedestrian injury risk during school travel hours: Bayesian changepoint and difference-in-differences analysis.

PubMed

DiMaggio, Charles; Chen, Qixuan; Muennig, Peter A; Li, Guohua

2014-12-01

In 2005, the US Congress allocated $612 million for a national Safe Routes to School (SRTS) program to encourage walking and bicycling to schools. We evaluated the effectiveness of a SRTS in controlling pedestrian injuries among school-age children. Bayesian changepoint analysis was applied to model the quarterly counts of pedestrian injuries among 5- to 19-year old children in New York City between 2001 and 2010 during school-travel hours in census tracts with and without SRTS. Overdispersed Poisson model was used to estimate difference-in-differences in injury risk between census tracts with and without SRTS following the changepoint. In SRTS-intervention census tracts, a change point in the quarterly counts of injuries was identified in the second quarter of 2008, which was consistent with the timing of the implementation of SRTS interventions. In census tracts with SRTS interventions, the estimated quarterly rates of pedestrian injury per 10,000 population among school-age children during school-travel hours were 3.47 (95% Credible Interval [CrI] 2.67, 4.39) prior to the changepoint, and 0.74 (95% CrI 0.30, 1.50) after the changepoint. There was no change in the average number of quarterly injuries in non-SRTS census tracts. Overdispersed Poisson modeling revealed that SRTS implementation was associated with a 44% reduction (95% Confidence Interval [CI] 87% decrease to 130% increase) in school-age pedestrian injury risk during school-travel hours. Bayesian changepoint analysis of quarterly counts of school-age pedestrian injuries successfully identified the timing of SRTS intervention in New York City. Implementation of the SRTS program in New York City appears to be effective in reducing school-age pedestrian injuries during school-travel hours.

A Bayesian framework for extracting human gait using strong prior knowledge.

PubMed

Zhou, Ziheng; Prügel-Bennett, Adam; Damper, Robert I

2006-11-01

Extracting full-body motion of walking people from monocular video sequences in complex, real-world environments is an important and difficult problem, going beyond simple tracking, whose satisfactory solution demands an appropriate balance between use of prior knowledge and learning from data. We propose a consistent Bayesian framework for introducing strong prior knowledge into a system for extracting human gait. In this work, the strong prior is built from a simple articulated model having both time-invariant (static) and time-variant (dynamic) parameters. The model is easily modified to cater to situations such as walkers wearing clothing that obscures the limbs. The statistics of the parameters are learned from high-quality (indoor laboratory) data and the Bayesian framework then allows us to "bootstrap" to accurate gait extraction on the noisy images typical of cluttered, outdoor scenes. To achieve automatic fitting, we use a hidden Markov model to detect the phases of images in a walking cycle. We demonstrate our approach on silhouettes extracted from fronto-parallel ("sideways on") sequences of walkers under both high-quality indoor and noisy outdoor conditions. As well as high-quality data with synthetic noise and occlusions added, we also test walkers with rucksacks, skirts, and trench coats. Results are quantified in terms of chamfer distance and average pixel error between automatically extracted body points and corresponding hand-labeled points. No one part of the system is novel in itself, but the overall framework makes it feasible to extract gait from very much poorer quality image sequences than hitherto. This is confirmed by comparing person identification by gait using our method and a well-established baseline recognition algorithm.

Bayesian estimation of differential transcript usage from RNA-seq data.

PubMed

Papastamoulis, Panagiotis; Rattray, Magnus

2017-11-27

Next generation sequencing allows the identification of genes consisting of differentially expressed transcripts, a term which usually refers to changes in the overall expression level. A specific type of differential expression is differential transcript usage (DTU) and targets changes in the relative within gene expression of a transcript. The contribution of this paper is to: (a) extend the use of cjBitSeq to the DTU context, a previously introduced Bayesian model which is originally designed for identifying changes in overall expression levels and (b) propose a Bayesian version of DRIMSeq, a frequentist model for inferring DTU. cjBitSeq is a read based model and performs fully Bayesian inference by MCMC sampling on the space of latent state of each transcript per gene. BayesDRIMSeq is a count based model and estimates the Bayes Factor of a DTU model against a null model using Laplace's approximation. The proposed models are benchmarked against the existing ones using a recent independent simulation study as well as a real RNA-seq dataset. Our results suggest that the Bayesian methods exhibit similar performance with DRIMSeq in terms of precision/recall but offer better calibration of False Discovery Rate.

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.

BUMPER: the Bayesian User-friendly Model for Palaeo-Environmental Reconstruction

NASA Astrophysics Data System (ADS)

Holden, Phil; Birks, John; Brooks, Steve; Bush, Mark; Hwang, Grace; Matthews-Bird, Frazer; Valencia, Bryan; van Woesik, Robert

2017-04-01

We describe the Bayesian User-friendly Model for Palaeo-Environmental Reconstruction (BUMPER), a Bayesian transfer function for inferring past climate and other environmental variables from microfossil assemblages. The principal motivation for a Bayesian approach is that the palaeoenvironment is treated probabilistically, and can be updated as additional data become available. Bayesian approaches therefore provide a reconstruction-specific quantification of the uncertainty in the data and in the model parameters. BUMPER is fully self-calibrating, straightforward to apply, and computationally fast, requiring 2 seconds to build a 100-taxon model from a 100-site training-set on a standard personal computer. We apply the model's probabilistic framework to generate thousands of artificial training-sets under ideal assumptions. We then use these to demonstrate both the general applicability of the model and the sensitivity of reconstructions to the characteristics of the training-set, considering assemblage richness, taxon tolerances, and the number of training sites. We demonstrate general applicability to real data, considering three different organism types (chironomids, diatoms, pollen) and different reconstructed variables. In all of these applications an identically configured model is used, the only change being the input files that provide the training-set environment and taxon-count data.

A feature-based developmental model of the infant brain in structural MRI.

PubMed

Toews, Matthew; Wells, William M; Zöllei, Lilla

2012-01-01

In this paper, anatomical development is modeled as a collection of distinctive image patterns localized in space and time. A Bayesian posterior probability is defined over a random variable of subject age, conditioned on data in the form of scale-invariant image features. The model is automatically learned from a large set of images exhibiting significant variation, used to discover anatomical structure related to age and development, and fit to new images to predict age. The model is applied to a set of 230 infant structural MRIs of 92 subjects acquired at multiple sites over an age range of 8-590 days. Experiments demonstrate that the model can be used to identify age-related anatomical structure, and to predict the age of new subjects with an average error of 72 days.

Meta-analysis of the effect of natural frequencies on Bayesian reasoning.

PubMed

McDowell, Michelle; Jacobs, Perke

2017-12-01

The natural frequency facilitation effect describes the finding that people are better able to solve descriptive Bayesian inference tasks when represented as joint frequencies obtained through natural sampling, known as natural frequencies, than as conditional probabilities. The present meta-analysis reviews 20 years of research seeking to address when, why, and for whom natural frequency formats are most effective. We review contributions from research associated with the 2 dominant theoretical perspectives, the ecological rationality framework and nested-sets theory, and test potential moderators of the effect. A systematic review of relevant literature yielded 35 articles representing 226 performance estimates. These estimates were statistically integrated using a bivariate mixed-effects model that yields summary estimates of average performances across the 2 formats and estimates of the effects of different study characteristics on performance. These study characteristics range from moderators representing individual characteristics (e.g., numeracy, expertise), to methodological differences (e.g., use of incentives, scoring criteria) and features of problem representation (e.g., short menu format, visual aid). Short menu formats (less computationally complex representations showing joint-events) and visual aids demonstrated some of the strongest moderation effects, improving performance for both conditional probability and natural frequency formats. A number of methodological factors (e.g., exposure to both problem formats) were also found to affect performance rates, emphasizing the importance of a systematic approach. We suggest how research on Bayesian reasoning can be strengthened by broadening the definition of successful Bayesian reasoning to incorporate choice and process and by applying different research methodologies. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Application of bayesian networks to real-time flood risk estimation

NASA Astrophysics Data System (ADS)

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

2003-04-01

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

Model-based Bayesian inference for ROC data analysis

NASA Astrophysics Data System (ADS)

Lei, Tianhu; Bae, K. Ty

2013-03-01

This paper presents a study of model-based Bayesian inference to Receiver Operating Characteristics (ROC) data. The model is a simple version of general non-linear regression model. Different from Dorfman model, it uses a probit link function with a covariate variable having zero-one two values to express binormal distributions in a single formula. Model also includes a scale parameter. Bayesian inference is implemented by Markov Chain Monte Carlo (MCMC) method carried out by Bayesian analysis Using Gibbs Sampling (BUGS). Contrast to the classical statistical theory, Bayesian approach considers model parameters as random variables characterized by prior distributions. With substantial amount of simulated samples generated by sampling algorithm, posterior distributions of parameters as well as parameters themselves can be accurately estimated. MCMC-based BUGS adopts Adaptive Rejection Sampling (ARS) protocol which requires the probability density function (pdf) which samples are drawing from be log concave with respect to the targeted parameters. Our study corrects a common misconception and proves that pdf of this regression model is log concave with respect to its scale parameter. Therefore, ARS's requirement is satisfied and a Gaussian prior which is conjugate and possesses many analytic and computational advantages is assigned to the scale parameter. A cohort of 20 simulated data sets and 20 simulations from each data set are used in our study. Output analysis and convergence diagnostics for MCMC method are assessed by CODA package. Models and methods by using continuous Gaussian prior and discrete categorical prior are compared. Intensive simulations and performance measures are given to illustrate our practice in the framework of model-based Bayesian inference using MCMC method.

Design considerations and analysis planning of a phase 2a proof of concept study in rheumatoid arthritis in the presence of possible non-monotonicity.

PubMed

Liu, Feng; Walters, Stephen J; Julious, Steven A

2017-10-02

It is important to quantify the dose response for a drug in phase 2a clinical trials so the optimal doses can then be selected for subsequent late phase trials. In a phase 2a clinical trial of new lead drug being developed for the treatment of rheumatoid arthritis (RA), a U-shaped dose response curve was observed. In the light of this result further research was undertaken to design an efficient phase 2a proof of concept (PoC) trial for a follow-on compound using the lessons learnt from the lead compound. The planned analysis for the Phase 2a trial for GSK123456 was a Bayesian Emax model which assumes the dose-response relationship follows a monotonic sigmoid "S" shaped curve. This model was found to be suboptimal to model the U-shaped dose response observed in the data from this trial and alternatives approaches were needed to be considered for the next compound for which a Normal dynamic linear model (NDLM) is proposed. This paper compares the statistical properties of the Bayesian Emax model and NDLM model and both models are evaluated using simulation in the context of adaptive Phase 2a PoC design under a variety of assumed dose response curves: linear, Emax model, U-shaped model, and flat response. It is shown that the NDLM method is flexible and can handle a wide variety of dose-responses, including monotonic and non-monotonic relationships. In comparison to the NDLM model the Emax model excelled with higher probability of selecting ED90 and smaller average sample size, when the true dose response followed Emax like curve. In addition, the type I error, probability of incorrectly concluding a drug may work when it does not, is inflated with the Bayesian NDLM model in all scenarios which would represent a development risk to pharmaceutical company. The bias, which is the difference between the estimated effect from the Emax and NDLM models and the simulated value, is comparable if the true dose response follows a placebo like curve, an Emax like curve, or log linear shape curve under fixed dose allocation, no adaptive allocation, half adaptive and adaptive scenarios. The bias though is significantly increased for the Emax model if the true dose response follows a U-shaped curve. In most cases the Bayesian Emax model works effectively and efficiently, with low bias and good probability of success in case of monotonic dose response. However, if there is a belief that the dose response could be non-monotonic then the NDLM is the superior model to assess the dose response.

Optimal Skin-to-Stone Distance Is a Positive Predictor for Successful Outcomes in Upper Ureter Calculi following Extracorporeal Shock Wave Lithotripsy: A Bayesian Model Averaging Approach

PubMed Central

Cho, Kang Su; Jung, Hae Do; Ham, Won Sik; Chung, Doo Yong; Kang, Yong Jin; Jang, Won Sik; Kwon, Jong Kyou; Choi, Young Deuk; Lee, Joo Yong

2015-01-01

Objectives To investigate whether skin-to-stone distance (SSD), which remains controversial in patients with ureter stones, can be a predicting factor for one session success following extracorporeal shock wave lithotripsy (ESWL) in patients with upper ureter stones. Patients and Methods We retrospectively reviewed the medical records of 1,519 patients who underwent their first ESWL between January 2005 and December 2013. Among these patients, 492 had upper ureter stones that measured 4–20 mm and were eligible for our analyses. Maximal stone length, mean stone density (HU), and SSD were determined on pretreatment non-contrast computed tomography (NCCT). For subgroup analyses, patients were divided into four groups. Group 1 consisted of patients with SSD<25th percentile, group 2 consisted of patients with SSD in the 25th to 50th percentile, group 3 patients had SSD in the 50th to 75th percentile, and group 4 patients had SSD≥75th percentile. Results In analyses of group 2 patients versus others, there were no statistical differences in mean age, stone length and density. However, the one session success rate in group 2 was higher than other groups (77.9% vs. 67.0%; P = 0.032). The multivariate logistic regression model revealed that shorter stone length, lower stone density, and the group 2 SSD were positive predictors for successful outcomes in ESWL. Using the Bayesian model-averaging approach, longer stone length, lower stone density, and group 2 SSD can be also positive predictors for successful outcomes following ESWL. Conclusions Our data indicate that a group 2 SSD of approximately 10 cm is a positive predictor for success following ESWL. PMID:26659086

Gesture Based Control and EMG Decomposition

NASA Technical Reports Server (NTRS)

Wheeler, Kevin R.; Chang, Mindy H.; Knuth, Kevin H.

2005-01-01

This paper presents two probabilistic developments for use with Electromyograms (EMG). First described is a new-electric interface for virtual device control based on gesture recognition. The second development is a Bayesian method for decomposing EMG into individual motor unit action potentials. This more complex technique will then allow for higher resolution in separating muscle groups for gesture recognition. All examples presented rely upon sampling EMG data from a subject's forearm. The gesture based recognition uses pattern recognition software that has been trained to identify gestures from among a given set of gestures. The pattern recognition software consists of hidden Markov models which are used to recognize the gestures as they are being performed in real-time from moving averages of EMG. Two experiments were conducted to examine the feasibility of this interface technology. The first replicated a virtual joystick interface, and the second replicated a keyboard. Moving averages of EMG do not provide easy distinction between fine muscle groups. To better distinguish between different fine motor skill muscle groups we present a Bayesian algorithm to separate surface EMG into representative motor unit action potentials. The algorithm is based upon differential Variable Component Analysis (dVCA) [l], [2] which was originally developed for Electroencephalograms. The algorithm uses a simple forward model representing a mixture of motor unit action potentials as seen across multiple channels. The parameters of this model are iteratively optimized for each component. Results are presented on both synthetic and experimental EMG data. The synthetic case has additive white noise and is compared with known components. The experimental EMG data was obtained using a custom linear electrode array designed for this study.

Comprehensive evaluation of Ensemble Multi-Satellite Precipitation Dataset using the Dynamic Bayesian Model Averaging scheme over the Tibetan plateau

NASA Astrophysics Data System (ADS)

Ma, Yingzhao; Yang, Yuan; Han, Zhongying; Tang, Guoqiang; Maguire, Lane; Chu, Zhigang; Hong, Yang

2018-01-01

The objective of this study is to comprehensively evaluate the new Ensemble Multi-Satellite Precipitation Dataset using the Dynamic Bayesian Model Averaging scheme (EMSPD-DBMA) at daily and 0.25° scales from 2001 to 2015 over the Tibetan Plateau (TP). Error analysis against gauge observations revealed that EMSPD-DBMA captured the spatiotemporal pattern of daily precipitation with an acceptable Correlation Coefficient (CC) of 0.53 and a Relative Bias (RB) of -8.28%. Moreover, EMSPD-DBMA outperformed IMERG and GSMaP-MVK in almost all metrics in the summers of 2014 and 2015, with the lowest RB and Root Mean Square Error (RMSE) values of -2.88% and 8.01 mm/d, respectively. It also better reproduced the Probability Density Function (PDF) in terms of daily rainfall amount and estimated moderate and heavy rainfall better than both IMERG and GSMaP-MVK. Further, hydrological evaluation with the Coupled Routing and Excess STorage (CREST) model in the Upper Yangtze River region indicated that the EMSPD-DBMA forced simulation showed satisfying hydrological performance in terms of streamflow prediction, with Nash-Sutcliffe coefficient of Efficiency (NSE) values of 0.82 and 0.58, compared to gauge forced simulation (0.88 and 0.60) at the calibration and validation periods, respectively. EMSPD-DBMA also performed a greater fitness for peak flow simulation than a new Multi-Source Weighted-Ensemble Precipitation Version 2 (MSWEP V2) product, indicating a promising prospect of hydrological utility for the ensemble satellite precipitation data. This study belongs to early comprehensive evaluation of the blended multi-satellite precipitation data across the TP, which would be significant for improving the DBMA algorithm in regions with complex terrain.

Bayesian Modeling of a Human MMORPG Player

NASA Astrophysics Data System (ADS)

Synnaeve, Gabriel; Bessière, Pierre

2011-03-01

This paper describes an application of Bayesian programming to the control of an autonomous avatar in a multiplayer role-playing game (the example is based on World of Warcraft). We model a particular task, which consists of choosing what to do and to select which target in a situation where allies and foes are present. We explain the model in Bayesian programming and show how we could learn the conditional probabilities from data gathered during human-played sessions.

A comment on priors for Bayesian occupancy models

PubMed Central

Gerber, Brian D.

2018-01-01

Understanding patterns of species occurrence and the processes underlying these patterns is fundamental to the study of ecology. One of the more commonly used approaches to investigate species occurrence patterns is occupancy modeling, which can account for imperfect detection of a species during surveys. In recent years, there has been a proliferation of Bayesian modeling in ecology, which includes fitting Bayesian occupancy models. The Bayesian framework is appealing to ecologists for many reasons, including the ability to incorporate prior information through the specification of prior distributions on parameters. While ecologists almost exclusively intend to choose priors so that they are “uninformative” or “vague”, such priors can easily be unintentionally highly informative. Here we report on how the specification of a “vague” normally distributed (i.e., Gaussian) prior on coefficients in Bayesian occupancy models can unintentionally influence parameter estimation. Using both simulated data and empirical examples, we illustrate how this issue likely compromises inference about species-habitat relationships. While the extent to which these informative priors influence inference depends on the data set, researchers fitting Bayesian occupancy models should conduct sensitivity analyses to ensure intended inference, or employ less commonly used priors that are less informative (e.g., logistic or t prior distributions). We provide suggestions for addressing this issue in occupancy studies, and an online tool for exploring this issue under different contexts. PMID:29481554

Diving into the consumer nutrition environment: A Bayesian spatial factor analysis of neighborhood restaurant environment.

PubMed

Luan, Hui; Law, Jane; Lysy, Martin

2018-02-01

Neighborhood restaurant environment (NRE) plays a vital role in shaping residents' eating behaviors. While NRE 'healthfulness' is a multi-facet concept, most studies evaluate it based only on restaurant type, thus largely ignoring variations of in-restaurant features. In the few studies that do account for such features, healthfulness scores are simply averaged over accessible restaurants, thereby concealing any uncertainty that attributed to neighborhoods' size or spatial correlation. To address these limitations, this paper presents a Bayesian Spatial Factor Analysis for assessing NRE healthfulness in the city of Kitchener, Canada. Several in-restaurant characteristics are included. By treating NRE healthfulness as a spatially correlated latent variable, the adopted modeling approach can: (i) identify specific indicators most relevant to NRE healthfulness, (ii) provide healthfulness estimates for neighborhoods without accessible restaurants, and (iii) readily quantify uncertainties in the healthfulness index. Implications of the analysis for intervention program development and community food planning are discussed. Copyright © 2017 Elsevier Ltd. All rights reserved.

Bayesian segregation analysis of production traits in two strains of laying chickens.

PubMed

Szydłowski, M; Szwaczkowski, T

2001-02-01

A bayesian marker-free segregation analysis was applied to search for evidence of segregating genes affecting production traits in two strains of laying hens under long-term selection. The study used data from 6 generations of Leghorn (H77) and New Hampshire (N88) breeding nuclei. Estimation of marginal posterior means of variance components and parameters of a single autosomal locus was performed by use of the Gibbs sampler. The results showed evidence for a mixed major gene: -polygenic inheritance of BW and age at sexual maturity (ASM) in both strains. Single genes affecting BW and ASM explained one-third of the genetic variance. For ASM large overdominance effect at single locus was estimated. Initial egg production (IEP) and average egg weight (EW) showed a polygenic model of inheritance. The polygenic heritability estimates for BW, ASM, IEP, and EW were 0.32, 0.25, 0.23, and 0.08 in Strain H77 and 0.25, 0.24, 0.11, and 0.38 in Strain N88, respectively.

The Bayesian boom: good thing or bad?

PubMed Central

Hahn, Ulrike

2014-01-01

A series of high-profile critiques of Bayesian models of cognition have recently sparked controversy. These critiques question the contribution of rational, normative considerations in the study of cognition. The present article takes central claims from these critiques and evaluates them in light of specific models. Closer consideration of actual examples of Bayesian treatments of different cognitive phenomena allows one to defuse these critiques showing that they cannot be sustained across the diversity of applications of the Bayesian framework for cognitive modeling. More generally, there is nothing in the Bayesian framework that would inherently give rise to the deficits that these critiques perceive, suggesting they have been framed at the wrong level of generality. At the same time, the examples are used to demonstrate the different ways in which consideration of rationality uniquely benefits both theory and practice in the study of cognition. PMID:25152738

Calibrating Bayesian Network Representations of Social-Behavioral Models

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

Whitney, Paul D.; Walsh, Stephen J.

2010-04-08

While human behavior has long been studied, recent and ongoing advances in computational modeling present opportunities for recasting research outcomes in human behavior. In this paper we describe how Bayesian networks can represent outcomes of human behavior research. We demonstrate a Bayesian network that represents political radicalization research – and show a corresponding visual representation of aspects of this research outcome. Since Bayesian networks can be quantitatively compared with external observations, the representation can also be used for empirical assessments of the research which the network summarizes. For a political radicalization model based on published research, we show this empiricalmore » comparison with data taken from the Minorities at Risk Organizational Behaviors database.« less

A comprehensive probabilistic analysis model of oil pipelines network based on Bayesian network

NASA Astrophysics Data System (ADS)

Zhang, C.; Qin, T. X.; Jiang, B.; Huang, C.

2018-02-01

Oil pipelines network is one of the most important facilities of energy transportation. But oil pipelines network accident may result in serious disasters. Some analysis models for these accidents have been established mainly based on three methods, including event-tree, accident simulation and Bayesian network. Among these methods, Bayesian network is suitable for probabilistic analysis. But not all the important influencing factors are considered and the deployment rule of the factors has not been established. This paper proposed a probabilistic analysis model of oil pipelines network based on Bayesian network. Most of the important influencing factors, including the key environment condition and emergency response are considered in this model. Moreover, the paper also introduces a deployment rule for these factors. The model can be used in probabilistic analysis and sensitive analysis of oil pipelines network accident.

An evaluation of Bayesian techniques for controlling model complexity and selecting inputs in a neural network for short-term load forecasting.

PubMed

Hippert, Henrique S; Taylor, James W

2010-04-01

Artificial neural networks have frequently been proposed for electricity load forecasting because of their capabilities for the nonlinear modelling of large multivariate data sets. Modelling with neural networks is not an easy task though; two of the main challenges are defining the appropriate level of model complexity, and choosing the input variables. This paper evaluates techniques for automatic neural network modelling within a Bayesian framework, as applied to six samples containing daily load and weather data for four different countries. We analyse input selection as carried out by the Bayesian 'automatic relevance determination', and the usefulness of the Bayesian 'evidence' for the selection of the best structure (in terms of number of neurones), as compared to methods based on cross-validation. Copyright 2009 Elsevier Ltd. All rights reserved.

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 analysis of CCDM models

NASA Astrophysics Data System (ADS)

Jesus, J. F.; Valentim, R.; Andrade-Oliveira, F.

2017-09-01

Creation of Cold Dark Matter (CCDM), in the context of Einstein Field Equations, produces a negative pressure term which can be used to explain the accelerated expansion of the Universe. In this work we tested six different spatially flat models for matter creation using statistical criteria, in light of SNe Ia data: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Bayesian Evidence (BE). These criteria allow to compare models considering goodness of fit and number of free parameters, penalizing excess of complexity. We find that JO model is slightly favoured over LJO/ΛCDM model, however, neither of these, nor Γ = 3αH0 model can be discarded from the current analysis. Three other scenarios are discarded either because poor fitting or because of the excess of free parameters. A method of increasing Bayesian evidence through reparameterization in order to reducing parameter degeneracy is also developed.

Refining value-at-risk estimates using a Bayesian Markov-switching GJR-GARCH copula-EVT model.

PubMed

Sampid, Marius Galabe; Hasim, Haslifah M; Dai, Hongsheng

2018-01-01

In this paper, we propose a model for forecasting Value-at-Risk (VaR) using a Bayesian Markov-switching GJR-GARCH(1,1) model with skewed Student's-t innovation, copula functions and extreme value theory. A Bayesian Markov-switching GJR-GARCH(1,1) model that identifies non-constant volatility over time and allows the GARCH parameters to vary over time following a Markov process, is combined with copula functions and EVT to formulate the Bayesian Markov-switching GJR-GARCH(1,1) copula-EVT VaR model, which is then used to forecast the level of risk on financial asset returns. We further propose a new method for threshold selection in EVT analysis, which we term the hybrid method. Empirical and back-testing results show that the proposed VaR models capture VaR reasonably well in periods of calm and in periods of crisis.

Bayesian demography 250 years after Bayes

PubMed Central

Bijak, Jakub; Bryant, John

2016-01-01

Bayesian statistics offers an alternative to classical (frequentist) statistics. It is distinguished by its use of probability distributions to describe uncertain quantities, which leads to elegant solutions to many difficult statistical problems. Although Bayesian demography, like Bayesian statistics more generally, is around 250 years old, only recently has it begun to flourish. The aim of this paper is to review the achievements of Bayesian demography, address some misconceptions, and make the case for wider use of Bayesian methods in population studies. We focus on three applications: demographic forecasts, limited data, and highly structured or complex models. The key advantages of Bayesian methods are the ability to integrate information from multiple sources and to describe uncertainty coherently. Bayesian methods also allow for including additional (prior) information next to the data sample. As such, Bayesian approaches are complementary to many traditional methods, which can be productively re-expressed in Bayesian terms. PMID:26902889

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

PubMed

Mila, A L; Ngugi, H K

2011-01-01

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

Introduction to Bayesian statistical approaches to compositional analyses of transgenic crops 1. Model validation and setting the stage.

PubMed

Harrison, Jay M; Breeze, Matthew L; Harrigan, George G

2011-08-01

Statistical comparisons of compositional data generated on genetically modified (GM) crops and their near-isogenic conventional (non-GM) counterparts typically rely on classical significance testing. This manuscript presents an introduction to Bayesian methods for compositional analysis along with recommendations for model validation. The approach is illustrated using protein and fat data from two herbicide tolerant GM soybeans (MON87708 and MON87708×MON89788) and a conventional comparator grown in the US in 2008 and 2009. Guidelines recommended by the US Food and Drug Administration (FDA) in conducting Bayesian analyses of clinical studies on medical devices were followed. This study is the first Bayesian approach to GM and non-GM compositional comparisons. The evaluation presented here supports a conclusion that a Bayesian approach to analyzing compositional data can provide meaningful and interpretable results. We further describe the importance of method validation and approaches to model checking if Bayesian approaches to compositional data analysis are to be considered viable by scientists involved in GM research and regulation. Copyright © 2011 Elsevier Inc. All rights reserved.

Bayesian phylogenetic estimation of fossil ages.

PubMed

Drummond, Alexei J; Stadler, Tanja

2016-07-19

Recent advances have allowed for both morphological fossil evidence and molecular sequences to be integrated into a single combined inference of divergence dates under the rule of Bayesian probability. In particular, the fossilized birth-death tree prior and the Lewis-Mk model of discrete morphological evolution allow for the estimation of both divergence times and phylogenetic relationships between fossil and extant taxa. We exploit this statistical framework to investigate the internal consistency of these models by producing phylogenetic estimates of the age of each fossil in turn, within two rich and well-characterized datasets of fossil and extant species (penguins and canids). We find that the estimation accuracy of fossil ages is generally high with credible intervals seldom excluding the true age and median relative error in the two datasets of 5.7% and 13.2%, respectively. The median relative standard error (RSD) was 9.2% and 7.2%, respectively, suggesting good precision, although with some outliers. In fact, in the two datasets we analyse, the phylogenetic estimate of fossil age is on average less than 2 Myr from the mid-point age of the geological strata from which it was excavated. The high level of internal consistency found in our analyses suggests that the Bayesian statistical model employed is an adequate fit for both the geological and morphological data, and provides evidence from real data that the framework used can accurately model the evolution of discrete morphological traits coded from fossil and extant taxa. We anticipate that this approach will have diverse applications beyond divergence time dating, including dating fossils that are temporally unconstrained, testing of the 'morphological clock', and for uncovering potential model misspecification and/or data errors when controversial phylogenetic hypotheses are obtained based on combined divergence dating analyses.This article is part of the themed issue 'Dating species divergences using rocks and clocks'. © 2016 The Authors.

Bayesian phylogenetic estimation of fossil ages

PubMed Central

Drummond, Alexei J.; Stadler, Tanja

2016-01-01

Recent advances have allowed for both morphological fossil evidence and molecular sequences to be integrated into a single combined inference of divergence dates under the rule of Bayesian probability. In particular, the fossilized birth–death tree prior and the Lewis-Mk model of discrete morphological evolution allow for the estimation of both divergence times and phylogenetic relationships between fossil and extant taxa. We exploit this statistical framework to investigate the internal consistency of these models by producing phylogenetic estimates of the age of each fossil in turn, within two rich and well-characterized datasets of fossil and extant species (penguins and canids). We find that the estimation accuracy of fossil ages is generally high with credible intervals seldom excluding the true age and median relative error in the two datasets of 5.7% and 13.2%, respectively. The median relative standard error (RSD) was 9.2% and 7.2%, respectively, suggesting good precision, although with some outliers. In fact, in the two datasets we analyse, the phylogenetic estimate of fossil age is on average less than 2 Myr from the mid-point age of the geological strata from which it was excavated. The high level of internal consistency found in our analyses suggests that the Bayesian statistical model employed is an adequate fit for both the geological and morphological data, and provides evidence from real data that the framework used can accurately model the evolution of discrete morphological traits coded from fossil and extant taxa. We anticipate that this approach will have diverse applications beyond divergence time dating, including dating fossils that are temporally unconstrained, testing of the ‘morphological clock', and for uncovering potential model misspecification and/or data errors when controversial phylogenetic hypotheses are obtained based on combined divergence dating analyses. This article is part of the themed issue ‘Dating species divergences using rocks and clocks’. PMID:27325827

Load Balancing Using Time Series Analysis for Soft Real Time Systems with Statistically Periodic Loads

NASA Technical Reports Server (NTRS)

Hailperin, M.

1993-01-01

This thesis provides design and analysis of techniques for global load balancing on ensemble architectures running soft-real-time object-oriented applications with statistically periodic loads. It focuses on estimating the instantaneous average load over all the processing elements. The major contribution is the use of explicit stochastic process models for both the loading and the averaging itself. These models are exploited via statistical time-series analysis and Bayesian inference to provide improved average load estimates, and thus to facilitate global load balancing. This thesis explains the distributed algorithms used and provides some optimality results. It also describes the algorithms' implementation and gives performance results from simulation. These results show that the authors' techniques allow more accurate estimation of the global system loading, resulting in fewer object migrations than local methods. The authors' method is shown to provide superior performance, relative not only to static load-balancing schemes but also to many adaptive load-balancing methods. Results from a preliminary analysis of another system and from simulation with a synthetic load provide some evidence of more general applicability.

Using Bayesian modelling to investigate factors governing antibiotic-induced Candida albicans colonization of the GI tract

PubMed Central

Shankar, Jyoti; Solis, Norma V.; Mounaud, Stephanie; Szpakowski, Sebastian; Liu, Hong; Losada, Liliana; Nierman, William C.; Filler, Scott G.

2015-01-01

Receipt of broad-spectrum antibiotics enhances Candida albicans colonization of the GI tract, a risk factor for haematogenously-disseminated candidiasis. To understand how antibiotics influence C. albicans colonization, we treated mice orally with vancomycin or a combination of penicillin, streptomycin, and gentamicin (PSG) and then inoculated them with C. albicans by gavage. Only PSG treatment resulted in sustained, high-level GI colonization with C. albicans. Furthermore, PSG reduced bacterial diversity in the colon much more than vancomycin. Both antibiotic regimens significantly reduced IL-17A, IL-21, IL-22 and IFN-γ mRNA levels in the terminal ileum but had limited effect on the GI fungal microbiome. Through a series of models that employed Bayesian model averaging, we investigated the associations between antibiotic treatment, GI microbiota, and host immune response and their collective impact on C. albicans colonization. Our analysis revealed that bacterial genera were typically associated with either C. albicans colonization or altered cytokine expression but not with both. The only exception was Veillonella, which was associated with both increased C. albicans colonization and reduced IL-21 expression. Overall, antibiotic-induced changes in the bacterial microbiome were much more consistent determinants of C. albicans colonization than either the GI fungal microbiota or the GI immune response. PMID:25644850

A surrogate-based sensitivity quantification and Bayesian inversion of a regional groundwater flow model

NASA Astrophysics Data System (ADS)

Chen, Mingjie; Izady, Azizallah; Abdalla, Osman A.; Amerjeed, Mansoor

2018-02-01

Bayesian inference using Markov Chain Monte Carlo (MCMC) provides an explicit framework for stochastic calibration of hydrogeologic models accounting for uncertainties; however, the MCMC sampling entails a large number of model calls, and could easily become computationally unwieldy if the high-fidelity hydrogeologic model simulation is time consuming. This study proposes a surrogate-based Bayesian framework to address this notorious issue, and illustrates the methodology by inverse modeling a regional MODFLOW model. The high-fidelity groundwater model is approximated by a fast statistical model using Bagging Multivariate Adaptive Regression Spline (BMARS) algorithm, and hence the MCMC sampling can be efficiently performed. In this study, the MODFLOW model is developed to simulate the groundwater flow in an arid region of Oman consisting of mountain-coast aquifers, and used to run representative simulations to generate training dataset for BMARS model construction. A BMARS-based Sobol' method is also employed to efficiently calculate input parameter sensitivities, which are used to evaluate and rank their importance for the groundwater flow model system. According to sensitivity analysis, insensitive parameters are screened out of Bayesian inversion of the MODFLOW model, further saving computing efforts. The posterior probability distribution of input parameters is efficiently inferred from the prescribed prior distribution using observed head data, demonstrating that the presented BMARS-based Bayesian framework is an efficient tool to reduce parameter uncertainties of a groundwater system.

A Bayesian model for estimating multi-state disease progression.

PubMed

Shen, Shiwen; Han, Simon X; Petousis, Panayiotis; Weiss, Robert E; Meng, Frank; Bui, Alex A T; Hsu, William

2017-02-01

A growing number of individuals who are considered at high risk of cancer are now routinely undergoing population screening. However, noted harms such as radiation exposure, overdiagnosis, and overtreatment underscore the need for better temporal models that predict who should be screened and at what frequency. The mean sojourn time (MST), an average duration period when a tumor can be detected by imaging but with no observable clinical symptoms, is a critical variable for formulating screening policy. Estimation of MST has been long studied using continuous Markov model (CMM) with Maximum likelihood estimation (MLE). However, a lot of traditional methods assume no observation error of the imaging data, which is unlikely and can bias the estimation of the MST. In addition, the MLE may not be stably estimated when data is sparse. Addressing these shortcomings, we present a probabilistic modeling approach for periodic cancer screening data. We first model the cancer state transition using a three state CMM model, while simultaneously considering observation error. We then jointly estimate the MST and observation error within a Bayesian framework. We also consider the inclusion of covariates to estimate individualized rates of disease progression. Our approach is demonstrated on participants who underwent chest x-ray screening in the National Lung Screening Trial (NLST) and validated using posterior predictive p-values and Pearson's chi-square test. Our model demonstrates more accurate and sensible estimates of MST in comparison to MLE. Copyright © 2016 Elsevier Ltd. All rights reserved.

Predicting the Future as Bayesian Inference: People Combine Prior Knowledge with Observations when Estimating Duration and Extent

ERIC Educational Resources Information Center

Griffiths, Thomas L.; Tenenbaum, Joshua B.

2011-01-01

Predicting the future is a basic problem that people have to solve every day and a component of planning, decision making, memory, and causal reasoning. In this article, we present 5 experiments testing a Bayesian model of predicting the duration or extent of phenomena from their current state. This Bayesian model indicates how people should…

Variations on Bayesian Prediction and Inference

DTIC Science & Technology

2016-05-09

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

Posterior Predictive Model Checking in Bayesian Networks

ERIC Educational Resources Information Center

Crawford, Aaron

2014-01-01

This simulation study compared the utility of various discrepancy measures within a posterior predictive model checking (PPMC) framework for detecting different types of data-model misfit in multidimensional Bayesian network (BN) models. The investigated conditions were motivated by an applied research program utilizing an operational complex…

Metrics for evaluating performance and uncertainty of Bayesian network models

Treesearch

Bruce G. Marcot

2012-01-01

This paper presents a selected set of existing and new metrics for gauging Bayesian network model performance and uncertainty. Selected existing and new metrics are discussed for conducting model sensitivity analysis (variance reduction, entropy reduction, case file simulation); evaluating scenarios (influence analysis); depicting model complexity (numbers of model...

Technical note: Bayesian calibration of dynamic ruminant nutrition models.

PubMed

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

2016-08-01

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

Bayesian logistic regression approaches to predict incorrect DRG assignment.

PubMed

Suleiman, Mani; Demirhan, Haydar; Boyd, Leanne; Girosi, Federico; Aksakalli, Vural

2018-05-07

Episodes of care involving similar diagnoses and treatments and requiring similar levels of resource utilisation are grouped to the same Diagnosis-Related Group (DRG). In jurisdictions which implement DRG based payment systems, DRGs are a major determinant of funding for inpatient care. Hence, service providers often dedicate auditing staff to the task of checking that episodes have been coded to the correct DRG. The use of statistical models to estimate an episode's probability of DRG error can significantly improve the efficiency of clinical coding audits. This study implements Bayesian logistic regression models with weakly informative prior distributions to estimate the likelihood that episodes require a DRG revision, comparing these models with each other and to classical maximum likelihood estimates. All Bayesian approaches had more stable model parameters than maximum likelihood. The best performing Bayesian model improved overall classification per- formance by 6% compared to maximum likelihood, with a 34% gain compared to random classification, respectively. We found that the original DRG, coder and the day of coding all have a significant effect on the likelihood of DRG error. Use of Bayesian approaches has improved model parameter stability and classification accuracy. This method has already lead to improved audit efficiency in an operational capacity.

Assessment of parametric uncertainty for groundwater reactive transport modeling,

USGS Publications Warehouse

Shi, Xiaoqing; Ye, Ming; Curtis, Gary P.; Miller, Geoffery L.; Meyer, Philip D.; Kohler, Matthias; Yabusaki, Steve; Wu, Jichun

2014-01-01

The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM(zs)) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris- and DREAM(ZS)-based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.

Prospective evaluation of a Bayesian model to predict organizational change.

PubMed

Molfenter, Todd; Gustafson, Dave; Kilo, Chuck; Bhattacharya, Abhik; Olsson, Jesper

2005-01-01

This research examines a subjective Bayesian model's ability to predict organizational change outcomes and sustainability of those outcomes for project teams participating in a multi-organizational improvement collaborative.

Automated MRI Cerebellar Size Measurements Using Active Appearance Modeling

PubMed Central

Price, Mathew; Cardenas, Valerie A.; Fein, George

2014-01-01

Although the human cerebellum has been increasingly identified as an important hub that shows potential for helping in the diagnosis of a large spectrum of disorders, such as alcoholism, autism, and fetal alcohol spectrum disorder, the high costs associated with manual segmentation, and low availability of reliable automated cerebellar segmentation tools, has resulted in a limited focus on cerebellar measurement in human neuroimaging studies. We present here the CATK (Cerebellar Analysis Toolkit), which is based on the Bayesian framework implemented in FMRIB’s FIRST. This approach involves training Active Appearance Models (AAM) using hand-delineated examples. CATK can currently delineate the cerebellar hemispheres and three vermal groups (lobules I–V, VI–VII, and VIII–X). Linear registration with the low-resolution MNI152 template is used to provide initial alignment, and Point Distribution Models (PDM) are parameterized using stellar sampling. The Bayesian approach models the relationship between shape and texture through computation of conditionals in the training set. Our method varies from the FIRST framework in that initial fitting is driven by 1D intensity profile matching, and the conditional likelihood function is subsequently used to refine fitting. The method was developed using T1-weighted images from 63 subjects that were imaged and manually labeled: 43 subjects were scanned once and were used for training models, and 20 subjects were imaged twice (with manual labeling applied to both runs) and used to assess reliability and validity. Intraclass correlation analysis shows that CATK is highly reliable (average test-retest ICCs of 0.96), and offers excellent agreement with the gold standard (average validity ICC of 0.87 against manual labels). Comparisons against an alternative atlas-based approach, SUIT (Spatially Unbiased Infratentorial Template), that registers images with a high-resolution template of the cerebellum, show that our AAM approach offers superior reliability and validity. Extensions of CATK to cerebellar hemisphere parcels is envisioned. PMID:25192657

Quantification of uncertainty in aerosol optical thickness retrieval arising from aerosol microphysical model and other sources, applied to Ozone Monitoring Instrument (OMI) measurements

NASA Astrophysics Data System (ADS)

Määttä, A.; Laine, M.; Tamminen, J.; Veefkind, J. P.

2014-05-01

Satellite instruments are nowadays successfully utilised for measuring atmospheric aerosol in many applications as well as in research. Therefore, there is a growing need for rigorous error characterisation of the measurements. Here, we introduce a methodology for quantifying the uncertainty in the retrieval of aerosol optical thickness (AOT). In particular, we concentrate on two aspects: uncertainty due to aerosol microphysical model selection and uncertainty due to imperfect forward modelling. We apply the introduced methodology for aerosol optical thickness retrieval of the Ozone Monitoring Instrument (OMI) on board NASA's Earth Observing System (EOS) Aura satellite, launched in 2004. We apply statistical methodologies that improve the uncertainty estimates of the aerosol optical thickness retrieval by propagating aerosol microphysical model selection and forward model error more realistically. For the microphysical model selection problem, we utilise Bayesian model selection and model averaging methods. Gaussian processes are utilised to characterise the smooth systematic discrepancies between the measured and modelled reflectances (i.e. residuals). The spectral correlation is composed empirically by exploring a set of residuals. The operational OMI multi-wavelength aerosol retrieval algorithm OMAERO is used for cloud-free, over-land pixels of the OMI instrument with the additional Bayesian model selection and model discrepancy techniques introduced here. The method and improved uncertainty characterisation is demonstrated by several examples with different aerosol properties: weakly absorbing aerosols, forest fires over Greece and Russia, and Sahara desert dust. The statistical methodology presented is general; it is not restricted to this particular satellite retrieval application.

Spatiotemporal modeling of ozone levels in Quebec (Canada): a comparison of kriging, land-use regression (LUR), and combined Bayesian maximum entropy-LUR approaches.

PubMed

Adam-Poupart, Ariane; Brand, Allan; Fournier, Michel; Jerrett, Michael; Smargiassi, Audrey

2014-09-01

Ambient air ozone (O3) is a pulmonary irritant that has been associated with respiratory health effects including increased lung inflammation and permeability, airway hyperreactivity, respiratory symptoms, and decreased lung function. Estimation of O3 exposure is a complex task because the pollutant exhibits complex spatiotemporal patterns. To refine the quality of exposure estimation, various spatiotemporal methods have been developed worldwide. We sought to compare the accuracy of three spatiotemporal models to predict summer ground-level O3 in Quebec, Canada. We developed a land-use mixed-effects regression (LUR) model based on readily available data (air quality and meteorological monitoring data, road networks information, latitude), a Bayesian maximum entropy (BME) model incorporating both O3 monitoring station data and the land-use mixed model outputs (BME-LUR), and a kriging method model based only on available O3 monitoring station data (BME kriging). We performed leave-one-station-out cross-validation and visually assessed the predictive capability of each model by examining the mean temporal and spatial distributions of the average estimated errors. The BME-LUR was the best predictive model (R2 = 0.653) with the lowest root mean-square error (RMSE ;7.06 ppb), followed by the LUR model (R2 = 0.466, RMSE = 8.747) and the BME kriging model (R2 = 0.414, RMSE = 9.164). Our findings suggest that errors of estimation in the interpolation of O3 concentrations with BME can be greatly reduced by incorporating outputs from a LUR model developed with readily available data.

Comparing models of the periodic variations in spin-down and beamwidth for PSR B1828-11

NASA Astrophysics Data System (ADS)

Ashton, G.; Jones, D. I.; Prix, R.

2016-05-01

We build a framework using tools from Bayesian data analysis to evaluate models explaining the periodic variations in spin-down and beamwidth of PSR B1828-11. The available data consist of the time-averaged spin-down rate, which displays a distinctive double-peaked modulation, and measurements of the beamwidth. Two concepts exist in the literature that are capable of explaining these variations; we formulate predictive models from these and quantitatively compare them. The first concept is phenomenological and stipulates that the magnetosphere undergoes periodic switching between two metastable states as first suggested by Lyne et al. The second concept, precession, was first considered as a candidate for the modulation of B1828-11 by Stairs et al. We quantitatively compare models built from these concepts using a Bayesian odds ratio. Because the phenomenological switching model itself was informed by these data in the first place, it is difficult to specify appropriate parameter-space priors that can be trusted for an unbiased model comparison. Therefore, we first perform a parameter estimation using the spin-down data, and then use the resulting posterior distributions as priors for model comparison on the beamwidth data. We find that a precession model with a simple circular Gaussian beam geometry fails to appropriately describe the data, while allowing for a more general beam geometry provides a good fit to the data. The resulting odds between the precession model (with a general beam geometry) and the switching model are estimated as 102.7±0.5 in favour of the precession model.

Factors contributing to academic achievement: a Bayesian structure equation modelling study

NASA Astrophysics Data System (ADS)

Payandeh Najafabadi, Amir T.; Omidi Najafabadi, Maryam; Farid-Rohani, Mohammad Reza

2013-06-01

In Iran, high school graduates enter university after taking a very difficult entrance exam called the Konkoor. Therefore, only the top-performing students are admitted by universities to continue their bachelor's education in statistics. Surprisingly, statistically, most of such students fall into the following categories: (1) do not succeed in their education despite their excellent performance on the Konkoor and in high school; (2) graduate with a grade point average (GPA) that is considerably lower than their high school GPA; (3) continue their master's education in majors other than statistics and (4) try to find jobs unrelated to statistics. This article employs the well-known and powerful statistical technique, the Bayesian structural equation modelling (SEM), to study the academic success of recent graduates who have studied statistics at Shahid Beheshti University in Iran. This research: (i) considered academic success as a latent variable, which was measured by GPA and other academic success (see below) of students in the target population; (ii) employed the Bayesian SEM, which works properly for small sample sizes and ordinal variables; (iii), which is taken from the literature, developed five main factors that affected academic success and (iv) considered several standard psychological tests and measured characteristics such as 'self-esteem' and 'anxiety'. We then study the impact of such factors on the academic success of the target population. Six factors that positively impact student academic success were identified in the following order of relative impact (from greatest to least): 'Teaching-Evaluation', 'Learner', 'Environment', 'Family', 'Curriculum' and 'Teaching Knowledge'. Particularly, influential variables within each factor have also been noted.

Code-division multiple-access multiuser demodulator by using quantum fluctuations.

PubMed

Otsubo, Yosuke; Inoue, Jun-Ichi; Nagata, Kenji; Okada, Masato

2014-07-01

We examine the average-case performance of a code-division multiple-access (CDMA) multiuser demodulator in which quantum fluctuations are utilized to demodulate the original message within the context of Bayesian inference. The quantum fluctuations are built into the system as a transverse field in the infinite-range Ising spin glass model. We evaluate the performance measurements by using statistical mechanics. We confirm that the CDMA multiuser modulator using quantum fluctuations achieve roughly the same performance as the conventional CDMA multiuser modulator through thermal fluctuations on average. We also find that the relationship between the quality of the original information retrieval and the amplitude of the transverse field is somehow a "universal feature" in typical probabilistic information processing, viz., in image restoration, error-correcting codes, and CDMA multiuser demodulation.

Code-division multiple-access multiuser demodulator by using quantum fluctuations

NASA Astrophysics Data System (ADS)

Otsubo, Yosuke; Inoue, Jun-ichi; Nagata, Kenji; Okada, Masato

2014-07-01

We examine the average-case performance of a code-division multiple-access (CDMA) multiuser demodulator in which quantum fluctuations are utilized to demodulate the original message within the context of Bayesian inference. The quantum fluctuations are built into the system as a transverse field in the infinite-range Ising spin glass model. We evaluate the performance measurements by using statistical mechanics. We confirm that the CDMA multiuser modulator using quantum fluctuations achieve roughly the same performance as the conventional CDMA multiuser modulator through thermal fluctuations on average. We also find that the relationship between the quality of the original information retrieval and the amplitude of the transverse field is somehow a "universal feature" in typical probabilistic information processing, viz., in image restoration, error-correcting codes, and CDMA multiuser demodulation.

A mathematical model approach toward combining information from multiple image projections of the same patient

NASA Astrophysics Data System (ADS)

Chawla, Amarpreet S.; Samei, Ehsan; Abbey, Craig

2007-03-01

In this study, we used a mathematical observer model to combine information obtained from multiple angular projections of the same breast to determine the overall detection performance of a multi-projection breast imaging system in detectability of a simulated mass. 82 subjects participated in the study and 25 angular projections of each breast were acquired. Projections from a simulated 3 mm 3-D lesion were added to the projection images. The lesion was assumed to be embedded in the compressed breast at a distance of 3 cm from the detector. Hotelling observer with Laguerre-Gauss channels (LG CHO) was applied to each image. Detectability was analyzed in terms of ROC curves and the area under ROC curves (AUC). The critical question studied is how to best integrate the individual decision variables across multiple (correlated) views. Towards that end, three different methods were investigated. Specifically, 1) ROCs from different projections were simply averaged; 2) the test statistics from different projections were averaged; and 3) a Bayesian decision fusion rule was used. Finally, AUC of the combined ROC was used as a parameter to optimize the acquisition parameters to maximize the performance of the system. It was found that the Bayesian decision fusion technique performs better than the other two techniques and likely offers the best approximation of the diagnostic process. Furthermore, if the total dose level is held constant at 1/25th of dual-view mammographic screening dose, the highest detectability performance is observed when considering only two projections spread along an angular span of 11.4°.

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

NASA Astrophysics Data System (ADS)

Melendez, Jordan; Wesolowski, Sarah; Furnstahl, Dick

2017-09-01

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

A 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 Bayesian model averaging method for improving SMT phrase table

NASA Astrophysics Data System (ADS)

Duan, Nan

2013-03-01

Previous methods on improving translation quality by employing multiple SMT models usually carry out as a second-pass decision procedure on hypotheses from multiple systems using extra features instead of using features in existing models in more depth. In this paper, we propose translation model generalization (TMG), an approach that updates probability feature values for the translation model being used based on the model itself and a set of auxiliary models, aiming to alleviate the over-estimation problem and enhance translation quality in the first-pass decoding phase. We validate our approach for translation models based on auxiliary models built by two different ways. We also introduce novel probability variance features into the log-linear models for further improvements. We conclude our approach can be developed independently and integrated into current SMT pipeline directly. We demonstrate BLEU improvements on the NIST Chinese-to-English MT tasks for single-system decodings.

Bayesian methods for characterizing unknown parameters of material models

DOE PAGES

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

2016-02-04

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed tomore » characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.« less

Bayesian methods for characterizing unknown parameters of material models

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

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed tomore » characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.« less

Bayesian methods in reliability

NASA Astrophysics Data System (ADS)

Sander, P.; Badoux, R.

1991-11-01

The present proceedings from a course on Bayesian methods in reliability encompasses Bayesian statistical methods and their computational implementation, models for analyzing censored data from nonrepairable systems, the traits of repairable systems and growth models, the use of expert judgment, and a review of the problem of forecasting software reliability. Specific issues addressed include the use of Bayesian methods to estimate the leak rate of a gas pipeline, approximate analyses under great prior uncertainty, reliability estimation techniques, and a nonhomogeneous Poisson process. Also addressed are the calibration sets and seed variables of expert judgment systems for risk assessment, experimental illustrations of the use of expert judgment for reliability testing, and analyses of the predictive quality of software-reliability growth models such as the Weibull order statistics.

Intelligent Decisions Need Intelligent Choice of Models and Data - a Bayesian Justifiability Analysis for Models with Vastly Different Complexity

NASA Astrophysics Data System (ADS)

Nowak, W.; Schöniger, A.; Wöhling, T.; Illman, W. A.

2016-12-01

Model-based decision support requires justifiable models with good predictive capabilities. This, in turn, calls for a fine adjustment between predictive accuracy (small systematic model bias that can be achieved with rather complex models), and predictive precision (small predictive uncertainties that can be achieved with simpler models with fewer parameters). The implied complexity/simplicity trade-off depends on the availability of informative data for calibration. If not available, additional data collection can be planned through optimal experimental design. We present a model justifiability analysis that can compare models of vastly different complexity. It rests on Bayesian model averaging (BMA) to investigate the complexity/performance trade-off dependent on data availability. Then, we disentangle the complexity component from the performance component. We achieve this by replacing actually observed data by realizations of synthetic data predicted by the models. This results in a "model confusion matrix". Based on this matrix, the modeler can identify the maximum model complexity that can be justified by the available (or planned) amount and type of data. As a side product, the matrix quantifies model (dis-)similarity. We apply this analysis to aquifer characterization via hydraulic tomography, comparing four models with a vastly different number of parameters (from a homogeneous model to geostatistical random fields). As a testing scenario, we consider hydraulic tomography data. Using subsets of these data, we determine model justifiability as a function of data set size. The test case shows that geostatistical parameterization requires a substantial amount of hydraulic tomography data to be justified, while a zonation-based model can be justified with more limited data set sizes. The actual model performance (as opposed to model justifiability), however, depends strongly on the quality of prior geological information.

Bayesian accounts of covert selective attention: A tutorial review.

PubMed

Vincent, Benjamin T

2015-05-01

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

Bayesian Action–Perception Computational Model: Interaction of Production and Recognition of Cursive Letters

PubMed Central

Gilet, Estelle; Diard, Julien; Bessière, Pierre

2011-01-01

In this paper, we study the collaboration of perception and action representations involved in cursive letter recognition and production. We propose a mathematical formulation for the whole perception–action loop, based on probabilistic modeling and Bayesian inference, which we call the Bayesian Action–Perception (BAP) model. Being a model of both perception and action processes, the purpose of this model is to study the interaction of these processes. More precisely, the model includes a feedback loop from motor production, which implements an internal simulation of movement. Motor knowledge can therefore be involved during perception tasks. In this paper, we formally define the BAP model and show how it solves the following six varied cognitive tasks using Bayesian inference: i) letter recognition (purely sensory), ii) writer recognition, iii) letter production (with different effectors), iv) copying of trajectories, v) copying of letters, and vi) letter recognition (with internal simulation of movements). We present computer simulations of each of these cognitive tasks, and discuss experimental predictions and theoretical developments. PMID:21674043

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

PubMed

Duarte, Belmiro P M; Wong, Weng Kee

2015-08-01

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

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

PubMed Central

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

2014-01-01

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

Bayesian Chance-Constrained Hydraulic Barrier Design under Geological Structure Uncertainty.

PubMed

Chitsazan, Nima; Pham, Hai V; Tsai, Frank T-C

2015-01-01

The groundwater community has widely recognized geological structure uncertainty as a major source of model structure uncertainty. Previous studies in aquifer remediation design, however, rarely discuss the impact of geological structure uncertainty. This study combines chance-constrained (CC) programming with Bayesian model averaging (BMA) as a BMA-CC framework to assess the impact of geological structure uncertainty in remediation design. To pursue this goal, the BMA-CC method is compared with traditional CC programming that only considers model parameter uncertainty. The BMA-CC method is employed to design a hydraulic barrier to protect public supply wells of the Government St. pump station from salt water intrusion in the "1500-foot" sand and the "1700-foot" sand of the Baton Rouge area, southeastern Louisiana. To address geological structure uncertainty, three groundwater models based on three different hydrostratigraphic architectures are developed. The results show that using traditional CC programming overestimates design reliability. The results also show that at least five additional connector wells are needed to achieve more than 90% design reliability level. The total amount of injected water from the connector wells is higher than the total pumpage of the protected public supply wells. While reducing the injection rate can be achieved by reducing the reliability level, the study finds that the hydraulic barrier design to protect the Government St. pump station may not be economically attractive. © 2014, National Ground Water Association.

A systematic review of Bayesian articles in psychology: The last 25 years.

PubMed

van de Schoot, Rens; Winter, Sonja D; Ryan, Oisín; Zondervan-Zwijnenburg, Mariëlle; Depaoli, Sarah

2017-06-01

Although the statistical tools most often used by researchers in the field of psychology over the last 25 years are based on frequentist statistics, it is often claimed that the alternative Bayesian approach to statistics is gaining in popularity. In the current article, we investigated this claim by performing the very first systematic review of Bayesian psychological articles published between 1990 and 2015 (n = 1,579). We aim to provide a thorough presentation of the role Bayesian statistics plays in psychology. This historical assessment allows us to identify trends and see how Bayesian methods have been integrated into psychological research in the context of different statistical frameworks (e.g., hypothesis testing, cognitive models, IRT, SEM, etc.). We also describe take-home messages and provide "big-picture" recommendations to the field as Bayesian statistics becomes more popular. Our review indicated that Bayesian statistics is used in a variety of contexts across subfields of psychology and related disciplines. There are many different reasons why one might choose to use Bayes (e.g., the use of priors, estimating otherwise intractable models, modeling uncertainty, etc.). We found in this review that the use of Bayes has increased and broadened in the sense that this methodology can be used in a flexible manner to tackle many different forms of questions. We hope this presentation opens the door for a larger discussion regarding the current state of Bayesian statistics, as well as future trends. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

A Gibbs sampler for Bayesian analysis of site-occupancy data

USGS Publications Warehouse

Dorazio, Robert M.; Rodriguez, Daniel Taylor

2012-01-01

1. A Bayesian analysis of site-occupancy data containing covariates of species occurrence and species detection probabilities is usually completed using Markov chain Monte Carlo methods in conjunction with software programs that can implement those methods for any statistical model, not just site-occupancy models. Although these software programs are quite flexible, considerable experience is often required to specify a model and to initialize the Markov chain so that summaries of the posterior distribution can be estimated efficiently and accurately. 2. As an alternative to these programs, we develop a Gibbs sampler for Bayesian analysis of site-occupancy data that include covariates of species occurrence and species detection probabilities. This Gibbs sampler is based on a class of site-occupancy models in which probabilities of species occurrence and detection are specified as probit-regression functions of site- and survey-specific covariate measurements. 3. To illustrate the Gibbs sampler, we analyse site-occupancy data of the blue hawker, Aeshna cyanea (Odonata, Aeshnidae), a common dragonfly species in Switzerland. Our analysis includes a comparison of results based on Bayesian and classical (non-Bayesian) methods of inference. We also provide code (based on the R software program) for conducting Bayesian and classical analyses of site-occupancy data.

Constraints on Average Radial Anisotropy in the Lower Mantle

NASA Astrophysics Data System (ADS)

Trampert, J.; De Wit, R. W. L.; Kaeufl, P.; Valentine, A. P.

2014-12-01

Quantifying uncertainties in seismological models is challenging, yet ideally quality assessment is an integral part of the inverse method. We invert centre frequencies for spheroidal and toroidal modes for three parameters of average radial anisotropy, density and P- and S-wave velocities in the lower mantle. We adopt a Bayesian machine learning approach to extract the information on the earth model that is available in the normal mode data. The method is flexible and allows us to infer probability density functions (pdfs), which provide a quantitative description of our knowledge of the individual earth model parameters. The parameters describing shear- and P-wave anisotropy show little deviations from isotropy, but the intermediate parameter η carries robust information on negative anisotropy of ~1% below 1900 km depth. The mass density in the deep mantle (below 1900 km) shows clear positive deviations from existing models. Other parameters (P- and shear-wave velocities) are close to PREM. Our results require that the average mantle is about 150K colder than commonly assumed adiabats and consist of a mixture of about 60% perovskite and 40% ferropericlase containing 10-15% iron. The anisotropy favours a specific orientation of the two minerals. This observation has important consequences for the nature of mantle flow.

Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A Jet-in-Crossflow Case Study

DOE PAGES

Ray, Jaideep; Lefantzi, Sophia; Arunajatesan, Srinivasan; ...

2017-09-07

In this paper, we demonstrate a statistical procedure for learning a high-order eddy viscosity model (EVM) from experimental data and using it to improve the predictive skill of a Reynolds-averaged Navier–Stokes (RANS) simulator. The method is tested in a three-dimensional (3D), transonic jet-in-crossflow (JIC) configuration. The process starts with a cubic eddy viscosity model (CEVM) developed for incompressible flows. It is fitted to limited experimental JIC data using shrinkage regression. The shrinkage process removes all the terms from the model, except an intercept, a linear term, and a quadratic one involving the square of the vorticity. The shrunk eddy viscositymore » model is implemented in an RANS simulator and calibrated, using vorticity measurements, to infer three parameters. The calibration is Bayesian and is solved using a Markov chain Monte Carlo (MCMC) method. A 3D probability density distribution for the inferred parameters is constructed, thus quantifying the uncertainty in the estimate. The phenomenal cost of using a 3D flow simulator inside an MCMC loop is mitigated by using surrogate models (“curve-fits”). A support vector machine classifier (SVMC) is used to impose our prior belief regarding parameter values, specifically to exclude nonphysical parameter combinations. The calibrated model is compared, in terms of its predictive skill, to simulations using uncalibrated linear and CEVMs. Finally, we find that the calibrated model, with one quadratic term, is more accurate than the uncalibrated simulator. The model is also checked at a flow condition at which the model was not calibrated.« less

Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A Jet-in-Crossflow Case Study

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

Ray, Jaideep; Lefantzi, Sophia; Arunajatesan, Srinivasan

In this paper, we demonstrate a statistical procedure for learning a high-order eddy viscosity model (EVM) from experimental data and using it to improve the predictive skill of a Reynolds-averaged Navier–Stokes (RANS) simulator. The method is tested in a three-dimensional (3D), transonic jet-in-crossflow (JIC) configuration. The process starts with a cubic eddy viscosity model (CEVM) developed for incompressible flows. It is fitted to limited experimental JIC data using shrinkage regression. The shrinkage process removes all the terms from the model, except an intercept, a linear term, and a quadratic one involving the square of the vorticity. The shrunk eddy viscositymore » model is implemented in an RANS simulator and calibrated, using vorticity measurements, to infer three parameters. The calibration is Bayesian and is solved using a Markov chain Monte Carlo (MCMC) method. A 3D probability density distribution for the inferred parameters is constructed, thus quantifying the uncertainty in the estimate. The phenomenal cost of using a 3D flow simulator inside an MCMC loop is mitigated by using surrogate models (“curve-fits”). A support vector machine classifier (SVMC) is used to impose our prior belief regarding parameter values, specifically to exclude nonphysical parameter combinations. The calibrated model is compared, in terms of its predictive skill, to simulations using uncalibrated linear and CEVMs. Finally, we find that the calibrated model, with one quadratic term, is more accurate than the uncalibrated simulator. The model is also checked at a flow condition at which the model was not calibrated.« less

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

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 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.

Bayesian Estimation of the Logistic Positive Exponent IRT Model

ERIC Educational Resources Information Center

Bolfarine, Heleno; Bazan, Jorge Luis

2010-01-01

A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric…

The Misidentified Identifiability Problem of Bayesian Knowledge Tracing

ERIC Educational Resources Information Center

Doroudi, Shayan; Brunskill, Emma

2017-01-01

In this paper, we investigate two purported problems with Bayesian Knowledge Tracing (BKT), a popular statistical model of student learning: "identifiability" and "semantic model degeneracy." In 2007, Beck and Chang stated that BKT is susceptible to an "identifiability problem"--various models with different…

Common quandaries and their practical solutions in Bayesian network modeling

Treesearch

Bruce G. Marcot

2017-01-01

Use and popularity of Bayesian network (BN) modeling has greatly expanded in recent years, but many common problems remain. Here, I summarize key problems in BN model construction and interpretation,along with suggested practical solutions. Problems in BN model construction include parameterizing probability values, variable definition, complex network structures,...

On the Bayesian Nonparametric Generalization of IRT-Type Models

ERIC Educational Resources Information Center

San Martin, Ernesto; Jara, Alejandro; Rolin, Jean-Marie; Mouchart, Michel

2011-01-01

We study the identification and consistency of Bayesian semiparametric IRT-type models, where the uncertainty on the abilities' distribution is modeled using a prior distribution on the space of probability measures. We show that for the semiparametric Rasch Poisson counts model, simple restrictions ensure the identification of a general…

Estimating micro area behavioural risk factor prevalence from large population-based surveys: a full Bayesian approach.

PubMed

Seliske, L; Norwood, T A; McLaughlin, J R; Wang, S; Palleschi, C; Holowaty, E

2016-06-07

An important public health goal is to decrease the prevalence of key behavioural risk factors, such as tobacco use and obesity. Survey information is often available at the regional level, but heterogeneity within large geographic regions cannot be assessed. Advanced spatial analysis techniques are demonstrated to produce sensible micro area estimates of behavioural risk factors that enable identification of areas with high prevalence. A spatial Bayesian hierarchical model was used to estimate the micro area prevalence of current smoking and excess bodyweight for the Erie-St. Clair region in southwestern Ontario. Estimates were mapped for male and female respondents of five cycles of the Canadian Community Health Survey (CCHS). The micro areas were 2006 Census Dissemination Areas, with an average population of 400-700 people. Two individual-level models were specified: one controlled for survey cycle and age group (model 1), and one controlled for survey cycle, age group and micro area median household income (model 2). Post-stratification was used to derive micro area behavioural risk factor estimates weighted to the population structure. SaTScan analyses were conducted on the granular, postal-code level CCHS data to corroborate findings of elevated prevalence. Current smoking was elevated in two urban areas for both sexes (Sarnia and Windsor), and an additional small community (Chatham) for males only. Areas of excess bodyweight were prevalent in an urban core (Windsor) among males, but not females. Precision of the posterior post-stratified current smoking estimates was improved in model 2, as indicated by narrower credible intervals and a lower coefficient of variation. For excess bodyweight, both models had similar precision. Aggregation of the micro area estimates to CCHS design-based estimates validated the findings. This is among the first studies to apply a full Bayesian model to complex sample survey data to identify micro areas with variation in risk factor prevalence, accounting for spatial correlation and other covariates. Application of micro area analysis techniques helps define areas for public health planning, and may be informative to surveillance and research modeling of relevant chronic disease outcomes.

A menu-driven software package of Bayesian nonparametric (and parametric) mixed models for regression analysis and density estimation.

PubMed

Karabatsos, George

2017-02-01

Most of applied statistics involves regression analysis of data. In practice, it is important to specify a regression model that has minimal assumptions which are not violated by data, to ensure that statistical inferences from the model are informative and not misleading. This paper presents a stand-alone and menu-driven software package, Bayesian Regression: Nonparametric and Parametric Models, constructed from MATLAB Compiler. Currently, this package gives the user a choice from 83 Bayesian models for data analysis. They include 47 Bayesian nonparametric (BNP) infinite-mixture regression models; 5 BNP infinite-mixture models for density estimation; and 31 normal random effects models (HLMs), including normal linear models. Each of the 78 regression models handles either a continuous, binary, or ordinal dependent variable, and can handle multi-level (grouped) data. All 83 Bayesian models can handle the analysis of weighted observations (e.g., for meta-analysis), and the analysis of left-censored, right-censored, and/or interval-censored data. Each BNP infinite-mixture model has a mixture distribution assigned one of various BNP prior distributions, including priors defined by either the Dirichlet process, Pitman-Yor process (including the normalized stable process), beta (two-parameter) process, normalized inverse-Gaussian process, geometric weights prior, dependent Dirichlet process, or the dependent infinite-probits prior. The software user can mouse-click to select a Bayesian model and perform data analysis via Markov chain Monte Carlo (MCMC) sampling. After the sampling completes, the software automatically opens text output that reports MCMC-based estimates of the model's posterior distribution and model predictive fit to the data. Additional text and/or graphical output can be generated by mouse-clicking other menu options. This includes output of MCMC convergence analyses, and estimates of the model's posterior predictive distribution, for selected functionals and values of covariates. The software is illustrated through the BNP regression analysis of real data.

Evaluating experimental design for soil-plant model selection using a Bootstrap Filter and Bayesian model averaging

NASA Astrophysics Data System (ADS)

Wöhling, T.; Schöniger, A.; Geiges, A.; Nowak, W.; Gayler, S.

2013-12-01

The objective selection of appropriate models for realistic simulations of coupled soil-plant processes is a challenging task since the processes are complex, not fully understood at larger scales, and highly non-linear. Also, comprehensive data sets are scarce, and measurements are uncertain. In the past decades, a variety of different models have been developed that exhibit a wide range of complexity regarding their approximation of processes in the coupled model compartments. We present a method for evaluating experimental design for maximum confidence in the model selection task. The method considers uncertainty in parameters, measurements and model structures. Advancing the ideas behind Bayesian Model Averaging (BMA), we analyze the changes in posterior model weights and posterior model choice uncertainty when more data are made available. This allows assessing the power of different data types, data densities and data locations in identifying the best model structure from among a suite of plausible models. The models considered in this study are the crop models CERES, SUCROS, GECROS and SPASS, which are coupled to identical routines for simulating soil processes within the modelling framework Expert-N. The four models considerably differ in the degree of detail at which crop growth and root water uptake are represented. Monte-Carlo simulations were conducted for each of these models considering their uncertainty in soil hydraulic properties and selected crop model parameters. Using a Bootstrap Filter (BF), the models were then conditioned on field measurements of soil moisture, matric potential, leaf-area index, and evapotranspiration rates (from eddy-covariance measurements) during a vegetation period of winter wheat at a field site at the Swabian Alb in Southwestern Germany. Following our new method, we derived model weights when using all data or different subsets thereof. We discuss to which degree the posterior mean outperforms the prior mean and all individual posterior models, how informative the data types were for reducing prediction uncertainty of evapotranspiration and deep drainage, and how well the model structure can be identified based on the different data types and subsets. We further analyze the impact of measurement uncertainty und systematic model errors on the effective sample size of the BF and the resulting model weights.

Relative importance of climatic, geographic and socio-economic determinants of malaria in Malawi

PubMed Central

2013-01-01

Background Malaria transmission is influenced by variations in meteorological conditions, which impact the biology of the parasite and its vector, but also socio-economic conditions, such as levels of urbanization, poverty and education, which impact human vulnerability and vector habitat. The many potential drivers of malaria, both extrinsic, such as climate, and intrinsic, such as population immunity are often difficult to disentangle. This presents a challenge for the modelling of malaria risk in space and time. Methods A statistical mixed model framework is proposed to model malaria risk at the district level in Malawi, using an age-stratified spatio-temporal dataset of malaria cases from July 2004 to June 2011. Several climatic, geographic and socio-economic factors thought to influence malaria incidence were tested in an exploratory model. In order to account for the unobserved confounding factors that influence malaria, which are not accounted for using measured covariates, a generalized linear mixed model was adopted, which included structured and unstructured spatial and temporal random effects. A hierarchical Bayesian framework using Markov chain Monte Carlo simulation was used for model fitting and prediction. Results Using a stepwise model selection procedure, several explanatory variables were identified to have significant associations with malaria including climatic, cartographic and socio-economic data. Once intervention variations, unobserved confounding factors and spatial correlation were considered in a Bayesian framework, a final model emerged with statistically significant predictor variables limited to average precipitation (quadratic relation) and average temperature during the three months previous to the month of interest. Conclusions When modelling malaria risk in Malawi it is important to account for spatial and temporal heterogeneity and correlation between districts. Once observed and unobserved confounding factors are allowed for, precipitation and temperature in the months prior to the malaria season of interest are found to significantly determine spatial and temporal variations of malaria incidence. Climate information was found to improve the estimation of malaria relative risk in 41% of the districts in Malawi, particularly at higher altitudes where transmission is irregular. This highlights the potential value of climate-driven seasonal malaria forecasts. PMID:24228784

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

PubMed

Nowakowska, Marzena

2017-04-01

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

Bayesian learning and the psychology of rule induction

PubMed Central

Endress, Ansgar D.

2014-01-01

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 spell out the underlying assumptions, and to confront them with the empirical results Frank and Tenenbaum (2011) propose to simulate, as well as with novel experiments. While rule-learning is arguably well suited to rational Bayesian approaches, I show that their models are neither psychologically plausible nor ideal observer models. Further, I show that their central assumption is unfounded: humans do not always preferentially learn more specific rules, but, at least in some situations, those rules that happen to be more salient. Even when granting the unsupported assumptions, I show that all of the experiments modeled by Frank and Tenenbaum (2011) either contradict their models, or have a large number of more plausible interpretations. I provide an alternative account of the experimental data based on simple psychological mechanisms, and show that this account both describes the data better, and is easier to falsify. I conclude that, despite the recent surge in Bayesian models of cognitive phenomena, psychological phenomena are best understood by developing and testing psychological theories rather than models that can be fit to virtually any data. PMID:23454791

Robust Bayesian clustering.

PubMed

Archambeau, Cédric; Verleysen, Michel

2007-01-01

A new variational Bayesian learning algorithm for Student-t mixture models is introduced. This algorithm leads to (i) robust density estimation, (ii) robust clustering and (iii) robust automatic model selection. Gaussian mixture models are learning machines which are based on a divide-and-conquer approach. They are commonly used for density estimation and clustering tasks, but are sensitive to outliers. The Student-t distribution has heavier tails than the Gaussian distribution and is therefore less sensitive to any departure of the empirical distribution from Gaussianity. As a consequence, the Student-t distribution is suitable for constructing robust mixture models. In this work, we formalize the Bayesian Student-t mixture model as a latent variable model in a different way from Svensén and Bishop [Svensén, M., & Bishop, C. M. (2005). Robust Bayesian mixture modelling. Neurocomputing, 64, 235-252]. The main difference resides in the fact that it is not necessary to assume a factorized approximation of the posterior distribution on the latent indicator variables and the latent scale variables in order to obtain a tractable solution. Not neglecting the correlations between these unobserved random variables leads to a Bayesian model having an increased robustness. Furthermore, it is expected that the lower bound on the log-evidence is tighter. Based on this bound, the model complexity, i.e. the number of components in the mixture, can be inferred with a higher confidence.

Advances in Bayesian Modeling in Educational Research

ERIC Educational Resources Information Center

Levy, Roy

2016-01-01

In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling…

Bayesian Analysis of Multidimensional Item Response Theory Models: A Discussion and Illustration of Three Response Style Models

ERIC Educational Resources Information Center

Leventhal, Brian C.; Stone, Clement A.

2018-01-01

Interest in Bayesian analysis of item response theory (IRT) models has grown tremendously due to the appeal of the paradigm among psychometricians, advantages of these methods when analyzing complex models, and availability of general-purpose software. Possible models include models which reflect multidimensionality due to designed test structure,…

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.

Tree Biomass Estimation of Chinese fir (Cunninghamia lanceolata) Based on Bayesian Method

PubMed Central

Zhang, Jianguo

2013-01-01

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass. PMID:24278198

Tree biomass estimation of Chinese fir (Cunninghamia lanceolata) based on Bayesian method.

PubMed

Zhang, Xiongqing; Duan, Aiguo; Zhang, Jianguo

2013-01-01

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation W = a(D2H)b was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass.

An ensemble approach to predicting the impact of vaccination on rotavirus disease in Niger.

PubMed

Park, Jaewoo; Goldstein, Joshua; Haran, Murali; Ferrari, Matthew

2017-10-13

Recently developed vaccines provide a new way of controlling rotavirus in sub-Saharan Africa. Models for the transmission dynamics of rotavirus are critical both for estimating current burden from imperfect surveillance and for assessing potential effects of vaccine intervention strategies. We examine rotavirus infection in the Maradi area in southern Niger using hospital surveillance data provided by Epicentre collected over two years. Additionally, a cluster survey of households in the region allows us to estimate the proportion of children with diarrhea who consulted at a health structure. Model fit and future projections are necessarily particular to a given model; thus, where there are competing models for the underlying epidemiology an ensemble approach can account for that uncertainty. We compare our results across several variants of Susceptible-Infectious-Recovered (SIR) compartmental models to quantify the impact of modeling assumptions on our estimates. Model-specific parameters are estimated by Bayesian inference using Markov chain Monte Carlo. We then use Bayesian model averaging to generate ensemble estimates of the current dynamics, including estimates of R 0 , the burden of infection in the region, as well as the impact of vaccination on both the short-term dynamics and the long-term reduction of rotavirus incidence under varying levels of coverage. The ensemble of models predicts that the current burden of severe rotavirus disease is 2.6-3.7% of the population each year and that a 2-dose vaccine schedule achieving 70% coverage could reduce burden by 39-42%. Copyright © 2017. Published by Elsevier Ltd.

Posterior Predictive Bayesian Phylogenetic Model Selection

PubMed Central

Lewis, Paul O.; Xie, Wangang; Chen, Ming-Hui; Fan, Yu; Kuo, Lynn

2014-01-01

We present two distinctly different posterior predictive approaches to Bayesian phylogenetic model selection and illustrate these methods using examples from green algal protein-coding cpDNA sequences and flowering plant rDNA sequences. The Gelfand–Ghosh (GG) approach allows dissection of an overall measure of model fit into components due to posterior predictive variance (GGp) and goodness-of-fit (GGg), which distinguishes this method from the posterior predictive P-value approach. The conditional predictive ordinate (CPO) method provides a site-specific measure of model fit useful for exploratory analyses and can be combined over sites yielding the log pseudomarginal likelihood (LPML) which is useful as an overall measure of model fit. CPO provides a useful cross-validation approach that is computationally efficient, requiring only a sample from the posterior distribution (no additional simulation is required). Both GG and CPO add new perspectives to Bayesian phylogenetic model selection based on the predictive abilities of models and complement the perspective provided by the marginal likelihood (including Bayes Factor comparisons) based solely on the fit of competing models to observed data. [Bayesian; conditional predictive ordinate; CPO; L-measure; LPML; model selection; phylogenetics; posterior predictive.] PMID:24193892

Use of limited data to construct Bayesian networks for probabilistic risk assessment.

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

Groth, Katrina M.; Swiler, Laura Painton

2013-03-01

Probabilistic Risk Assessment (PRA) is a fundamental part of safety/quality assurance for nuclear power and nuclear weapons. Traditional PRA very effectively models complex hardware system risks using binary probabilistic models. However, traditional PRA models are not flexible enough to accommodate non-binary soft-causal factors, such as digital instrumentation&control, passive components, aging, common cause failure, and human errors. Bayesian Networks offer the opportunity to incorporate these risks into the PRA framework. This report describes the results of an early career LDRD project titled %E2%80%9CUse of Limited Data to Construct Bayesian Networks for Probabilistic Risk Assessment%E2%80%9D. The goal of the work was tomore » establish the capability to develop Bayesian Networks from sparse data, and to demonstrate this capability by producing a data-informed Bayesian Network for use in Human Reliability Analysis (HRA) as part of nuclear power plant Probabilistic Risk Assessment (PRA). This report summarizes the research goal and major products of the research.« less

Robust Bayesian Analysis of Heavy-tailed Stochastic Volatility Models using Scale Mixtures of Normal Distributions

PubMed Central

Abanto-Valle, C. A.; Bandyopadhyay, D.; Lachos, V. H.; Enriquez, I.

2009-01-01

A Bayesian analysis of stochastic volatility (SV) models using the class of symmetric scale mixtures of normal (SMN) distributions is considered. In the face of non-normality, this provides an appealing robust alternative to the routine use of the normal distribution. Specific distributions examined include the normal, student-t, slash and the variance gamma distributions. Using a Bayesian paradigm, an efficient Markov chain Monte Carlo (MCMC) algorithm is introduced for parameter estimation. Moreover, the mixing parameters obtained as a by-product of the scale mixture representation can be used to identify outliers. The methods developed are applied to analyze daily stock returns data on S&P500 index. Bayesian model selection criteria as well as out-of- sample forecasting results reveal that the SV models based on heavy-tailed SMN distributions provide significant improvement in model fit as well as prediction to the S&P500 index data over the usual normal model. PMID:20730043

Application of a predictive Bayesian model to environmental accounting.

PubMed

Anex, R P; Englehardt, J D

2001-03-30

Environmental accounting techniques are intended to capture important environmental costs and benefits that are often overlooked in standard accounting practices. Environmental accounting methods themselves often ignore or inadequately represent large but highly uncertain environmental costs and costs conditioned by specific prior events. Use of a predictive Bayesian model is demonstrated for the assessment of such highly uncertain environmental and contingent costs. The predictive Bayesian approach presented generates probability distributions for the quantity of interest (rather than parameters thereof). A spreadsheet implementation of a previously proposed predictive Bayesian model, extended to represent contingent costs, is described and used to evaluate whether a firm should undertake an accelerated phase-out of its PCB containing transformers. Variability and uncertainty (due to lack of information) in transformer accident frequency and severity are assessed simultaneously using a combination of historical accident data, engineering model-based cost estimates, and subjective judgement. Model results are compared using several different risk measures. Use of the model for incorporation of environmental risk management into a company's overall risk management strategy is discussed.

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

A Feature-based Developmental Model of the Infant Brain in Structural MRI

PubMed Central

Toews, Matthew; Wells, William M.; Zöllei, Lilla

2014-01-01

In this paper, anatomical development is modeled as a collection of distinctive image patterns localized in space and time. A Bayesian posterior probability is defined over a random variable of subject age, conditioned on data in the form of scale-invariant image features. The model is automatically learned from a large set of images exhibiting significant variation, used to discover anatomical structure related to age and development, and fit to new images to predict age. The model is applied to a set of 230 infant structural MRIs of 92 subjects acquired at multiple sites over an age range of 8-590 days. Experiments demonstrate that the model can be used to identify age-related anatomical structure, and to predict the age of new subjects with an average error of 72 days. PMID:23286050

An integrated Bayesian model for estimating the long-term health effects of air pollution by fusing modelled and measured pollution data: A case study of nitrogen dioxide concentrations in Scotland.

PubMed

Huang, Guowen; Lee, Duncan; Scott, Marian

2015-01-01

The long-term health effects of air pollution can be estimated using a spatio-temporal ecological study, where the disease data are counts of hospital admissions from populations in small areal units at yearly intervals. Spatially representative pollution concentrations for each areal unit are typically estimated by applying Kriging to data from a sparse monitoring network, or by computing averages over grid level concentrations from an atmospheric dispersion model. We propose a novel fusion model for estimating spatially aggregated pollution concentrations using both the modelled and monitored data, and relate these concentrations to respiratory disease in a new study in Scotland between 2007 and 2011. Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.

A Bayesian modification to the Jelinski-Moranda software reliability growth model

NASA Technical Reports Server (NTRS)

Littlewood, B.; Sofer, A.

1983-01-01

The Jelinski-Moranda (JM) model for software reliability was examined. It is suggested that a major reason for the poor results given by this model is the poor performance of the maximum likelihood method (ML) of parameter estimation. A reparameterization and Bayesian analysis, involving a slight modelling change, are proposed. It is shown that this new Bayesian-Jelinski-Moranda model (BJM) is mathematically quite tractable, and several metrics of interest to practitioners are obtained. The BJM and JM models are compared by using several sets of real software failure data collected and in all cases the BJM model gives superior reliability predictions. A change in the assumption which underlay both models to present the debugging process more accurately is discussed.

Bayesian inference for the distribution of grams of marijuana in a joint.

PubMed

Ridgeway, Greg; Kilmer, Beau

2016-08-01

The average amount of marijuana in a joint is unknown, yet this figure is a critical quantity for creating credible measures of marijuana consumption. It is essential for projecting tax revenues post-legalization, estimating the size of illicit marijuana markets, and learning about how much marijuana users are consuming in order to understand health and behavioral consequences. Arrestee Drug Abuse Monitoring data collected between 2000 and 2010 contain relevant information on 10,628 marijuana transactions, joints and loose marijuana purchases, including the city in which the purchase occurred and the price paid for the marijuana. Using the Brown-Silverman drug pricing model to link marijuana price and weight, we are able to infer the distribution of grams of marijuana in a joint and provide a Bayesian posterior distribution for the mean weight of marijuana in a joint. We estimate that the mean weight of marijuana in a joint is 0.32g (95% Bayesian posterior interval: 0.30-0.35). Our estimate of the mean weight of marijuana in a joint is lower than figures commonly used to make estimates of marijuana consumption. These estimates can be incorporated into drug policy discussions to produce better understanding about illicit marijuana markets, the size of potential legalized marijuana markets, and health and behavior outcomes. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Inverse modeling of Asian (222)Rn flux using surface air (222)Rn concentration.

PubMed

Hirao, Shigekazu; Yamazawa, Hiromi; Moriizumi, Jun

2010-11-01

When used with an atmospheric transport model, the (222)Rn flux distribution estimated in our previous study using soil transport theory caused underestimation of atmospheric (222)Rn concentrations as compared with measurements in East Asia. In this study, we applied a Bayesian synthesis inverse method to produce revised estimates of the annual (222)Rn flux density in Asia by using atmospheric (222)Rn concentrations measured at seven sites in East Asia. The Bayesian synthesis inverse method requires a prior estimate of the flux distribution and its uncertainties. The atmospheric transport model MM5/HIRAT and our previous estimate of the (222)Rn flux distribution as the prior value were used to generate new flux estimates for the eastern half of the Eurasian continent dividing into 10 regions. The (222)Rn flux densities estimated using the Bayesian inversion technique were generally higher than the prior flux densities. The area-weighted average (222)Rn flux density for Asia was estimated to be 33.0 mBq m(-2) s(-1), which is substantially higher than the prior value (16.7 mBq m(-2) s(-1)). The estimated (222)Rn flux densities decrease with increasing latitude as follows: Southeast Asia (36.7 mBq m(-2) s(-1)); East Asia (28.6 mBq m(-2) s(-1)) including China, Korean Peninsula and Japan; and Siberia (14.1 mBq m(-2) s(-1)). Increase of the newly estimated fluxes in Southeast Asia, China, Japan, and the southern part of Eastern Siberia from the prior ones contributed most significantly to improved agreement of the model-calculated concentrations with the atmospheric measurements. The sensitivity analysis of prior flux errors and effects of locally exhaled (222)Rn showed that the estimated fluxes in Northern and Central China, Korea, Japan, and the southern part of Eastern Siberia were robust, but that in Central Asia had a large uncertainty.

Learning Parsimonious Classification Rules from Gene Expression Data Using Bayesian Networks with Local Structure.

PubMed

Lustgarten, Jonathan Lyle; Balasubramanian, Jeya Balaji; Visweswaran, Shyam; Gopalakrishnan, Vanathi

2017-03-01

The comprehensibility of good predictive models learned from high-dimensional gene expression data is attractive because it can lead to biomarker discovery. Several good classifiers provide comparable predictive performance but differ in their abilities to summarize the observed data. We extend a Bayesian Rule Learning (BRL-GSS) algorithm, previously shown to be a significantly better predictor than other classical approaches in this domain. It searches a space of Bayesian networks using a decision tree representation of its parameters with global constraints, and infers a set of IF-THEN rules. The number of parameters and therefore the number of rules are combinatorial to the number of predictor variables in the model. We relax these global constraints to a more generalizable local structure (BRL-LSS). BRL-LSS entails more parsimonious set of rules because it does not have to generate all combinatorial rules. The search space of local structures is much richer than the space of global structures. We design the BRL-LSS with the same worst-case time-complexity as BRL-GSS while exploring a richer and more complex model space. We measure predictive performance using Area Under the ROC curve (AUC) and Accuracy. We measure model parsimony performance by noting the average number of rules and variables needed to describe the observed data. We evaluate the predictive and parsimony performance of BRL-GSS, BRL-LSS and the state-of-the-art C4.5 decision tree algorithm, across 10-fold cross-validation using ten microarray gene-expression diagnostic datasets. In these experiments, we observe that BRL-LSS is similar to BRL-GSS in terms of predictive performance, while generating a much more parsimonious set of rules to explain the same observed data. BRL-LSS also needs fewer variables than C4.5 to explain the data with similar predictive performance. We also conduct a feasibility study to demonstrate the general applicability of our BRL methods on the newer RNA sequencing gene-expression data.

Optimal population prediction of sandhill crane recruitment based on climate-mediated habitat limitations

USGS Publications Warehouse

Gerber, Brian D.; Kendall, William L.; Hooten, Mevin B.; Dubovsky, James A.; Drewien, Roderick C.

2015-01-01

Prediction is fundamental to scientific enquiry and application; however, ecologists tend to favour explanatory modelling. We discuss a predictive modelling framework to evaluate ecological hypotheses and to explore novel/unobserved environmental scenarios to assist conservation and management decision-makers. We apply this framework to develop an optimal predictive model for juvenile (<1 year old) sandhill crane Grus canadensis recruitment of the Rocky Mountain Population (RMP). We consider spatial climate predictors motivated by hypotheses of how drought across multiple time-scales and spring/summer weather affects recruitment.Our predictive modelling framework focuses on developing a single model that includes all relevant predictor variables, regardless of collinearity. This model is then optimized for prediction by controlling model complexity using a data-driven approach that marginalizes or removes irrelevant predictors from the model. Specifically, we highlight two approaches of statistical regularization, Bayesian least absolute shrinkage and selection operator (LASSO) and ridge regression.Our optimal predictive Bayesian LASSO and ridge regression models were similar and on average 37% superior in predictive accuracy to an explanatory modelling approach. Our predictive models confirmed a priori hypotheses that drought and cold summers negatively affect juvenile recruitment in the RMP. The effects of long-term drought can be alleviated by short-term wet spring–summer months; however, the alleviation of long-term drought has a much greater positive effect on juvenile recruitment. The number of freezing days and snowpack during the summer months can also negatively affect recruitment, while spring snowpack has a positive effect.Breeding habitat, mediated through climate, is a limiting factor on population growth of sandhill cranes in the RMP, which could become more limiting with a changing climate (i.e. increased drought). These effects are likely not unique to cranes. The alteration of hydrological patterns and water levels by drought may impact many migratory, wetland nesting birds in the Rocky Mountains and beyond.Generalizable predictive models (trained by out-of-sample fit and based on ecological hypotheses) are needed by conservation and management decision-makers. Statistical regularization improves predictions and provides a general framework for fitting models with a large number of predictors, even those with collinearity, to simultaneously identify an optimal predictive model while conducting rigorous Bayesian model selection. Our framework is important for understanding population dynamics under a changing climate and has direct applications for making harvest and habitat management decisions.

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.

Sequential Inverse Problems Bayesian Principles and the Logistic Map Example

NASA Astrophysics Data System (ADS)

Duan, Lian; Farmer, Chris L.; Moroz, Irene M.

2010-09-01

Bayesian statistics provides a general framework for solving inverse problems, but is not without interpretation and implementation problems. This paper discusses difficulties arising from the fact that forward models are always in error to some extent. Using a simple example based on the one-dimensional logistic map, we argue that, when implementation problems are minimal, the Bayesian framework is quite adequate. In this paper the Bayesian Filter is shown to be able to recover excellent state estimates in the perfect model scenario (PMS) and to distinguish the PMS from the imperfect model scenario (IMS). Through a quantitative comparison of the way in which the observations are assimilated in both the PMS and the IMS scenarios, we suggest that one can, sometimes, measure the degree of imperfection.

Multi-model ensemble hydrologic prediction using Bayesian model averaging

NASA Astrophysics Data System (ADS)

Duan, Qingyun; Ajami, Newsha K.; Gao, Xiaogang; Sorooshian, Soroosh

2007-05-01

Multi-model ensemble strategy is a means to exploit the diversity of skillful predictions from different models. This paper studies the use of Bayesian model averaging (BMA) scheme to develop more skillful and reliable probabilistic hydrologic predictions from multiple competing predictions made by several hydrologic models. BMA is a statistical procedure that infers consensus predictions by weighing individual predictions based on their probabilistic likelihood measures, with the better performing predictions receiving higher weights than the worse performing ones. Furthermore, BMA provides a more reliable description of the total predictive uncertainty than the original ensemble, leading to a sharper and better calibrated probability density function (PDF) for the probabilistic predictions. In this study, a nine-member ensemble of hydrologic predictions was used to test and evaluate the BMA scheme. This ensemble was generated by calibrating three different hydrologic models using three distinct objective functions. These objective functions were chosen in a way that forces the models to capture certain aspects of the hydrograph well (e.g., peaks, mid-flows and low flows). Two sets of numerical experiments were carried out on three test basins in the US to explore the best way of using the BMA scheme. In the first set, a single set of BMA weights was computed to obtain BMA predictions, while the second set employed multiple sets of weights, with distinct sets corresponding to different flow intervals. In both sets, the streamflow values were transformed using Box-Cox transformation to ensure that the probability distribution of the prediction errors is approximately Gaussian. A split sample approach was used to obtain and validate the BMA predictions. The test results showed that BMA scheme has the advantage of generating more skillful and equally reliable probabilistic predictions than original ensemble. The performance of the expected BMA predictions in terms of daily root mean square error (DRMS) and daily absolute mean error (DABS) is generally superior to that of the best individual predictions. Furthermore, the BMA predictions employing multiple sets of weights are generally better than those using single set of weights.

Bayesian state space models for dynamic genetic network construction across multiple tissues.

PubMed

Liang, Yulan; Kelemen, Arpad

2016-08-01

Construction of gene-gene interaction networks and potential pathways is a challenging and important problem in genomic research for complex diseases while estimating the dynamic changes of the temporal correlations and non-stationarity are the keys in this process. In this paper, we develop dynamic state space models with hierarchical Bayesian settings to tackle this challenge for inferring the dynamic profiles and genetic networks associated with disease treatments. We treat both the stochastic transition matrix and the observation matrix time-variant and include temporal correlation structures in the covariance matrix estimations in the multivariate Bayesian state space models. The unevenly spaced short time courses with unseen time points are treated as hidden state variables. Hierarchical Bayesian approaches with various prior and hyper-prior models with Monte Carlo Markov Chain and Gibbs sampling algorithms are used to estimate the model parameters and the hidden state variables. We apply the proposed Hierarchical Bayesian state space models to multiple tissues (liver, skeletal muscle, and kidney) Affymetrix time course data sets following corticosteroid (CS) drug administration. Both simulation and real data analysis results show that the genomic changes over time and gene-gene interaction in response to CS treatment can be well captured by the proposed models. The proposed dynamic Hierarchical Bayesian state space modeling approaches could be expanded and applied to other large scale genomic data, such as next generation sequence (NGS) combined with real time and time varying electronic health record (EHR) for more comprehensive and robust systematic and network based analysis in order to transform big biomedical data into predictions and diagnostics for precision medicine and personalized healthcare with better decision making and patient outcomes.

A comparison of machine learning and Bayesian modelling for molecular serotyping.

PubMed

Newton, Richard; Wernisch, Lorenz

2017-08-11

Streptococcus pneumoniae is a human pathogen that is a major cause of infant mortality. Identifying the pneumococcal serotype is an important step in monitoring the impact of vaccines used to protect against disease. Genomic microarrays provide an effective method for molecular serotyping. Previously we developed an empirical Bayesian model for the classification of serotypes from a molecular serotyping array. With only few samples available, a model driven approach was the only option. In the meanwhile, several thousand samples have been made available to us, providing an opportunity to investigate serotype classification by machine learning methods, which could complement the Bayesian model. We compare the performance of the original Bayesian model with two machine learning algorithms: Gradient Boosting Machines and Random Forests. We present our results as an example of a generic strategy whereby a preliminary probabilistic model is complemented or replaced by a machine learning classifier once enough data are available. Despite the availability of thousands of serotyping arrays, a problem encountered when applying machine learning methods is the lack of training data containing mixtures of serotypes; due to the large number of possible combinations. Most of the available training data comprises samples with only a single serotype. To overcome the lack of training data we implemented an iterative analysis, creating artificial training data of serotype mixtures by combining raw data from single serotype arrays. With the enhanced training set the machine learning algorithms out perform the original Bayesian model. However, for serotypes currently lacking sufficient training data the best performing implementation was a combination of the results of the Bayesian Model and the Gradient Boosting Machine. As well as being an effective method for classifying biological data, machine learning can also be used as an efficient method for revealing subtle biological insights, which we illustrate with an example.

Number-Knower Levels in Young Children: Insights from Bayesian Modeling

ERIC Educational Resources Information Center

Lee, Michael D.; Sarnecka, Barbara W.

2011-01-01

Lee and Sarnecka (2010) developed a Bayesian model of young children's behavior on the Give-N test of number knowledge. This paper presents two new extensions of the model, and applies the model to new data. In the first extension, the model is used to evaluate competing theories about the conceptual knowledge underlying children's behavior. One,…

Theory-based Bayesian Models of Inductive Inference

DTIC Science & Technology

2010-07-19

Subjective randomness and natural scene statistics. Psychonomic Bulletin & Review . http://cocosci.berkeley.edu/tom/papers/randscenes.pdf Page 1...in press). Exemplar models as a mechanism for performing Bayesian inference. Psychonomic Bulletin & Review . http://cocosci.berkeley.edu/tom

Modeling Error Distributions of Growth Curve Models through Bayesian Methods

ERIC Educational Resources Information Center

Zhang, Zhiyong

2016-01-01

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is…

Bayesian Semiparametric Structural Equation Models with Latent Variables

ERIC Educational Resources Information Center

Yang, Mingan; Dunson, David B.

2010-01-01

Structural equation models (SEMs) with latent variables are widely useful for sparse covariance structure modeling and for inferring relationships among latent variables. Bayesian SEMs are appealing in allowing for the incorporation of prior information and in providing exact posterior distributions of unknowns, including the latent variables. In…

Dynamic Bayesian Networks for Student Modeling

ERIC Educational Resources Information Center

Kaser, Tanja; Klingler, Severin; Schwing, Alexander G.; Gross, Markus

2017-01-01

Intelligent tutoring systems adapt the curriculum to the needs of the individual student. Therefore, an accurate representation and prediction of student knowledge is essential. Bayesian Knowledge Tracing (BKT) is a popular approach for student modeling. The structure of BKT models, however, makes it impossible to represent the hierarchy and…

On the Estimation of Disease Prevalence by Latent Class Models for Screening Studies Using Two Screening Tests with Categorical Disease Status Verified in Test Positives Only

PubMed Central

Chu, Haitao; Zhou, Yijie; Cole, Stephen R.; Ibrahim, Joseph G.

2010-01-01

Summary To evaluate the probabilities of a disease state, ideally all subjects in a study should be diagnosed by a definitive diagnostic or gold standard test. However, since definitive diagnostic tests are often invasive and expensive, it is generally unethical to apply them to subjects whose screening tests are negative. In this article, we consider latent class models for screening studies with two imperfect binary diagnostic tests and a definitive categorical disease status measured only for those with at least one positive screening test. Specifically, we discuss a conditional independent and three homogeneous conditional dependent latent class models and assess the impact of misspecification of the dependence structure on the estimation of disease category probabilities using frequentist and Bayesian approaches. Interestingly, the three homogeneous dependent models can provide identical goodness-of-fit but substantively different estimates for a given study. However, the parametric form of the assumed dependence structure itself is not “testable” from the data, and thus the dependence structure modeling considered here can only be viewed as a sensitivity analysis concerning a more complicated non-identifiable model potentially involving heterogeneous dependence structure. Furthermore, we discuss Bayesian model averaging together with its limitations as an alternative way to partially address this particularly challenging problem. The methods are applied to two cancer screening studies, and simulations are conducted to evaluate the performance of these methods. In summary, further research is needed to reduce the impact of model misspecification on the estimation of disease prevalence in such settings. PMID:20191614

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

PubMed

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

2016-05-01

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

Computational statistics using the Bayesian Inference Engine

NASA Astrophysics Data System (ADS)

Weinberg, Martin D.

2013-09-01

This paper introduces the Bayesian Inference Engine (BIE), a general parallel, optimized software package for parameter inference and model selection. This package is motivated by the analysis needs of modern astronomical surveys and the need to organize and reuse expensive derived data. The BIE is the first platform for computational statistics designed explicitly to enable Bayesian update and model comparison for astronomical problems. Bayesian update is based on the representation of high-dimensional posterior distributions using metric-ball-tree based kernel density estimation. Among its algorithmic offerings, the BIE emphasizes hybrid tempered Markov chain Monte Carlo schemes that robustly sample multimodal posterior distributions in high-dimensional parameter spaces. Moreover, the BIE implements a full persistence or serialization system that stores the full byte-level image of the running inference and previously characterized posterior distributions for later use. Two new algorithms to compute the marginal likelihood from the posterior distribution, developed for and implemented in the BIE, enable model comparison for complex models and data sets. Finally, the BIE was designed to be a collaborative platform for applying Bayesian methodology to astronomy. It includes an extensible object-oriented and easily extended framework that implements every aspect of the Bayesian inference. By providing a variety of statistical algorithms for all phases of the inference problem, a scientist may explore a variety of approaches with a single model and data implementation. Additional technical details and download details are available from http://www.astro.umass.edu/bie. The BIE is distributed under the GNU General Public License.

Integrating chronological uncertainties for annually laminated lake sediments using layer counting, independent chronologies and Bayesian age modelling (Lake Ohau, South Island, New Zealand)

NASA Astrophysics Data System (ADS)

Vandergoes, Marcus J.; Howarth, Jamie D.; Dunbar, Gavin B.; Turnbull, Jocelyn C.; Roop, Heidi A.; Levy, Richard H.; Li, Xun; Prior, Christine; Norris, Margaret; Keller, Liz D.; Baisden, W. Troy; Ditchburn, Robert; Fitzsimons, Sean J.; Bronk Ramsey, Christopher

2018-05-01

Annually resolved (varved) lake sequences are important palaeoenvironmental archives as they offer a direct incremental dating technique for high-frequency reconstruction of environmental and climate change. Despite the importance of these records, establishing a robust chronology and quantifying its precision and accuracy (estimations of error) remains an essential but challenging component of their development. We outline an approach for building reliable independent chronologies, testing the accuracy of layer counts and integrating all chronological uncertainties to provide quantitative age and error estimates for varved lake sequences. The approach incorporates (1) layer counts and estimates of counting precision; (2) radiometric and biostratigrapic dating techniques to derive independent chronology; and (3) the application of Bayesian age modelling to produce an integrated age model. This approach is applied to a case study of an annually resolved sediment record from Lake Ohau, New Zealand. The most robust age model provides an average error of 72 years across the whole depth range. This represents a fractional uncertainty of ∼5%, higher than the <3% quoted for most published varve records. However, the age model and reported uncertainty represent the best fit between layer counts and independent chronology and the uncertainties account for both layer counting precision and the chronological accuracy of the layer counts. This integrated approach provides a more representative estimate of age uncertainty and therefore represents a statistically more robust chronology.

Bootstrap study of genome-enabled prediction reliabilities using haplotype blocks across Nordic Red cattle breeds.

PubMed

Cuyabano, B C D; Su, G; Rosa, G J M; Lund, M S; Gianola, D

2015-10-01

This study compared the accuracy of genome-enabled prediction models using individual single nucleotide polymorphisms (SNP) or haplotype blocks as covariates when using either a single breed or a combined population of Nordic Red cattle. The main objective was to compare predictions of breeding values of complex traits using a combined training population with haplotype blocks, with predictions using a single breed as training population and individual SNP as predictors. To compare the prediction reliabilities, bootstrap samples were taken from the test data set. With the bootstrapped samples of prediction reliabilities, we built and graphed confidence ellipses to allow comparisons. Finally, measures of statistical distances were used to calculate the gain in predictive ability. Our analyses are innovative in the context of assessment of predictive models, allowing a better understanding of prediction reliabilities and providing a statistical basis to effectively calibrate whether one prediction scenario is indeed more accurate than another. An ANOVA indicated that use of haplotype blocks produced significant gains mainly when Bayesian mixture models were used but not when Bayesian BLUP was fitted to the data. Furthermore, when haplotype blocks were used to train prediction models in a combined Nordic Red cattle population, we obtained up to a statistically significant 5.5% average gain in prediction accuracy, over predictions using individual SNP and training the model with a single breed. Copyright © 2015 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

A Bayesian method for characterizing distributed micro-releases: II. inference under model uncertainty with short time-series data.

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

Marzouk, Youssef; Fast P.; Kraus, M.

2006-01-01

Terrorist attacks using an aerosolized pathogen preparation have gained credibility as a national security concern after the anthrax attacks of 2001. The ability to characterize such attacks, i.e., to estimate the number of people infected, the time of infection, and the average dose received, is important when planning a medical response. We address this question of characterization by formulating a Bayesian inverse problem predicated on a short time-series of diagnosed patients exhibiting symptoms. To be of relevance to response planning, we limit ourselves to 3-5 days of data. In tests performed with anthrax as the pathogen, we find that thesemore » data are usually sufficient, especially if the model of the outbreak used in the inverse problem is an accurate one. In some cases the scarcity of data may initially support outbreak characterizations at odds with the true one, but with sufficient data the correct inferences are recovered; in other words, the inverse problem posed and its solution methodology are consistent. We also explore the effect of model error-situations for which the model used in the inverse problem is only a partially accurate representation of the outbreak; here, the model predictions and the observations differ by more than a random noise. We find that while there is a consistent discrepancy between the inferred and the true characterizations, they are also close enough to be of relevance when planning a response.« less

Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics.

PubMed

Wu, Xiao-Lin; Sun, Chuanyu; Beissinger, Timothy M; Rosa, Guilherme Jm; Weigel, Kent A; Gatti, Natalia de Leon; Gianola, Daniel

2012-09-25

Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics. Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes. Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs.

Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics

PubMed Central

2012-01-01

Background Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics. Results Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes. Conclusions Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs. PMID:23009363

Bayesian dynamic regression models for interval censored survival data with application to children dental health.

PubMed

Wang, Xiaojing; Chen, Ming-Hui; Yan, Jun

2013-07-01

Cox models with time-varying coefficients offer great flexibility in capturing the temporal dynamics of covariate effects on event times, which could be hidden from a Cox proportional hazards model. Methodology development for varying coefficient Cox models, however, has been largely limited to right censored data; only limited work on interval censored data has been done. In most existing methods for varying coefficient models, analysts need to specify which covariate coefficients are time-varying and which are not at the time of fitting. We propose a dynamic Cox regression model for interval censored data in a Bayesian framework, where the coefficient curves are piecewise constant but the number of pieces and the jump points are covariate specific and estimated from the data. The model automatically determines the extent to which the temporal dynamics is needed for each covariate, resulting in smoother and more stable curve estimates. The posterior computation is carried out via an efficient reversible jump Markov chain Monte Carlo algorithm. Inference of each coefficient is based on an average of models with different number of pieces and jump points. A simulation study with three covariates, each with a coefficient of different degree in temporal dynamics, confirmed that the dynamic model is preferred to the existing time-varying model in terms of model comparison criteria through conditional predictive ordinate. When applied to a dental health data of children with age between 7 and 12 years, the dynamic model reveals that the relative risk of emergence of permanent tooth 24 between children with and without an infected primary predecessor is the highest at around age 7.5, and that it gradually reduces to one after age 11. These findings were not seen from the existing studies with Cox proportional hazards models.

Bayesian survival analysis in clinical trials: What methods are used in practice?

PubMed

Brard, Caroline; Le Teuff, Gwénaël; Le Deley, Marie-Cécile; Hampson, Lisa V

2017-02-01

Background Bayesian statistics are an appealing alternative to the traditional frequentist approach to designing, analysing, and reporting of clinical trials, especially in rare diseases. Time-to-event endpoints are widely used in many medical fields. There are additional complexities to designing Bayesian survival trials which arise from the need to specify a model for the survival distribution. The objective of this article was to critically review the use and reporting of Bayesian methods in survival trials. Methods A systematic review of clinical trials using Bayesian survival analyses was performed through PubMed and Web of Science databases. This was complemented by a full text search of the online repositories of pre-selected journals. Cost-effectiveness, dose-finding studies, meta-analyses, and methodological papers using clinical trials were excluded. Results In total, 28 articles met the inclusion criteria, 25 were original reports of clinical trials and 3 were re-analyses of a clinical trial. Most trials were in oncology (n = 25), were randomised controlled (n = 21) phase III trials (n = 13), and half considered a rare disease (n = 13). Bayesian approaches were used for monitoring in 14 trials and for the final analysis only in 14 trials. In the latter case, Bayesian survival analyses were used for the primary analysis in four cases, for the secondary analysis in seven cases, and for the trial re-analysis in three cases. Overall, 12 articles reported fitting Bayesian regression models (semi-parametric, n = 3; parametric, n = 9). Prior distributions were often incompletely reported: 20 articles did not define the prior distribution used for the parameter of interest. Over half of the trials used only non-informative priors for monitoring and the final analysis (n = 12) when it was specified. Indeed, no articles fitting Bayesian regression models placed informative priors on the parameter of interest. The prior for the treatment effect was based on historical data in only four trials. Decision rules were pre-defined in eight cases when trials used Bayesian monitoring, and in only one case when trials adopted a Bayesian approach to the final analysis. Conclusion Few trials implemented a Bayesian survival analysis and few incorporated external data into priors. There is scope to improve the quality of reporting of Bayesian methods in survival trials. Extension of the Consolidated Standards of Reporting Trials statement for reporting Bayesian clinical trials is recommended.

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

NASA Astrophysics Data System (ADS)

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

2007-06-01

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

A Bayesian Approach for Analyzing Longitudinal Structural Equation Models

ERIC Educational Resources Information Center

Song, Xin-Yuan; Lu, Zhao-Hua; Hser, Yih-Ing; Lee, Sik-Yum

2011-01-01

This article considers a Bayesian approach for analyzing a longitudinal 2-level nonlinear structural equation model with covariates, and mixed continuous and ordered categorical variables. The first-level model is formulated for measures taken at each time point nested within individuals for investigating their characteristics that are dynamically…

Model Diagnostics for Bayesian Networks. Research Report. ETS RR-04-17

ERIC Educational Resources Information Center

Sinharay, Sandip

2004-01-01

Assessing fit of psychometric models has always been an issue of enormous interest, but there exists no unanimously agreed upon item fit diagnostic for the models. Bayesian networks, frequently used in educational assessments (see, for example, Mislevy, Almond, Yan, & Steinberg, 2001) primarily for learning about students' knowledge and…

Bayesian Unimodal Density Regression for Causal Inference

ERIC Educational Resources Information Center

Karabatsos, George; Walker, Stephen G.

2011-01-01

Karabatsos and Walker (2011) introduced a new Bayesian nonparametric (BNP) regression model. Through analyses of real and simulated data, they showed that the BNP regression model outperforms other parametric and nonparametric regression models of common use, in terms of predictive accuracy of the outcome (dependent) variable. The other,…

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

Ng, B

This survey gives an overview of popular generative models used in the modeling of stochastic temporal systems. In particular, this survey is organized into two parts. The first part discusses the discrete-time representations of dynamic Bayesian networks and dynamic relational probabilistic models, while the second part discusses the continuous-time representation of continuous-time Bayesian networks.

Bayesian Estimation of the DINA Model with Gibbs Sampling

ERIC Educational Resources Information Center

Culpepper, Steven Andrew

2015-01-01

A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…

Protein degradation rate is the dominant mechanism accounting for the differences in protein abundance of basal p53 in a human breast and colorectal cancer cell line.

PubMed

Lakatos, Eszter; Salehi-Reyhani, Ali; Barclay, Michael; Stumpf, Michael P H; Klug, David R

2017-01-01

We determine p53 protein abundances and cell to cell variation in two human cancer cell lines with single cell resolution, and show that the fractional width of the distributions is the same in both cases despite a large difference in average protein copy number. We developed a computational framework to identify dominant mechanisms controlling the variation of protein abundance in a simple model of gene expression from the summary statistics of single cell steady state protein expression distributions. Our results, based on single cell data analysed in a Bayesian framework, lends strong support to a model in which variation in the basal p53 protein abundance may be best explained by variations in the rate of p53 protein degradation. This is supported by measurements of the relative average levels of mRNA which are very similar despite large variation in the level of protein.

ABrox-A user-friendly Python module for approximate Bayesian computation with a focus on model comparison.

PubMed

Mertens, Ulf Kai; Voss, Andreas; Radev, Stefan

2018-01-01

We give an overview of the basic principles of approximate Bayesian computation (ABC), a class of stochastic methods that enable flexible and likelihood-free model comparison and parameter estimation. Our new open-source software called ABrox is used to illustrate ABC for model comparison on two prominent statistical tests, the two-sample t-test and the Levene-Test. We further highlight the flexibility of ABC compared to classical Bayesian hypothesis testing by computing an approximate Bayes factor for two multinomial processing tree models. Last but not least, throughout the paper, we introduce ABrox using the accompanied graphical user interface.

Semisupervised learning using Bayesian interpretation: application to LS-SVM.

PubMed

Adankon, Mathias M; Cheriet, Mohamed; Biem, Alain

2011-04-01

Bayesian reasoning provides an ideal basis for representing and manipulating uncertain knowledge, with the result that many interesting algorithms in machine learning are based on Bayesian inference. In this paper, we use the Bayesian approach with one and two levels of inference to model the semisupervised learning problem and give its application to the successful kernel classifier support vector machine (SVM) and its variant least-squares SVM (LS-SVM). Taking advantage of Bayesian interpretation of LS-SVM, we develop a semisupervised learning algorithm for Bayesian LS-SVM using our approach based on two levels of inference. Experimental results on both artificial and real pattern recognition problems show the utility of our method.

Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis

PubMed Central

Fancher, Chris M.; Han, Zhen; Levin, Igor; Page, Katharine; Reich, Brian J.; Smith, Ralph C.; Wilson, Alyson G.; Jones, Jacob L.

2016-01-01

A Bayesian inference method for refining crystallographic structures is presented. The distribution of model parameters is stochastically sampled using Markov chain Monte Carlo. Posterior probability distributions are constructed for all model parameters to properly quantify uncertainty by appropriately modeling the heteroskedasticity and correlation of the error structure. The proposed method is demonstrated by analyzing a National Institute of Standards and Technology silicon standard reference material. The results obtained by Bayesian inference are compared with those determined by Rietveld refinement. Posterior probability distributions of model parameters provide both estimates and uncertainties. The new method better estimates the true uncertainties in the model as compared to the Rietveld method. PMID:27550221

Using Bayesian belief networks in adaptive management.

Treesearch

J.B. Nyberg; B.G. Marcot; R. Sulyma

2006-01-01

Bayesian belief and decision networks are relatively new modeling methods that are especially well suited to adaptive-management applications, but they appear not to have been widely used in adaptive management to date. Bayesian belief networks (BBNs) can serve many purposes for practioners of adaptive management, from illustrating system relations conceptually to...

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 generalized least squares regression with application to log Pearson type 3 regional skew estimation

NASA Astrophysics Data System (ADS)

Reis, D. S.; Stedinger, J. R.; Martins, E. S.

2005-10-01

This paper develops a Bayesian approach to analysis of a generalized least squares (GLS) regression model for regional analyses of hydrologic data. The new approach allows computation of the posterior distributions of the parameters and the model error variance using a quasi-analytic approach. Two regional skew estimation studies illustrate the value of the Bayesian GLS approach for regional statistical analysis of a shape parameter and demonstrate that regional skew models can be relatively precise with effective record lengths in excess of 60 years. With Bayesian GLS the marginal posterior distribution of the model error variance and the corresponding mean and variance of the parameters can be computed directly, thereby providing a simple but important extension of the regional GLS regression procedures popularized by Tasker and Stedinger (1989), which is sensitive to the likely values of the model error variance when it is small relative to the sampling error in the at-site estimator.

Modeling haul-out behavior of walruses in Bering Sea ice

USGS Publications Warehouse

Udevitz, M.S.; Jay, C.V.; Fischbach, Anthony S.; Garlich-Miller, J. L.

2009-01-01

Understanding haul-out behavior of ice-associated pinnipeds is essential for designing and interpreting popula-tion surveys and for assessing effects of potential changes in their ice environments. We used satellite-linked transmitters to obtain sequential information about location and haul-out state for Pacific walruses, Odobenus rosmarus divergens (Il-liger, 1815), in the Bering Sea during April of 2004, 2005, and 2006. We used these data in a generalized mixed model of haul-out bout durations and a hierarchical Bayesian model of haul-out probabilities to assess factors related to walrus haul-out behavior, and provide the first predictive model of walrus haul-out behavior in sea ice habitat. Average haul-out bout duration was 9 h, but durations of haul-out bouts tended to increase with durations of preceding in-water bouts. On aver-age, tagged walruses spent only about 17% of their time hauled out on sea ice. Probability of being hauled out decreased with wind speed, increased with temperature, and followed a diurnal cycle with the highest values in the evening. Our haul-out probability model can be used to estimate the proportion of the population that is unavailable for detection in spring surveys of Pacific walruses on sea ice.

A cross-comparison of different techniques for modeling macro-level cyclist crashes.

PubMed

Guo, Yanyong; Osama, Ahmed; Sayed, Tarek

2018-04-01

Despite the recognized benefits of cycling as a sustainable mode of transportation, cyclists are considered vulnerable road users and there are concerns about their safety. Therefore, it is essential to investigate the factors affecting cyclist safety. The goal of this study is to evaluate and compare different approaches of modeling macro-level cyclist safety as well as investigating factors that contribute to cyclist crashes using a comprehensive list of covariates. Data from 134 traffic analysis zones (TAZs) in the City of Vancouver were used to develop macro-level crash models (CM) incorporating variables related to actual traffic exposure, socio-economics, land use, built environment, and bike network. Four types of CMs were developed under a full Bayesian framework: Poisson lognormal model (PLN), random intercepts PLN model (RIPLN), random parameters PLN model (RPPLN), and spatial PLN model (SPLN). The SPLN model had the best goodness of fit, and the results highlighted the significant effects of spatial correlation. The models showed that the cyclist crashes were positively associated with bike and vehicle exposure measures, households, commercial area density, and signal density. On the other hand, negative associations were found between cyclist crashes and some bike network indicators such as average edge length, average zonal slope, and off-street bike links. Copyright © 2018 Elsevier Ltd. All rights reserved.

Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring

Treesearch

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

2010-01-01

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...

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.

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.

Using Bayesian Stable Isotope Mixing Models to Enhance Marine Ecosystem Models

EPA Science Inventory

The use of stable isotopes in food web studies has proven to be a valuable tool for ecologists. We investigated the use of Bayesian stable isotope mixing models as constraints for an ecosystem model of a temperate seagrass system on the Atlantic coast of France. δ13C and δ15N i...

Effect of Bayesian Student Modeling on Academic Achievement in Foreign Language Teaching (University Level English Preparatory School Example)

ERIC Educational Resources Information Center

Aslan, Burak Galip; Öztürk, Özlem; Inceoglu, Mustafa Murat

2014-01-01

Considering the increasing importance of adaptive approaches in CALL systems, this study implemented a machine learning based student modeling middleware with Bayesian networks. The profiling approach of the student modeling system is based on Felder and Silverman's Learning Styles Model and Felder and Soloman's Index of Learning Styles…

Competing risk models in reliability systems, a weibull distribution model with bayesian analysis approach

NASA Astrophysics Data System (ADS)

Iskandar, Ismed; Satria Gondokaryono, Yudi

2016-02-01

In reliability theory, the most important problem is to determine the reliability of a complex system from the reliability of its components. The weakness of most reliability theories is that the systems are described and explained as simply functioning or failed. In many real situations, the failures may be from many causes depending upon the age and the environment of the system and its components. Another problem in reliability theory is one of estimating the parameters of the assumed failure models. The estimation may be based on data collected over censored or uncensored life tests. In many reliability problems, the failure data are simply quantitatively inadequate, especially in engineering design and maintenance system. The Bayesian analyses are more beneficial than the classical one in such cases. The Bayesian estimation analyses allow us to combine past knowledge or experience in the form of an apriori distribution with life test data to make inferences of the parameter of interest. In this paper, we have investigated the application of the Bayesian estimation analyses to competing risk systems. The cases are limited to the models with independent causes of failure by using the Weibull distribution as our model. A simulation is conducted for this distribution with the objectives of verifying the models and the estimators and investigating the performance of the estimators for varying sample size. The simulation data are analyzed by using Bayesian and the maximum likelihood analyses. The simulation results show that the change of the true of parameter relatively to another will change the value of standard deviation in an opposite direction. For a perfect information on the prior distribution, the estimation methods of the Bayesian analyses are better than those of the maximum likelihood. The sensitivity analyses show some amount of sensitivity over the shifts of the prior locations. They also show the robustness of the Bayesian analysis within the range between the true value and the maximum likelihood estimated value lines.

Bayesian Factor Analysis as a Variable Selection Problem: Alternative Priors and Consequences

PubMed Central

Lu, Zhao-Hua; Chow, Sy-Miin; Loken, Eric

2016-01-01

Factor analysis is a popular statistical technique for multivariate data analysis. Developments in the structural equation modeling framework have enabled the use of hybrid confirmatory/exploratory approaches in which factor loading structures can be explored relatively flexibly within a confirmatory factor analysis (CFA) framework. Recently, a Bayesian structural equation modeling (BSEM) approach (Muthén & Asparouhov, 2012) has been proposed as a way to explore the presence of cross-loadings in CFA models. We show that the issue of determining factor loading patterns may be formulated as a Bayesian variable selection problem in which Muthén and Asparouhov’s approach can be regarded as a BSEM approach with ridge regression prior (BSEM-RP). We propose another Bayesian approach, denoted herein as the Bayesian structural equation modeling with spike and slab prior (BSEM-SSP), which serves as a one-stage alternative to the BSEM-RP. We review the theoretical advantages and disadvantages of both approaches and compare their empirical performance relative to two modification indices-based approaches and exploratory factor analysis with target rotation. A teacher stress scale data set (Byrne, 2012; Pettegrew & Wolf, 1982) is used to demonstrate our approach. PMID:27314566

Bayesian Inference and Online Learning in Poisson Neuronal Networks.

PubMed

Huang, Yanping; Rao, Rajesh P N

2016-08-01

Motivated by the growing evidence for Bayesian computation in the brain, we show how a two-layer recurrent network of Poisson neurons can perform both approximate Bayesian inference and learning for any hidden Markov model. The lower-layer sensory neurons receive noisy measurements of hidden world states. The higher-layer neurons infer a posterior distribution over world states via Bayesian inference from inputs generated by sensory neurons. We demonstrate how such a neuronal network with synaptic plasticity can implement a form of Bayesian inference similar to Monte Carlo methods such as particle filtering. Each spike in a higher-layer neuron represents a sample of a particular hidden world state. The spiking activity across the neural population approximates the posterior distribution over hidden states. In this model, variability in spiking is regarded not as a nuisance but as an integral feature that provides the variability necessary for sampling during inference. We demonstrate how the network can learn the likelihood model, as well as the transition probabilities underlying the dynamics, using a Hebbian learning rule. We present results illustrating the ability of the network to perform inference and learning for arbitrary hidden Markov models.

Impact assessment of extreme storm events using a Bayesian network

USGS Publications Warehouse

den Heijer, C.(Kees); Knipping, Dirk T.J.A.; Plant, Nathaniel G.; van Thiel de Vries, Jaap S. M.; Baart, Fedor; van Gelder, Pieter H. A. J. M.

2012-01-01

This paper describes an investigation on the usefulness of Bayesian Networks in the safety assessment of dune coasts. A network has been created that predicts the erosion volume based on hydraulic boundary conditions and a number of cross-shore profile indicators. Field measurement data along a large part of the Dutch coast has been used to train the network. Corresponding storm impact on the dunes was calculated with an empirical dune erosion model named duros+. Comparison between the Bayesian Network predictions and the original duros+ results, here considered as observations, results in a skill up to 0.88, provided that the training data covers the range of predictions. Hence, the predictions from a deterministic model (duros+) can be captured in a probabilistic model (Bayesian Network) such that both the process knowledge and uncertainties can be included in impact and vulnerability assessments.

BAYESIAN METHODS FOR REGIONAL-SCALE EUTROPHICATION MODELS. (R830887)

EPA Science Inventory

We demonstrate a Bayesian classification and regression tree (CART) approach to link multiple environmental stressors to biological responses and quantify uncertainty in model predictions. Such an approach can: (1) report prediction uncertainty, (2) be consistent with the amou...

Bayesian stable isotope mixing models

EPA Science Inventory

In this paper we review recent advances in Stable Isotope Mixing Models (SIMMs) and place them into an over-arching Bayesian statistical framework which allows for several useful extensions. SIMMs are used to quantify the proportional contributions of various sources to a mixtur...

Bayesian conditional-independence modeling of the AIDS epidemic in England and Wales

NASA Astrophysics Data System (ADS)

Gilks, Walter R.; De Angelis, Daniela; Day, Nicholas E.

We describe the use of conditional-independence modeling, Bayesian inference and Markov chain Monte Carlo, to model and project the HIV-AIDS epidemic in homosexual/bisexual males in England and Wales. Complexity in this analysis arises through selectively missing data, indirectly observed underlying processes, and measurement error. Our emphasis is on presentation and discussion of the concepts, not on the technicalities of this analysis, which can be found elsewhere [D. De Angelis, W.R. Gilks, N.E. Day, Bayesian projection of the the acquired immune deficiency syndrome epidemic (with discussion), Applied Statistics, in press].

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

NASA Astrophysics Data System (ADS)

Varvia, Petri; Rautiainen, Miina; Seppänen, Aku

2018-03-01

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

Generalized seasonal autoregressive integrated moving average models for count data with application to malaria time series with low case numbers.

PubMed

Briët, Olivier J T; Amerasinghe, Priyanie H; Vounatsou, Penelope

2013-01-01

With the renewed drive towards malaria elimination, there is a need for improved surveillance tools. While time series analysis is an important tool for surveillance, prediction and for measuring interventions' impact, approximations by commonly used Gaussian methods are prone to inaccuracies when case counts are low. Therefore, statistical methods appropriate for count data are required, especially during "consolidation" and "pre-elimination" phases. Generalized autoregressive moving average (GARMA) models were extended to generalized seasonal autoregressive integrated moving average (GSARIMA) models for parsimonious observation-driven modelling of non Gaussian, non stationary and/or seasonal time series of count data. The models were applied to monthly malaria case time series in a district in Sri Lanka, where malaria has decreased dramatically in recent years. The malaria series showed long-term changes in the mean, unstable variance and seasonality. After fitting negative-binomial Bayesian models, both a GSARIMA and a GARIMA deterministic seasonality model were selected based on different criteria. Posterior predictive distributions indicated that negative-binomial models provided better predictions than Gaussian models, especially when counts were low. The G(S)ARIMA models were able to capture the autocorrelation in the series. G(S)ARIMA models may be particularly useful in the drive towards malaria elimination, since episode count series are often seasonal and non-stationary, especially when control is increased. Although building and fitting GSARIMA models is laborious, they may provide more realistic prediction distributions than do Gaussian methods and may be more suitable when counts are low.

Generalized Seasonal Autoregressive Integrated Moving Average Models for Count Data with Application to Malaria Time Series with Low Case Numbers

PubMed Central

Briët, Olivier J. T.; Amerasinghe, Priyanie H.; Vounatsou, Penelope

2013-01-01

Introduction With the renewed drive towards malaria elimination, there is a need for improved surveillance tools. While time series analysis is an important tool for surveillance, prediction and for measuring interventions’ impact, approximations by commonly used Gaussian methods are prone to inaccuracies when case counts are low. Therefore, statistical methods appropriate for count data are required, especially during “consolidation” and “pre-elimination” phases. Methods Generalized autoregressive moving average (GARMA) models were extended to generalized seasonal autoregressive integrated moving average (GSARIMA) models for parsimonious observation-driven modelling of non Gaussian, non stationary and/or seasonal time series of count data. The models were applied to monthly malaria case time series in a district in Sri Lanka, where malaria has decreased dramatically in recent years. Results The malaria series showed long-term changes in the mean, unstable variance and seasonality. After fitting negative-binomial Bayesian models, both a GSARIMA and a GARIMA deterministic seasonality model were selected based on different criteria. Posterior predictive distributions indicated that negative-binomial models provided better predictions than Gaussian models, especially when counts were low. The G(S)ARIMA models were able to capture the autocorrelation in the series. Conclusions G(S)ARIMA models may be particularly useful in the drive towards malaria elimination, since episode count series are often seasonal and non-stationary, especially when control is increased. Although building and fitting GSARIMA models is laborious, they may provide more realistic prediction distributions than do Gaussian methods and may be more suitable when counts are low. PMID:23785448

Using a web-based application to define the accuracy of diagnostic tests when the gold standard is imperfect.

PubMed

Lim, Cherry; Wannapinij, Prapass; White, Lisa; Day, Nicholas P J; Cooper, Ben S; Peacock, Sharon J; Limmathurotsakul, Direk

2013-01-01

Estimates of the sensitivity and specificity for new diagnostic tests based on evaluation against a known gold standard are imprecise when the accuracy of the gold standard is imperfect. Bayesian latent class models (LCMs) can be helpful under these circumstances, but the necessary analysis requires expertise in computational programming. Here, we describe open-access web-based applications that allow non-experts to apply Bayesian LCMs to their own data sets via a user-friendly interface. Applications for Bayesian LCMs were constructed on a web server using R and WinBUGS programs. The models provided (http://mice.tropmedres.ac) include two Bayesian LCMs: the two-tests in two-population model (Hui and Walter model) and the three-tests in one-population model (Walter and Irwig model). Both models are available with simplified and advanced interfaces. In the former, all settings for Bayesian statistics are fixed as defaults. Users input their data set into a table provided on the webpage. Disease prevalence and accuracy of diagnostic tests are then estimated using the Bayesian LCM, and provided on the web page within a few minutes. With the advanced interfaces, experienced researchers can modify all settings in the models as needed. These settings include correlation among diagnostic test results and prior distributions for all unknown parameters. The web pages provide worked examples with both models using the original data sets presented by Hui and Walter in 1980, and by Walter and Irwig in 1988. We also illustrate the utility of the advanced interface using the Walter and Irwig model on a data set from a recent melioidosis study. The results obtained from the web-based applications were comparable to those published previously. The newly developed web-based applications are open-access and provide an important new resource for researchers worldwide to evaluate new diagnostic tests.

Precise Network Modeling of Systems Genetics Data Using the Bayesian Network Webserver.

PubMed

Ziebarth, Jesse D; Cui, Yan

2017-01-01

The Bayesian Network Webserver (BNW, http://compbio.uthsc.edu/BNW ) is an integrated platform for Bayesian network modeling of biological datasets. It provides a web-based network modeling environment that seamlessly integrates advanced algorithms for probabilistic causal modeling and reasoning with Bayesian networks. BNW is designed for precise modeling of relatively small networks that contain less than 20 nodes. The structure learning algorithms used by BNW guarantee the discovery of the best (most probable) network structure given the data. To facilitate network modeling across multiple biological levels, BNW provides a very flexible interface that allows users to assign network nodes into different tiers and define the relationships between and within the tiers. This function is particularly useful for modeling systems genetics datasets that often consist of multiscalar heterogeneous genotype-to-phenotype data. BNW enables users to, within seconds or minutes, go from having a simply formatted input file containing a dataset to using a network model to make predictions about the interactions between variables and the potential effects of experimental interventions. In this chapter, we will introduce the functions of BNW and show how to model systems genetics datasets with BNW.

Proximity to mining industry and respiratory diseases in children in a community in Northern Chile: A cross-sectional study.

PubMed

Herrera, Ronald; Radon, Katja; von Ehrenstein, Ondine S; Cifuentes, Stella; Muñoz, Daniel Moraga; Berger, Ursula

2016-06-07

In a community in northern Chile, explosive procedures are used by two local industrial mines (gold, copper). We hypothesized that the prevalence of asthma and rhinoconjunctivitis in the community may be associated with air pollution emissions generated by the mines. A cross-sectional study of 288 children (aged 6-15 years) was conducted in a community in northern Chile using a validated questionnaire in 2009. The proximity between each child's place of residence and the mines was assessed as indicator of exposure to mining related air pollutants. Logistic regression, semiparametric models and spatial Bayesian models with a parametric form for distance were used to calculate odds ratios and 95 % confidence intervals. The prevalence of asthma and rhinoconjunctivitis was 24 and 34 %, respectively. For rhinoconjunctivitis, the odds ratio for average distance between both mines and child's residence was 1.72 (95 % confidence interval 1.00, 3.04). The spatial Bayesian models suggested a considerable increase in the risk for respiratory diseases closer to the mines, and only beyond a minimum distance of more than 1800 m the health impact was considered to be negligible. The findings indicate that air pollution emissions related to industrial gold or copper mines mainly occurring in rural Chilean communities might increase the risk of respiratory diseases in children.

Gene network reconstruction from transcriptional dynamics under kinetic model uncertainty: a case for the second derivative

PubMed Central

Bickel, David R.; Montazeri, Zahra; Hsieh, Pei-Chun; Beatty, Mary; Lawit, Shai J.; Bate, Nicholas J.

2009-01-01

Motivation: Measurements of gene expression over time enable the reconstruction of transcriptional networks. However, Bayesian networks and many other current reconstruction methods rely on assumptions that conflict with the differential equations that describe transcriptional kinetics. Practical approximations of kinetic models would enable inferring causal relationships between genes from expression data of microarray, tag-based and conventional platforms, but conclusions are sensitive to the assumptions made. Results: The representation of a sufficiently large portion of genome enables computation of an upper bound on how much confidence one may place in influences between genes on the basis of expression data. Information about which genes encode transcription factors is not necessary but may be incorporated if available. The methodology is generalized to cover cases in which expression measurements are missing for many of the genes that might control the transcription of the genes of interest. The assumption that the gene expression level is roughly proportional to the rate of translation led to better empirical performance than did either the assumption that the gene expression level is roughly proportional to the protein level or the Bayesian model average of both assumptions. Availability: http://www.oisb.ca points to R code implementing the methods (R Development Core Team 2004). Contact: dbickel@uottawa.ca Supplementary information: http://www.davidbickel.com PMID:19218351

Fragment virtual screening based on Bayesian categorization for discovering novel VEGFR-2 scaffolds.

PubMed

Zhang, Yanmin; Jiao, Yu; Xiong, Xiao; Liu, Haichun; Ran, Ting; Xu, Jinxing; Lu, Shuai; Xu, Anyang; Pan, Jing; Qiao, Xin; Shi, Zhihao; Lu, Tao; Chen, Yadong

2015-11-01

The discovery of novel scaffolds against a specific target has long been one of the most significant but challengeable goals in discovering lead compounds. A scaffold that binds in important regions of the active pocket is more favorable as a starting point because scaffolds generally possess greater optimization possibilities. However, due to the lack of sufficient chemical space diversity of the databases and the ineffectiveness of the screening methods, it still remains a great challenge to discover novel active scaffolds. Since the strengths and weaknesses of both fragment-based drug design and traditional virtual screening (VS), we proposed a fragment VS concept based on Bayesian categorization for the discovery of novel scaffolds. This work investigated the proposal through an application on VEGFR-2 target. Firstly, scaffold and structural diversity of chemical space for 10 compound databases were explicitly evaluated. Simultaneously, a robust Bayesian classification model was constructed for screening not only compound databases but also their corresponding fragment databases. Although analysis of the scaffold diversity demonstrated a very unevenly distribution of scaffolds over molecules, results showed that our Bayesian model behaved better in screening fragments than molecules. Through a literature retrospective research, several generated fragments with relatively high Bayesian scores indeed exhibit VEGFR-2 biological activity, which strongly proved the effectiveness of fragment VS based on Bayesian categorization models. This investigation of Bayesian-based fragment VS can further emphasize the necessity for enrichment of compound databases employed in lead discovery by amplifying the diversity of databases with novel structures.

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.

Inhaled Cannabis for Chronic Neuropathic Pain: A Meta-analysis of Individual Patient Data.

PubMed

Andreae, Michael H; Carter, George M; Shaparin, Naum; Suslov, Kathryn; Ellis, Ronald J; Ware, Mark A; Abrams, Donald I; Prasad, Hannah; Wilsey, Barth; Indyk, Debbie; Johnson, Matthew; Sacks, Henry S

2015-12-01

Chronic neuropathic pain, the most frequent condition affecting the peripheral nervous system, remains underdiagnosed and difficult to treat. Inhaled cannabis may alleviate chronic neuropathic pain. Our objective was to synthesize the evidence on the use of inhaled cannabis for chronic neuropathic pain. We performed a systematic review and a meta-analysis of individual patient data. We registered our protocol with PROSPERO CRD42011001182. We searched in Cochrane Central, PubMed, EMBASE, and AMED. We considered all randomized controlled trials investigating chronic painful neuropathy and comparing inhaled cannabis with placebo. We pooled treatment effects following a hierarchical random-effects Bayesian responder model for the population-averaged subject-specific effect. Our evidence synthesis of individual patient data from 178 participants with 405 observed responses in 5 randomized controlled trials following patients for days to weeks provides evidence that inhaled cannabis results in short-term reductions in chronic neuropathic pain for 1 in every 5 to 6 patients treated (number needed to treat = 5.6 with a Bayesian 95% credible interval ranging between 3.4 and 14). Our inferences were insensitive to model assumptions, priors, and parameter choices. We caution that the small number of studies and participants, the short follow-up, shortcomings in allocation concealment, and considerable attrition limit the conclusions that can be drawn from the review. The Bayes factor is 332, corresponding to a posterior probability of effect of 99.7%. This novel Bayesian meta-analysis of individual patient data from 5 randomized trials suggests that inhaled cannabis may provide short-term relief for 1 in 5 to 6 patients with neuropathic pain. Pragmatic trials are needed to evaluate the long-term benefits and risks of this treatment. Copyright © 2015 American Pain Society. Published by Elsevier Inc. All rights reserved.

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.

How to interpret the results of medical time series data analysis: Classical statistical approaches versus dynamic Bayesian network modeling.

PubMed

Onisko, Agnieszka; Druzdzel, Marek J; Austin, R Marshall

2016-01-01

Classical statistics is a well-established approach in the analysis of medical data. While the medical community seems to be familiar with the concept of a statistical analysis and its interpretation, the Bayesian approach, argued by many of its proponents to be superior to the classical frequentist approach, is still not well-recognized in the analysis of medical data. The goal of this study is to encourage data analysts to use the Bayesian approach, such as modeling with graphical probabilistic networks, as an insightful alternative to classical statistical analysis of medical data. This paper offers a comparison of two approaches to analysis of medical time series data: (1) classical statistical approach, such as the Kaplan-Meier estimator and the Cox proportional hazards regression model, and (2) dynamic Bayesian network modeling. Our comparison is based on time series cervical cancer screening data collected at Magee-Womens Hospital, University of Pittsburgh Medical Center over 10 years. The main outcomes of our comparison are cervical cancer risk assessments produced by the three approaches. However, our analysis discusses also several aspects of the comparison, such as modeling assumptions, model building, dealing with incomplete data, individualized risk assessment, results interpretation, and model validation. Our study shows that the Bayesian approach is (1) much more flexible in terms of modeling effort, and (2) it offers an individualized risk assessment, which is more cumbersome for classical statistical approaches.

Diagnosis support system based on clinical guidelines: comparison between case-based fuzzy cognitive maps and Bayesian networks.

PubMed

Douali, Nassim; Csaba, Huszka; De Roo, Jos; Papageorgiou, Elpiniki I; Jaulent, Marie-Christine

2014-01-01

Several studies have described the prevalence and severity of diagnostic errors. Diagnostic errors can arise from cognitive, training, educational and other issues. Examples of cognitive issues include flawed reasoning, incomplete knowledge, faulty information gathering or interpretation, and inappropriate use of decision-making heuristics. We describe a new approach, case-based fuzzy cognitive maps, for medical diagnosis and evaluate it by comparison with Bayesian belief networks. We created a semantic web framework that supports the two reasoning methods. We used database of 174 anonymous patients from several European hospitals: 80 of the patients were female and 94 male with an average age 45±16 (average±stdev). Thirty of the 80 female patients were pregnant. For each patient, signs/symptoms/observables/age/sex were taken into account by the system. We used a statistical approach to compare the two methods. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.