Hierarchical Bayesian Models of Subtask Learning
ERIC Educational Resources Information Center
Anglim, Jeromy; Wynton, Sarah K. A.
2015-01-01
The current study used Bayesian hierarchical methods to challenge and extend previous work on subtask learning consistency. A general model of individual-level subtask learning was proposed focusing on power and exponential functions with constraints to test for inconsistency. To study subtask learning, we developed a novel computer-based booking…
Hierarchical Bayesian model updating for structural identification
NASA Astrophysics Data System (ADS)
Behmanesh, Iman; Moaveni, Babak; Lombaert, Geert; Papadimitriou, Costas
2015-12-01
A new probabilistic finite element (FE) model updating technique based on Hierarchical Bayesian modeling is proposed for identification of civil structural systems under changing ambient/environmental conditions. The performance of the proposed technique is investigated for (1) uncertainty quantification of model updating parameters, and (2) probabilistic damage identification of the structural systems. Accurate estimation of the uncertainty in modeling parameters such as mass or stiffness is a challenging task. Several Bayesian model updating frameworks have been proposed in the literature that can successfully provide the "parameter estimation uncertainty" of model parameters with the assumption that there is no underlying inherent variability in the updating parameters. However, this assumption may not be valid for civil structures where structural mass and stiffness have inherent variability due to different sources of uncertainty such as changing ambient temperature, temperature gradient, wind speed, and traffic loads. Hierarchical Bayesian model updating is capable of predicting the overall uncertainty/variability of updating parameters by assuming time-variability of the underlying linear system. A general solution based on Gibbs Sampler is proposed to estimate the joint probability distributions of the updating parameters. The performance of the proposed Hierarchical approach is evaluated numerically for uncertainty quantification and damage identification of a 3-story shear building model. Effects of modeling errors and incomplete modal data are considered in the numerical study.
Sparse Event Modeling with Hierarchical Bayesian Kernel Methods
2016-01-05
events (and subsequently, their likelihood of occurrence) based on historical evidence of the counts of previous event occurrences. The novel Bayesian...Aug-2014 22-May-2015 Approved for Public Release; Distribution Unlimited Final Report: Sparse Event Modeling with Hierarchical Bayesian Kernel Methods...Sparse Event Modeling with Hierarchical Bayesian Kernel Methods Report Title The research objective of this proposal was to develop a predictive Bayesian
A Hierarchical Bayesian Model for Crowd Emotions
Urizar, Oscar J.; Baig, Mirza S.; Barakova, Emilia I.; Regazzoni, Carlo S.; Marcenaro, Lucio; Rauterberg, Matthias
2016-01-01
Estimation of emotions is an essential aspect in developing intelligent systems intended for crowded environments. However, emotion estimation in crowds remains a challenging problem due to the complexity in which human emotions are manifested and the capability of a system to perceive them in such conditions. This paper proposes a hierarchical Bayesian model to learn in unsupervised manner the behavior of individuals and of the crowd as a single entity, and explore the relation between behavior and emotions to infer emotional states. Information about the motion patterns of individuals are described using a self-organizing map, and a hierarchical Bayesian network builds probabilistic models to identify behaviors and infer the emotional state of individuals and the crowd. This model is trained and tested using data produced from simulated scenarios that resemble real-life environments. The conducted experiments tested the efficiency of our method to learn, detect and associate behaviors with emotional states yielding accuracy levels of 74% for individuals and 81% for the crowd, similar in performance with existing methods for pedestrian behavior detection but with novel concepts regarding the analysis of crowds. PMID:27458366
Hierarchical Bayesian models of subtask learning.
Anglim, Jeromy; Wynton, Sarah K A
2015-07-01
The current study used Bayesian hierarchical methods to challenge and extend previous work on subtask learning consistency. A general model of individual-level subtask learning was proposed focusing on power and exponential functions with constraints to test for inconsistency. To study subtask learning, we developed a novel computer-based booking task, which logged participant actions, enabling measurement of strategy use and subtask performance. Model comparison was performed using deviance information criterion (DIC), posterior predictive checks, plots of model fits, and model recovery simulations. Results showed that although learning tended to be monotonically decreasing and decelerating, and approaching an asymptote for all subtasks, there was substantial inconsistency in learning curves both at the group- and individual-levels. This inconsistency was most apparent when constraining both the rate and the ratio of learning to asymptote to be equal across subtasks, thereby giving learning curves only 1 parameter for scaling. The inclusion of 6 strategy covariates provided improved prediction of subtask performance capturing different subtask learning processes and subtask trade-offs. In addition, strategy use partially explained the inconsistency in subtask learning. Overall, the model provided a more nuanced representation of how complex tasks can be decomposed in terms of simpler learning mechanisms.
A Generalizable Hierarchical Bayesian Model for Persistent SAR Change Detection
2012-04-01
6] K. Ranney and M. Soumekh, “Signal subspace change detection in averaged multilook sar imagery,” Geoscience and Remote Sensing, IEEE Transactions on...A Generalizable Hierarchical Bayesian Model for Persistent SAR Change Detection Gregory E. Newstadta, Edmund G. Zelniob, and Alfred O. Hero IIIa...Base, OH, 45433, USA ABSTRACT This paper proposes a hierarchical Bayesian model for multiple-pass, multiple antenna synthetic aperture radar ( SAR
Constructive Epistemic Modeling: A Hierarchical Bayesian Model Averaging Method
NASA Astrophysics Data System (ADS)
Tsai, F. T. C.; Elshall, A. S.
2014-12-01
Constructive epistemic modeling is the idea that our understanding of a natural system through a scientific model is a mental construct that continually develops through learning about and from the model. Using the hierarchical Bayesian model averaging (HBMA) method [1], this study shows that segregating different uncertain model components through a BMA tree of posterior model probabilities, model prediction, within-model variance, between-model variance and total model variance serves as a learning tool [2]. First, the BMA tree of posterior model probabilities permits the comparative evaluation of the candidate propositions of each uncertain model component. Second, systemic model dissection is imperative for understanding the individual contribution of each uncertain model component to the model prediction and variance. Third, the hierarchical representation of the between-model variance facilitates the prioritization of the contribution of each uncertain model component to the overall model uncertainty. We illustrate these concepts using the groundwater modeling of a siliciclastic aquifer-fault system. The sources of uncertainty considered are from geological architecture, formation dip, boundary conditions and model parameters. The study shows that the HBMA analysis helps in advancing knowledge about the model rather than forcing the model to fit a particularly understanding or merely averaging several candidate models. [1] Tsai, F. T.-C., and A. S. Elshall (2013), Hierarchical Bayesian model averaging for hydrostratigraphic modeling: Uncertainty segregation and comparative evaluation. Water Resources Research, 49, 5520-5536, doi:10.1002/wrcr.20428. [2] Elshall, A.S., and F. T.-C. Tsai (2014). Constructive epistemic modeling of groundwater flow with geological architecture and boundary condition uncertainty under Bayesian paradigm, Journal of Hydrology, 517, 105-119, doi: 10.1016/j.jhydrol.2014.05.027.
Bayesian and maximum likelihood estimation of hierarchical response time models
Farrell, Simon; Ludwig, Casimir
2008-01-01
Hierarchical (or multilevel) statistical models have become increasingly popular in psychology in the last few years. We consider the application of multilevel modeling to the ex-Gaussian, a popular model of response times. Single-level estimation is compared with hierarchical estimation of parameters of the ex-Gaussian distribution. Additionally, for each approach maximum likelihood (ML) estimation is compared with Bayesian estimation. A set of simulations and analyses of parameter recovery show that although all methods perform adequately well, hierarchical methods are better able to recover the parameters of the ex-Gaussian by reducing the variability in recovered parameters. At each level, little overall difference was observed between the ML and Bayesian methods. PMID:19001592
Bayesian hierarchical model for large-scale covariance matrix estimation.
Zhu, Dongxiao; Hero, Alfred O
2007-12-01
Many bioinformatics problems implicitly depend on estimating large-scale covariance matrix. The traditional approaches tend to give rise to high variance and low accuracy due to "overfitting." We cast the large-scale covariance matrix estimation problem into the Bayesian hierarchical model framework, and introduce dependency between covariance parameters. We demonstrate the advantages of our approaches over the traditional approaches using simulations and OMICS data analysis.
Hierarchical Approximate Bayesian Computation
Turner, Brandon M.; Van Zandt, Trisha
2013-01-01
Approximate Bayesian computation (ABC) is a powerful technique for estimating the posterior distribution of a model’s parameters. It is especially important when the model to be fit has no explicit likelihood function, which happens for computational (or simulation-based) models such as those that are popular in cognitive neuroscience and other areas in psychology. However, ABC is usually applied only to models with few parameters. Extending ABC to hierarchical models has been difficult because high-dimensional hierarchical models add computational complexity that conventional ABC cannot accommodate. In this paper we summarize some current approaches for performing hierarchical ABC and introduce a new algorithm called Gibbs ABC. This new algorithm incorporates well-known Bayesian techniques to improve the accuracy and efficiency of the ABC approach for estimation of hierarchical models. We then use the Gibbs ABC algorithm to estimate the parameters of two models of signal detection, one with and one without a tractable likelihood function. PMID:24297436
Road network safety evaluation using Bayesian hierarchical joint model.
Wang, Jie; Huang, Helai
2016-05-01
Safety and efficiency are commonly regarded as two significant performance indicators of transportation systems. In practice, road network planning has focused on road capacity and transport efficiency whereas the safety level of a road network has received little attention in the planning stage. This study develops a Bayesian hierarchical joint model for road network safety evaluation to help planners take traffic safety into account when planning a road network. The proposed model establishes relationships between road network risk and micro-level variables related to road entities and traffic volume, as well as socioeconomic, trip generation and network density variables at macro level which are generally used for long term transportation plans. In addition, network spatial correlation between intersections and their connected road segments is also considered in the model. A road network is elaborately selected in order to compare the proposed hierarchical joint model with a previous joint model and a negative binomial model. According to the results of the model comparison, the hierarchical joint model outperforms the joint model and negative binomial model in terms of the goodness-of-fit and predictive performance, which indicates the reasonableness of considering the hierarchical data structure in crash prediction and analysis. Moreover, both random effects at the TAZ level and the spatial correlation between intersections and their adjacent segments are found to be significant, supporting the employment of the hierarchical joint model as an alternative in road-network-level safety modeling as well.
Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring.
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
Spatial Bayesian hierarchical modelling of extreme sea states
NASA Astrophysics Data System (ADS)
Clancy, Colm; O'Sullivan, John; Sweeney, Conor; Dias, Frédéric; Parnell, Andrew C.
2016-11-01
A Bayesian hierarchical framework is used to model extreme sea states, incorporating a latent spatial process to more effectively capture the spatial variation of the extremes. The model is applied to a 34-year hindcast of significant wave height off the west coast of Ireland. The generalised Pareto distribution is fitted to declustered peaks over a threshold given by the 99.8th percentile of the data. Return levels of significant wave height are computed and compared against those from a model based on the commonly-used maximum likelihood inference method. The Bayesian spatial model produces smoother maps of return levels. Furthermore, this approach greatly reduces the uncertainty in the estimates, thus providing information on extremes which is more useful for practical applications.
DISSECTING MAGNETAR VARIABILITY WITH BAYESIAN HIERARCHICAL MODELS
Huppenkothen, Daniela; Elenbaas, Chris; Watts, Anna L.; Horst, Alexander J. van der; Brewer, Brendon J.; Hogg, David W.; Murray, Iain; Frean, Marcus; Levin, Yuri; Kouveliotou, Chryssa
2015-09-01
Neutron stars are a prime laboratory for testing physical processes under conditions of strong gravity, high density, and extreme magnetic fields. Among the zoo of neutron star phenomena, magnetars stand out for their bursting behavior, ranging from extremely bright, rare giant flares to numerous, less energetic recurrent bursts. The exact trigger and emission mechanisms for these bursts are not known; favored models involve either a crust fracture and subsequent energy release into the magnetosphere, or explosive reconnection of magnetic field lines. In the absence of a predictive model, understanding the physical processes responsible for magnetar burst variability is difficult. Here, we develop an empirical model that decomposes magnetar bursts into a superposition of small spike-like features with a simple functional form, where the number of model components is itself part of the inference problem. The cascades of spikes that we model might be formed by avalanches of reconnection, or crust rupture aftershocks. Using Markov Chain Monte Carlo sampling augmented with reversible jumps between models with different numbers of parameters, we characterize the posterior distributions of the model parameters and the number of components per burst. We relate these model parameters to physical quantities in the system, and show for the first time that the variability within a burst does not conform to predictions from ideas of self-organized criticality. We also examine how well the properties of the spikes fit the predictions of simplified cascade models for the different trigger mechanisms.
A Bayesian hierarchical model for categorical data with nonignorable nonresponse.
Green, Paul E; Park, Taesung
2003-12-01
Log-linear models have been shown to be useful for smoothing contingency tables when categorical outcomes are subject to nonignorable nonresponse. A log-linear model can be fit to an augmented data table that includes an indicator variable designating whether subjects are respondents or nonrespondents. Maximum likelihood estimates calculated from the augmented data table are known to suffer from instability due to boundary solutions. Park and Brown (1994, Journal of the American Statistical Association 89, 44-52) and Park (1998, Biometrics 54, 1579-1590) developed empirical Bayes models that tend to smooth estimates away from the boundary. In those approaches, estimates for nonrespondents were calculated using an EM algorithm by maximizing a posterior distribution. As an extension of their earlier work, we develop a Bayesian hierarchical model that incorporates a log-linear model in the prior specification. In addition, due to uncertainty in the variable selection process associated with just one log-linear model, we simultaneously consider a finite number of models using a stochastic search variable selection (SSVS) procedure due to George and McCulloch (1997, Statistica Sinica 7, 339-373). The integration of the SSVS procedure into a Markov chain Monte Carlo (MCMC) sampler is straightforward, and leads to estimates of cell frequencies for the nonrespondents that are averages resulting from several log-linear models. The methods are demonstrated with a data example involving serum creatinine levels of patients who survived renal transplants. A simulation study is conducted to investigate properties of the model.
A Bayesian hierarchical model for wind gust prediction
NASA Astrophysics Data System (ADS)
Friederichs, Petra; Oesting, Marco; Schlather, Martin
2014-05-01
A postprocessing method for ensemble wind gust forecasts given by a mesoscale limited area numerical weather prediction (NWP) model is presented, which is based on extreme value theory. A process layer for the parameters of a generalized extreme value distribution (GEV) is introduced using a Bayesian hierarchical model (BHM). Incorporating the information of the COMSO-DE forecasts, the process parameters model the spatial response surfaces of the GEV parameters as Gaussian random fields. The spatial BHM provides area wide forecasts of wind gusts in terms of a conditional GEV. It models the marginal distribution of the spatial gust process and provides not only forecasts of the conditional GEV at locations without observations, but also uncertainty information about the estimates. A disadvantages of BHM model is that it assumes conditional independent observations. In order to incorporate the dependence between gusts at neighboring locations as well as the spatial random fields of observed and forecasted maximal wind gusts, we propose to model them jointly by a bivariate Brown-Resnick process.
Predicting individual brain functional connectivity using a Bayesian hierarchical model.
Dai, Tian; Guo, Ying
2017-02-15
Network-oriented analysis of functional magnetic resonance imaging (fMRI), especially resting-state fMRI, has revealed important association between abnormal connectivity and brain disorders such as schizophrenia, major depression and Alzheimer's disease. Imaging-based brain connectivity measures have become a useful tool for investigating the pathophysiology, progression and treatment response of psychiatric disorders and neurodegenerative diseases. Recent studies have started to explore the possibility of using functional neuroimaging to help predict disease progression and guide treatment selection for individual patients. These studies provide the impetus to develop statistical methodology that would help provide predictive information on disease progression-related or treatment-related changes in neural connectivity. To this end, we propose a prediction method based on Bayesian hierarchical model that uses individual's baseline fMRI scans, coupled with relevant subject characteristics, to predict the individual's future functional connectivity. A key advantage of the proposed method is that it can improve the accuracy of individualized prediction of connectivity by combining information from both group-level connectivity patterns that are common to subjects with similar characteristics as well as individual-level connectivity features that are particular to the specific subject. Furthermore, our method also offers statistical inference tools such as predictive intervals that help quantify the uncertainty or variability of the predicted outcomes. The proposed prediction method could be a useful approach to predict the changes in individual patient's brain connectivity with the progression of a disease. It can also be used to predict a patient's post-treatment brain connectivity after a specified treatment regimen. Another utility of the proposed method is that it can be applied to test-retest imaging data to develop a more reliable estimator for individual
Hierarchical Bayesian cognitive processing models to analyze clinical trial data.
Shankle, William R; Hara, Junko; Mangrola, Tushar; Hendrix, Suzanne; Alva, Gus; Lee, Michael D
2013-07-01
Identifying disease-modifying treatment effects in earlier stages of Alzheimer's disease (AD)-when changes are subtle-will require improved trial design and more sensitive analytical methods. We applied hierarchical Bayesian analysis with cognitive processing (HBCP) models to the Alzheimer's Disease Assessment Scale-Cognitive subscale (ADAS-Cog) and MCI (mild cognitive impairment) Screen word list memory task data from 14 Alzheimer's disease AD patients of the Myriad Pharmaceuticals' phase III clinical trial of Flurizan (a γ-secretase modulator) versus placebo. The original analysis of 1649 patients found no treatment group differences. HBCP analysis and the original ADAS-Cog analysis were performed on the small sample. HBCP analysis detected impaired memory storage during delayed recall, whereas the original ADAS-Cog analytical method did not. The HBCP model identified a harmful treatment effect in a small sample, which has been independently confirmed from the results of other γ-secretase inhibitor. The original analytical method applied to the ADAS-Cog data did not detect this harmful treatment effect on either the full or the small sample. These findings suggest that HBCP models can detect treatment effects more sensitively than currently used analytical methods required by the Food and Drug Administration, and they do so using small patient samples.
Hierarchical Bayesian Model Averaging for Chance Constrained Remediation Designs
NASA Astrophysics Data System (ADS)
Chitsazan, N.; Tsai, F. T.
2012-12-01
Groundwater remediation designs are heavily relying on simulation models which are subjected to various sources of uncertainty in their predictions. To develop a robust remediation design, it is crucial to understand the effect of uncertainty sources. In this research, we introduce a hierarchical Bayesian model averaging (HBMA) framework to segregate and prioritize sources of uncertainty in a multi-layer frame, where each layer targets a source of uncertainty. The HBMA framework provides an insight to uncertainty priorities and propagation. In addition, HBMA allows evaluating model weights in different hierarchy levels and assessing the relative importance of models in each level. To account for uncertainty, we employ a chance constrained (CC) programming for stochastic remediation design. Chance constrained programming was implemented traditionally to account for parameter uncertainty. Recently, many studies suggested that model structure uncertainty is not negligible compared to parameter uncertainty. Using chance constrained programming along with HBMA can provide a rigorous tool for groundwater remediation designs under uncertainty. In this research, the HBMA-CC was applied to a remediation design in a synthetic aquifer. The design was to develop a scavenger well approach to mitigate saltwater intrusion toward production wells. HBMA was employed to assess uncertainties from model structure, parameter estimation and kriging interpolation. An improved harmony search optimization method was used to find the optimal location of the scavenger well. We evaluated prediction variances of chloride concentration at the production wells through the HBMA framework. The results showed that choosing the single best model may lead to a significant error in evaluating prediction variances for two reasons. First, considering the single best model, variances that stem from uncertainty in the model structure will be ignored. Second, considering the best model with non
A Bayesian hierarchical diffusion model decomposition of performance in Approach–Avoidance Tasks
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
Bayesian Hierarchical Classes Analysis
ERIC Educational Resources Information Center
Leenen, Iwin; Van Mechelen, Iven; Gelman, Andrew; De Knop, Stijn
2008-01-01
Hierarchical classes models are models for "N"-way "N"-mode data that represent the association among the "N" modes and simultaneously yield, for each mode, a hierarchical classification of its elements. In this paper we present a stochastic extension of the hierarchical classes model for two-way two-mode binary data. In line with the original…
Hierarchical models and Bayesian analysis of bird survey information
Sauer, J.R.; Link, W.A.; Royle, J. Andrew; Ralph, C. John; Rich, Terrell D.
2005-01-01
Summary of bird survey information is a critical component of conservation activities, but often our summaries rely on statistical methods that do not accommodate the limitations of the information. Prioritization of species requires ranking and analysis of species by magnitude of population trend, but often magnitude of trend is a misleading measure of actual decline when trend is poorly estimated. Aggregation of population information among regions is also complicated by varying quality of estimates among regions. Hierarchical models provide a reasonable means of accommodating concerns about aggregation and ranking of quantities of varying precision. In these models the need to consider multiple scales is accommodated by placing distributional assumptions on collections of parameters. For collections of species trends, this allows probability statements to be made about the collections of species-specific parameters, rather than about the estimates. We define and illustrate hierarchical models for two commonly encountered situations in bird conservation: (1) Estimating attributes of collections of species estimates, including ranking of trends, estimating number of species with increasing populations, and assessing population stability with regard to predefined trend magnitudes; and (2) estimation of regional population change, aggregating information from bird surveys over strata. User-friendly computer software makes hierarchical models readily accessible to scientists.
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
Hierarchical Bayesian Model (HBM) - Derived Estimates of Air Quality for 2007: Annual Report
This report describes EPA's Hierarchical Bayesian model generated (HBM) estimates of ozone (O_{3}) and fine particulate matter (PM_{2.5} particles with aerodynamic diameter < 2.5 microns)concentrations throughout the continental United States during the 2007 calen...
Hierarchical Bayesian Model (HBM)-Derived Estimates of Air Quality for 2004 - Annual Report
This report describes EPA's Hierarchical Bayesian model-generated (HBM) estimates of O_{3} and PM_{2.5} concentrations throughout the continental United States during the 2004 calendar year. HBM estimates provide the spatial and temporal variance of O_{3} ...
Hierarchical Bayesian Model (HBM)-Derived Estimates of Air Quality for 2002– Annual Report
This report describes EPA's Hierarchical Bayesian model-generated (HBM) estimates of O_{3} and PM_{2.5} concentrations throughout the continental United States during the 2002 calendar year. HBM estimates provide the spatial and temporal variance of O_{3} ...
Hierarchical Bayesian Model (HBM)-Derived Estimates of Air Quality for 2001 - Annual Report
This report describes EPA's Hierarchical Bayesian model-generated (HBM) estimates of O_{3} and PM_{2.5} concentrations throughout the continental United States during the 2001 calendar year. HBM estimates provide the spatial and temporal variance of O_{ 3}...
Hierarchical Bayesian Model (HBM)-Derived Estimates of Air Quality for 2003 – Annual Report
This report describes EPA's Hierarchical Bayesian model-generated (HBM) estimates of O_{3} and PM_{2.5} concentrations throughout the continental United States during the 2003 calendar year. HBM estimates provide the spatial and temporal variance of O_{3} ...
Hierarchical Bayesian Model (HBM)-Derived Estimates of Air Quality for 2005 - Annual Report
This report describes EPA's Hierarchical Bayesian model-generated (HBM) estimates of O_{3} and PM_{2.5} concentrations throughout the continental United States during the 2005 calendar year. HBM estimates provide the spatial and temporal variance of O_{3} ...
Hierarchical Bayesian Model (HBM) - Derived Estimates of Air Quality for 2008: Annual Report
This report describes EPA’s Hierarchical Bayesian model generated (HBM) estimates of ozone (O_{3}) and fine particulate matter (PM_{2.5}, particles with aerodynamic diameter < 2.5 microns) concentrations throughout the continental United States during the 2007 ca...
Hierarchical Bayesian Model (HBM)-Derived Estimates of Air Quality for 2006 - Annual Report
This report describes EPA's Hierarchical Bayesian model-generated (HBM) estimates of O_{3} and PM_{2.5} concentrations throughout the continental United States during the 2006 calendar year. HBM estimates provide the spatial and temporal variance of O_{3} ...
Hierarchical Bayesian Modeling, Estimation, and Sampling for Multigroup Shape Analysis
Yu, Yen-Yun; Fletcher, P. Thomas; Awate, Suyash P.
2016-01-01
This paper proposes a novel method for the analysis of anatomical shapes present in biomedical image data. Motivated by the natural organization of population data into multiple groups, this paper presents a novel hierarchical generative statistical model on shapes. The proposed method represents shapes using pointsets and defines a joint distribution on the population’s (i) shape variables and (ii) object-boundary data. The proposed method solves for optimal (i) point locations, (ii) correspondences, and (iii) model-parameter values as a single optimization problem. The optimization uses expectation maximization relying on a novel Markov-chain Monte-Carlo algorithm for sampling in Kendall shape space. Results on clinical brain images demonstrate advantages over the state of the art. PMID:25320776
A Bayesian hierarchical surrogate outcome model for multiple sclerosis.
Pozzi, Luca; Schmidli, Heinz; Ohlssen, David I
2016-07-01
The development of novel therapies in multiple sclerosis (MS) is one area where a range of surrogate outcomes are used in various stages of clinical research. While the aim of treatments in MS is to prevent disability, a clinical trial for evaluating a drugs effect on disability progression would require a large sample of patients with many years of follow-up. The early stage of MS is characterized by relapses. To reduce study size and duration, clinical relapses are accepted as primary endpoints in phase III trials. For phase II studies, the primary outcomes are typically lesion counts based on magnetic resonance imaging (MRI), as these are considerably more sensitive than clinical measures for detecting MS activity. Recently, Sormani and colleagues in 'Surrogate endpoints for EDSS worsening in multiple sclerosis' provided a systematic review and used weighted regression analyses to examine the role of either MRI lesions or relapses as trial level surrogate outcomes for disability. We build on this work by developing a Bayesian three-level model, accommodating the two surrogates and the disability endpoint, and properly taking into account that treatment effects are estimated with errors. Specifically, a combination of treatment effects based on MRI lesion count outcomes and clinical relapse was used to develop a study-level surrogate outcome model for the corresponding treatment effects based on disability progression. While the primary aim for developing this model was to support decision-making in drug development, the proposed model may also be considered for future validation. Copyright © 2016 John Wiley & Sons, Ltd.
Wu, Stephen; Angelikopoulos, Panagiotis; Tauriello, Gerardo; Papadimitriou, Costas; Koumoutsakos, Petros
2016-12-28
We propose a hierarchical Bayesian framework to systematically integrate heterogeneous data for the calibration of force fields in Molecular Dynamics (MD) simulations. Our approach enables the fusion of diverse experimental data sets of the physico-chemical properties of a system at different thermodynamic conditions. We demonstrate the value of this framework for the robust calibration of MD force-fields for water using experimental data of its diffusivity, radial distribution function, and density. In order to address the high computational cost associated with the hierarchical Bayesian models, we develop a novel surrogate model based on the empirical interpolation method. Further computational savings are achieved by implementing a highly parallel transitional Markov chain Monte Carlo technique. The present method bypasses possible subjective weightings of the experimental data in identifying MD force-field parameters.
NASA Astrophysics Data System (ADS)
Werner, Johannes; Tingley, Martin
2015-04-01
Reconstructions of late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurement on tree rings, ice cores, and varved lake sediments. Considerable advances may be achievable if time uncertain proxies could be included within these multiproxy reconstructions, and if time uncertainties were recognized and correctly modeled for proxies commonly treated as free of age model errors. Current approaches to accounting for time uncertainty are generally limited to repeating the reconstruction using each of an ensemble of age models, thereby inflating the final estimated uncertainty - in effect, each possible age model is given equal weighting. Uncertainties can be reduced by exploiting the inferred space-time covariance structure of the climate to re-weight the possible age models. Here we demonstrate how Bayesian Hierarchical climate reconstruction models can be augmented to account for time uncertain proxies. Critically, while a priori all age models are given equal probability of being correct, the probabilities associated with the age models are formally updated within the Bayesian framework, thereby reducing uncertainties. Numerical experiments show that updating the age model probabilities decreases uncertainty in the climate reconstruction, as compared with the current de-facto standard of sampling over all age models, provided there is sufficient information from other data sources in the region of the time-uncertain proxy. This approach can readily be generalized to non-layer counted proxies, such as those derived from marine sediments. Werner and Tingley, Climate of the Past Discussions (2014)
NASA Astrophysics Data System (ADS)
Werner, J. P.; Tingley, M. P.
2015-03-01
Reconstructions of the late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurements of tree rings, ice cores, and varved lake sediments. Considerable advances could be achieved if time-uncertain proxies were able to be included within these multiproxy reconstructions, and if time uncertainties were recognized and correctly modeled for proxies commonly treated as free of age model errors. Current approaches for accounting for time uncertainty are generally limited to repeating the reconstruction using each one of an ensemble of age models, thereby inflating the final estimated uncertainty - in effect, each possible age model is given equal weighting. Uncertainties can be reduced by exploiting the inferred space-time covariance structure of the climate to re-weight the possible age models. Here, we demonstrate how Bayesian hierarchical climate reconstruction models can be augmented to account for time-uncertain proxies. Critically, although a priori all age models are given equal probability of being correct, the probabilities associated with the age models are formally updated within the Bayesian framework, thereby reducing uncertainties. Numerical experiments show that updating the age model probabilities decreases uncertainty in the resulting reconstructions, as compared with the current de facto standard of sampling over all age models, provided there is sufficient information from other data sources in the spatial region of the time-uncertain proxy. This approach can readily be generalized to non-layer-counted proxies, such as those derived from marine sediments.
NASA Astrophysics Data System (ADS)
Werner, J. P.; Tingley, M. P.
2014-12-01
Reconstructions of late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurement on tree rings, ice cores, and varved lake sediments. Considerable advances may be achievable if time uncertain proxies could be included within these multiproxy reconstructions, and if time uncertainties were recognized and correctly modeled for proxies commonly treated as free of age model errors. Current approaches to accounting for time uncertainty are generally limited to repeating the reconstruction using each of an ensemble of age models, thereby inflating the final estimated uncertainty - in effect, each possible age model is given equal weighting. Uncertainties can be reduced by exploiting the inferred space-time covariance structure of the climate to re-weight the possible age models. Here we demonstrate how Bayesian Hierarchical climate reconstruction models can be augmented to account for time uncertain proxies. Critically, while a priori all age models are given equal probability of being correct, the probabilities associated with the age models are formally updated within the Bayesian framework, thereby reducing uncertainties. Numerical experiments show that updating the age-model probabilities decreases uncertainty in the climate reconstruction, as compared with the current de-facto standard of sampling over all age models, provided there is sufficient information from other data sources in the region of the time-uncertain proxy. This approach can readily be generalized to non-layer counted proxies, such as those derived from marine sediments.
NASA Astrophysics Data System (ADS)
Chen, X.; Hao, Z.; Devineni, N.; Lall, U.
2013-09-01
A Hierarchal Bayesian model for forecasting regional summer rainfall and streamflow season-ahead using exogenous climate variables for East Central China is presented. The model provides estimates of the posterior forecasted probability distribution for 12 rainfall and 2 streamflow stations considering parameter uncertainty, and cross-site correlation. The model has a multilevel structure with regression coefficients modeled from a common multivariate normal distribution results in partial-pooling of information across multiple stations and better representation of parameter and posterior distribution uncertainty. Covariance structure of the residuals across stations is explicitly modeled. Model performance is tested under leave-10-out cross-validation. Frequentist and Bayesian performance metrics used include Receiver Operating Characteristic, Reduction of Error, Coefficient of Efficiency, Rank Probability Skill Scores, and coverage by posterior credible intervals. The ability of the model to reliably forecast regional summer rainfall and streamflow season-ahead offers potential for developing adaptive water risk management strategies.
NASA Astrophysics Data System (ADS)
Chen, X.; Hao, Z.; Devineni, N.; Lall, U.
2014-04-01
A Hierarchal Bayesian model is presented for one season-ahead forecasts of summer rainfall and streamflow using exogenous climate variables for east central China. The model provides estimates of the posterior forecasted probability distribution for 12 rainfall and 2 streamflow stations considering parameter uncertainty, and cross-site correlation. The model has a multi-level structure with regression coefficients modeled from a common multi-variate normal distribution resulting in partial pooling of information across multiple stations and better representation of parameter and posterior distribution uncertainty. Covariance structure of the residuals across stations is explicitly modeled. Model performance is tested under leave-10-out cross-validation. Frequentist and Bayesian performance metrics used include receiver operating characteristic, reduction of error, coefficient of efficiency, rank probability skill scores, and coverage by posterior credible intervals. The ability of the model to reliably forecast season-ahead regional summer rainfall and streamflow offers potential for developing adaptive water risk management strategies.
The use of sampling weights in Bayesian hierarchical models for small area estimation
Chen, Cici; Wakefield, Jon; Lumely, Thomas
2015-01-01
Hierarchical modeling has been used extensively for small area estimation. However, design weights that are required to reflect complex surveys are rarely considered in these models. We develop computationally efficient, Bayesian spatial smoothing models that acknowledge the design weights. Computation is carried out using the integrated nested Laplace approximation, which is fast. A simulation study is presented that considers the effects of non-response and non-random selection of individuals. We examine the impact of ignoring the design weights and the benefits of spatial smoothing. The results show that, when compared with standard approaches, mean squared error can be greatly reduced with the proposed models. Bias reduction occurs through the inclusion of the design weights, with variance reduction being achieved through hierarchical smoothing. We analyze data from the Washington State 2006 Behavioral Risk Factor Surveillance System. The models are easily and quickly fitted within the R environment, using existing packages. PMID:25457595
Bayesian Multidimensional IRT Models with a Hierarchical Structure
ERIC Educational Resources Information Center
Sheng, Yanyan; Wikle, Christopher K.
2008-01-01
As item response models gain increased popularity in large-scale educational and measurement testing situations, many studies have been conducted on the development and applications of unidimensional and multidimensional models. Recently, attention has been paid to IRT-based models with an overall ability dimension underlying several ability…
BAYESIAN HIERARCHICAL MODELING FOR SIGNALING PATHWAY INFERENCE FROM SINGLE CELL INTERVENTIONAL DATA1
Luo, Ruiyan; Zhao, Hongyu
2011-01-01
Recent technological advances have made it possible to simultaneously measure multiple protein activities at the single cell level. With such data collected under different stimulatory or inhibitory conditions, it is possible to infer the causal relationships among proteins from single cell interventional data. In this article we propose a Bayesian hierarchical modeling framework to infer the signaling pathway based on the posterior distributions of parameters in the model. Under this framework, we consider network sparsity and model the existence of an association between two proteins both at the overall level across all experiments and at each individual experimental level. This allows us to infer the pairs of proteins that are associated with each other and their causal relationships. We also explicitly consider both intrinsic noise and measurement error. Markov chain Monte Carlo is implemented for statistical inference. We demonstrate that this hierarchical modeling can effectively pool information from different interventional experiments through simulation studies and real data analysis. PMID:22162986
Application of Bayesian hierarchical models for phase I/II clinical trials in oncology.
Yada, Shinjo; Hamada, Chikuma
2017-03-01
Treatment during cancer clinical trials sometimes involves the combination of multiple drugs. In addition, in recent years there has been a trend toward phase I/II trials in which a phase I and a phase II trial are combined into a single trial to accelerate drug development. Methods for the seamless combination of phases I and II parts are currently under investigation. In the phase II part, adaptive randomization on the basis of patient efficacy outcomes allocates more patients to the dose combinations considered to have higher efficacy. Patient toxicity outcomes are used for determining admissibility to each dose combination and are not used for selection of the dose combination itself. In cases where the objective is not to find the optimum dose combination solely for efficacy but regarding both toxicity and efficacy, the need exists to allocate patients to dose combinations with consideration of the balance of existing trade-offs between toxicity and efficacy. We propose a Bayesian hierarchical model and an adaptive randomization with consideration for the relationship with toxicity and efficacy. Using the toxicity and efficacy outcomes of patients, the Bayesian hierarchical model is used to estimate the toxicity probability and efficacy probability in each of the dose combinations. Here, we use Bayesian moving-reference adaptive randomization on the basis of desirability computed from the obtained estimator. Computer simulations suggest that the proposed method will likely recommend a higher percentage of target dose combinations than a previously proposed method.
Calibration of Automatically Generated Items Using Bayesian Hierarchical Modeling.
ERIC Educational Resources Information Center
Johnson, Matthew S.; Sinharay, Sandip
For complex educational assessments, there is an increasing use of "item families," which are groups of related items. However, calibration or scoring for such an assessment requires fitting models that take into account the dependence structure inherent among the items that belong to the same item family. C. Glas and W. van der Linden…
Gas turbine engine prognostics using Bayesian hierarchical models: A variational approach
NASA Astrophysics Data System (ADS)
Zaidan, Martha A.; Mills, Andrew R.; Harrison, Robert F.; Fleming, Peter J.
2016-03-01
Prognostics is an emerging requirement of modern health monitoring that aims to increase the fidelity of failure-time predictions by the appropriate use of sensory and reliability information. In the aerospace industry it is a key technology to reduce life-cycle costs, improve reliability and asset availability for a diverse fleet of gas turbine engines. In this work, a Bayesian hierarchical model is selected to utilise fleet data from multiple assets to perform probabilistic estimation of remaining useful life (RUL) for civil aerospace gas turbine engines. The hierarchical formulation allows Bayesian updates of an individual predictive model to be made, based upon data received asynchronously from a fleet of assets with different in-service lives and for the entry of new assets into the fleet. In this paper, variational inference is applied to the hierarchical formulation to overcome the computational and convergence concerns that are raised by the numerical sampling techniques needed for inference in the original formulation. The algorithm is tested on synthetic data, where the quality of approximation is shown to be satisfactory with respect to prediction performance, computational speed, and ease of use. A case study of in-service gas turbine engine data demonstrates the value of integrating fleet data for accurately predicting degradation trajectories of assets.
NASA Astrophysics Data System (ADS)
Tsai, Frank T.-C.; Elshall, Ahmed S.
2013-09-01
Analysts are often faced with competing propositions for each uncertain model component. How can we judge that we select a correct proposition(s) for an uncertain model component out of numerous possible propositions? We introduce the hierarchical Bayesian model averaging (HBMA) method as a multimodel framework for uncertainty analysis. The HBMA allows for segregating, prioritizing, and evaluating different sources of uncertainty and their corresponding competing propositions through a hierarchy of BMA models that forms a BMA tree. We apply the HBMA to conduct uncertainty analysis on the reconstructed hydrostratigraphic architectures of the Baton Rouge aquifer-fault system, Louisiana. Due to uncertainty in model data, structure, and parameters, multiple possible hydrostratigraphic models are produced and calibrated as base models. The study considers four sources of uncertainty. With respect to data uncertainty, the study considers two calibration data sets. With respect to model structure, the study considers three different variogram models, two geological stationarity assumptions and two fault conceptualizations. The base models are produced following a combinatorial design to allow for uncertainty segregation. Thus, these four uncertain model components with their corresponding competing model propositions result in 24 base models. The results show that the systematic dissection of the uncertain model components along with their corresponding competing propositions allows for detecting the robust model propositions and the major sources of uncertainty.
A Hierarchical Bayesian Model to Quantify Uncertainty of Stream Water Temperature Forecasts
Bal, Guillaume; Rivot, Etienne; Baglinière, Jean-Luc; White, Jonathan; Prévost, Etienne
2014-01-01
Providing generic and cost effective modelling approaches to reconstruct and forecast freshwater temperature using predictors as air temperature and water discharge is a prerequisite to understanding ecological processes underlying the impact of water temperature and of global warming on continental aquatic ecosystems. Using air temperature as a simple linear predictor of water temperature can lead to significant bias in forecasts as it does not disentangle seasonality and long term trends in the signal. Here, we develop an alternative approach based on hierarchical Bayesian statistical time series modelling of water temperature, air temperature and water discharge using seasonal sinusoidal periodic signals and time varying means and amplitudes. Fitting and forecasting performances of this approach are compared with that of simple linear regression between water and air temperatures using i) an emotive simulated example, ii) application to three French coastal streams with contrasting bio-geographical conditions and sizes. The time series modelling approach better fit data and does not exhibit forecasting bias in long term trends contrary to the linear regression. This new model also allows for more accurate forecasts of water temperature than linear regression together with a fair assessment of the uncertainty around forecasting. Warming of water temperature forecast by our hierarchical Bayesian model was slower and more uncertain than that expected with the classical regression approach. These new forecasts are in a form that is readily usable in further ecological analyses and will allow weighting of outcomes from different scenarios to manage climate change impacts on freshwater wildlife. PMID:25541732
Xu, Lizhen; Paterson, Andrew D; Xu, Wei
2017-04-01
Motivated by the multivariate nature of microbiome data with hierarchical taxonomic clusters, counts that are often skewed and zero inflated, and repeated measures, we propose a Bayesian latent variable methodology to jointly model multiple operational taxonomic units within a single taxonomic cluster. This novel method can incorporate both negative binomial and zero-inflated negative binomial responses, and can account for serial and familial correlations. We develop a Markov chain Monte Carlo algorithm that is built on a data augmentation scheme using Pólya-Gamma random variables. Hierarchical centering and parameter expansion techniques are also used to improve the convergence of the Markov chain. We evaluate the performance of our proposed method through extensive simulations. We also apply our method to a human microbiome study.
Xu, Lei; Johnson, Timothy D.; Nichols, Thomas E.; Nee, Derek E.
2010-01-01
Summary The aim of this work is to develop a spatial model for multi-subject fMRI data. There has been extensive work on univariate modeling of each voxel for single and multi-subject data, some work on spatial modeling of single-subject data, and some recent work on spatial modeling of multi-subject data. However, there has been no work on spatial models that explicitly account for inter-subject variability in activation locations. In this work, we use the idea of activation centers and model the inter-subject variability in activation locations directly. Our model is specified in a Bayesian hierarchical frame work which allows us to draw inferences at all levels: the population level, the individual level and the voxel level. We use Gaussian mixtures for the probability that an individual has a particular activation. This helps answer an important question which is not addressed by any of the previous methods: What proportion of subjects had a significant activity in a given region. Our approach incorporates the unknown number of mixture components into the model as a parameter whose posterior distribution is estimated by reversible jump Markov Chain Monte Carlo. We demonstrate our method with a fMRI study of resolving proactive interference and show dramatically better precision of localization with our method relative to the standard mass-univariate method. Although we are motivated by fMRI data, this model could easily be modified to handle other types of imaging data. PMID:19210732
NASA Astrophysics Data System (ADS)
Skataric, Maja; Bose, Sandip; Zeroug, Smaine; Tilke, Peter
2017-02-01
It is not uncommon in the field of non-destructive evaluation that multiple measurements encompassing a variety of modalities are available for analysis and interpretation for determining the underlying states of nature of the materials or parts being tested. Despite and sometimes due to the richness of data, significant challenges arise in the interpretation manifested as ambiguities and inconsistencies due to various uncertain factors in the physical properties (inputs), environment, measurement device properties, human errors, and the measurement data (outputs). Most of these uncertainties cannot be described by any rigorous mathematical means, and modeling of all possibilities is usually infeasible for many real time applications. In this work, we will discuss an approach based on Hierarchical Bayesian Graphical Models (HBGM) for the improved interpretation of complex (multi-dimensional) problems with parametric uncertainties that lack usable physical models. In this setting, the input space of the physical properties is specified through prior distributions based on domain knowledge and expertise, which are represented as Gaussian mixtures to model the various possible scenarios of interest for non-destructive testing applications. Forward models are then used offline to generate the expected distribution of the proposed measurements which are used to train a hierarchical Bayesian network. In Bayesian analysis, all model parameters are treated as random variables, and inference of the parameters is made on the basis of posterior distribution given the observed data. Learned parameters of the posterior distribution obtained after the training can therefore be used to build an efficient classifier for differentiating new observed data in real time on the basis of pre-trained models. We will illustrate the implementation of the HBGM approach to ultrasonic measurements used for cement evaluation of cased wells in the oil industry.
NASA Astrophysics Data System (ADS)
Cahill, Niamh; Kemp, Andrew C.; Horton, Benjamin P.; Parnell, Andrew C.
2016-02-01
We present a Bayesian hierarchical model for reconstructing the continuous and dynamic evolution of relative sea-level (RSL) change with quantified uncertainty. The reconstruction is produced from biological (foraminifera) and geochemical (δ13C) sea-level indicators preserved in dated cores of salt-marsh sediment. Our model is comprised of three modules: (1) a new Bayesian transfer (B-TF) function for the calibration of biological indicators into tidal elevation, which is flexible enough to formally accommodate additional proxies; (2) an existing chronology developed using the Bchron age-depth model, and (3) an existing Errors-In-Variables integrated Gaussian process (EIV-IGP) model for estimating rates of sea-level change. Our approach is illustrated using a case study of Common Era sea-level variability from New Jersey, USA We develop a new B-TF using foraminifera, with and without the additional (δ13C) proxy and compare our results to those from a widely used weighted-averaging transfer function (WA-TF). The formal incorporation of a second proxy into the B-TF model results in smaller vertical uncertainties and improved accuracy for reconstructed RSL. The vertical uncertainty from the multi-proxy B-TF is ˜ 28 % smaller on average compared to the WA-TF. When evaluated against historic tide-gauge measurements, the multi-proxy B-TF most accurately reconstructs the RSL changes observed in the instrumental record (mean square error = 0.003 m2). The Bayesian hierarchical model provides a single, unifying framework for reconstructing and analyzing sea-level change through time. This approach is suitable for reconstructing other paleoenvironmental variables (e.g., temperature) using biological proxies.
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
Scheel, Ida; Ferkingstad, Egil; Frigessi, Arnoldo; Haug, Ola; Hinnerichsen, Mikkel; Meze-Hausken, Elisabeth
2013-01-01
Climate change will affect the insurance industry. We develop a Bayesian hierarchical statistical approach to explain and predict insurance losses due to weather events at a local geographic scale. The number of weather-related insurance claims is modelled by combining generalized linear models with spatially smoothed variable selection. Using Gibbs sampling and reversible jump Markov chain Monte Carlo methods, this model is fitted on daily weather and insurance data from each of the 319 municipalities which constitute southern and central Norway for the period 1997–2006. Precise out-of-sample predictions validate the model. Our results show interesting regional patterns in the effect of different weather covariates. In addition to being useful for insurance pricing, our model can be used for short-term predictions based on weather forecasts and for long-term predictions based on downscaled climate models. PMID:23396890
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.
Prion Amplification and Hierarchical Bayesian Modeling Refine Detection of Prion Infection
NASA Astrophysics Data System (ADS)
Wyckoff, A. Christy; Galloway, Nathan; Meyerett-Reid, Crystal; Powers, Jenny; Spraker, Terry; Monello, Ryan J.; Pulford, Bruce; Wild, Margaret; Antolin, Michael; Vercauteren, Kurt; Zabel, Mark
2015-02-01
Prions are unique infectious agents that replicate without a genome and cause neurodegenerative diseases that include chronic wasting disease (CWD) of cervids. Immunohistochemistry (IHC) is currently considered the gold standard for diagnosis of a prion infection but may be insensitive to early or sub-clinical CWD that are important to understanding CWD transmission and ecology. We assessed the potential of serial protein misfolding cyclic amplification (sPMCA) to improve detection of CWD prior to the onset of clinical signs. We analyzed tissue samples from free-ranging Rocky Mountain elk (Cervus elaphus nelsoni) and used hierarchical Bayesian analysis to estimate the specificity and sensitivity of IHC and sPMCA conditional on simultaneously estimated disease states. Sensitivity estimates were higher for sPMCA (99.51%, credible interval (CI) 97.15-100%) than IHC of obex (brain stem, 76.56%, CI 57.00-91.46%) or retropharyngeal lymph node (90.06%, CI 74.13-98.70%) tissues, or both (98.99%, CI 90.01-100%). Our hierarchical Bayesian model predicts the prevalence of prion infection in this elk population to be 18.90% (CI 15.50-32.72%), compared to previous estimates of 12.90%. Our data reveal a previously unidentified sub-clinical prion-positive portion of the elk population that could represent silent carriers capable of significantly impacting CWD ecology.
Dodds, Michael G; Vicini, Paolo
2004-09-01
Advances in computer hardware and the associated computer-intensive algorithms made feasible by these advances [like Markov chain Monte Carlo (MCMC) data analysis techniques] have made possible the application of hierarchical full Bayesian methods in analyzing pharmacokinetic and pharmacodynamic (PK-PD) data sets that are multivariate in nature. Pharmacokinetic data analysis in particular has been one area that has seized upon this technology to refine estimates of drug parameters from sparse data gathered in a large, highly variable population of patients. A drawback in this type of analysis is that it is difficult to quantitatively assess convergence of the Markov chains to a target distribution, and thus, it is sometimes difficult to assess the reliability of estimates gained from this procedure. Another complicating factor is that, although the application of MCMC methods to population PK-PD problems has been facilitated by new software designed for the PK-PD domain (specifically PKBUGS), experts in PK-PD may not have the necessary experience with MCMC methods to detect and understand problems with model convergence. The objective of this work is to provide an example of a set of diagnostics useful to investigators, by analyzing in detail three convergence criteria (namely the Raftery and Lewis, Geweke, and Heidelberger and Welch methods) on a simulated problem and with a rule of thumb of 10,000 chain elements in the Markov chain. We used two publicly available software packages to assess convergence of MCMC parameter estimates; the first performs Bayesian parameter estimation (PKBUGS/WinBUGS), and the second is focused on posterior analysis of estimates (BOA). The main message that seems to emerge is that accurately estimating confidence regions for the parameters of interest is more demanding than estimating the parameter means. Together, these tools provide numerical means by which an investigator can establish confidence in convergence and thus in the
A Bayesian hierarchical nonhomogeneous hidden Markov model for multisite streamflow reconstructions
NASA Astrophysics Data System (ADS)
Bracken, C.; Rajagopalan, B.; Woodhouse, C.
2016-10-01
In many complex water supply systems, the next generation of water resources planning models will require simultaneous probabilistic streamflow inputs at multiple locations on an interconnected network. To make use of the valuable multicentury records provided by tree-ring data, reconstruction models must be able to produce appropriate multisite inputs. Existing streamflow reconstruction models typically focus on one site at a time, not addressing intersite dependencies and potentially misrepresenting uncertainty. To this end, we develop a model for multisite streamflow reconstruction with the ability to capture intersite correlations. The proposed model is a hierarchical Bayesian nonhomogeneous hidden Markov model (NHMM). A NHMM is fit to contemporary streamflow at each location using lognormal component distributions. Leading principal components of tree rings are used as covariates to model nonstationary transition probabilities and the parameters of the lognormal component distributions. Spatial dependence between sites is captured with a Gaussian elliptical copula. Parameters of the model are estimated in a fully Bayesian framework, in that marginal posterior distributions of all the parameters are obtained. The model is applied to reconstruct flows at 20 sites in the Upper Colorado River Basin (UCRB) from 1473 to 1906. Many previous reconstructions are available for this basin, making it ideal for testing this new method. The results show some improvements over regression-based methods in terms of validation statistics. Key advantages of the Bayesian NHMM over traditional approaches are a dynamic representation of uncertainty and the ability to make long multisite simulations that capture at-site statistics and spatial correlations between sites.
A Flexible Hierarchical Bayesian Modeling Technique for Risk Analysis of Major Accidents.
Yu, Hongyang; Khan, Faisal; Veitch, Brian
2017-02-28
Safety analysis of rare events with potentially catastrophic consequences is challenged by data scarcity and uncertainty. Traditional causation-based approaches, such as fault tree and event tree (used to model rare event), suffer from a number of weaknesses. These include the static structure of the event causation, lack of event occurrence data, and need for reliable prior information. In this study, a new hierarchical Bayesian modeling based technique is proposed to overcome these drawbacks. The proposed technique can be used as a flexible technique for risk analysis of major accidents. It enables both forward and backward analysis in quantitative reasoning and the treatment of interdependence among the model parameters. Source-to-source variability in data sources is also taken into account through a robust probabilistic safety analysis. The applicability of the proposed technique has been demonstrated through a case study in marine and offshore industry.
NASA Astrophysics Data System (ADS)
Cahill, N.; Kemp, A. C.; Horton, B. P.; Parnell, A. C.
2015-10-01
We present a holistic Bayesian hierarchical model for reconstructing the continuous and dynamic evolution of relative sea-level (RSL) change with fully quantified uncertainty. The reconstruction is produced from biological (foraminifera) and geochemical (δ13C) sea-level indicators preserved in dated cores of salt-marsh sediment. Our model is comprised of three modules: (1) A Bayesian transfer function for the calibration of foraminifera into tidal elevation, which is flexible enough to formally accommodate additional proxies (in this case bulk-sediment δ13C values), (2) A chronology developed from an existing Bchron age-depth model, and (3) An existing errors-in-variables integrated Gaussian process (EIV-IGP) model for estimating rates of sea-level change. We illustrate our approach using a case study of Common Era sea-level variability from New Jersey. USA We develop a new Bayesian transfer function (B-TF), with and without the δ13C proxy and compare our results to those from a widely-used weighted-averaging transfer function (WA-TF). The formal incorporation of a second proxy into the B-TF model results in smaller vertical uncertainties and improved accuracy for reconstructed RSL. The vertical uncertainty from the multi-proxy B-TF is ∼ 28 % smaller on average compared to the WA-TF. When evaluated against historic tide-gauge measurements, the multi-proxy B-TF most accurately reconstructs the RSL changes observed in the instrumental record (MSE = 0.003 m2). The holistic model provides a single, unifying framework for reconstructing and analysing sea level through time. This approach is suitable for reconstructing other paleoenvironmental variables using biological proxies.
Epigenetic change detection and pattern recognition via Bayesian hierarchical hidden Markov models.
Wang, Xinlei; Zang, Miao; Xiao, Guanghua
2013-06-15
Epigenetics is the study of changes to the genome that can switch genes on or off and determine which proteins are transcribed without altering the DNA sequence. Recently, epigenetic changes have been linked to the development and progression of disease such as psychiatric disorders. High-throughput epigenetic experiments have enabled researchers to measure genome-wide epigenetic profiles and yield data consisting of intensity ratios of immunoprecipitation versus reference samples. The intensity ratios can provide a view of genomic regions where protein binding occur under one experimental condition and further allow us to detect epigenetic alterations through comparison between two different conditions. However, such experiments can be expensive, with only a few replicates available. Moreover, epigenetic data are often spatially correlated with high noise levels. In this paper, we develop a Bayesian hierarchical model, combined with hidden Markov processes with four states for modeling spatial dependence, to detect genomic sites with epigenetic changes from two-sample experiments with paired internal control. One attractive feature of the proposed method is that the four states of the hidden Markov process have well-defined biological meanings and allow us to directly call the change patterns based on the corresponding posterior probabilities. In contrast, none of existing methods can offer this advantage. In addition, the proposed method offers great power in statistical inference by spatial smoothing (via hidden Markov modeling) and information pooling (via hierarchical modeling). Both simulation studies and real data analysis in a cocaine addiction study illustrate the reliability and success of this method.
Holan, S.H.; Davis, G.M.; Wildhaber, M.L.; DeLonay, A.J.; Papoulias, D.M.
2009-01-01
The timing of spawning in fish is tightly linked to environmental factors; however, these factors are not very well understood for many species. Specifically, little information is available to guide recruitment efforts for endangered species such as the sturgeon. Therefore, we propose a Bayesian hierarchical model for predicting the success of spawning of the shovelnose sturgeon which uses both biological and behavioural (longitudinal) data. In particular, we use data that were produced from a tracking study that was conducted in the Lower Missouri River. The data that were produced from this study consist of biological variables associated with readiness to spawn along with longitudinal behavioural data collected by using telemetry and archival data storage tags. These high frequency data are complex both biologically and in the underlying behavioural process. To accommodate such complexity we developed a hierarchical linear regression model that uses an eigenvalue predictor, derived from the transition probability matrix of a two-state Markov switching model with generalized auto-regressive conditional heteroscedastic dynamics. Finally, to minimize the computational burden that is associated with estimation of this model, a parallel computing approach is proposed. ?? Journal compilation 2009 Royal Statistical Society.
Merging information from multi-model flood projections in a hierarchical Bayesian framework
NASA Astrophysics Data System (ADS)
Le Vine, Nataliya
2016-04-01
Multi-model ensembles are becoming widely accepted for flood frequency change analysis. The use of multiple models results in large uncertainty around estimates of flood magnitudes, due to both uncertainty in model selection and natural variability of river flow. The challenge is therefore to extract the most meaningful signal from the multi-model predictions, accounting for both model quality and uncertainties in individual model estimates. The study demonstrates the potential of a recently proposed hierarchical Bayesian approach to combine information from multiple models. The approach facilitates explicit treatment of shared multi-model discrepancy as well as the probabilistic nature of the flood estimates, by treating the available models as a sample from a hypothetical complete (but unobserved) set of models. The advantages of the approach are: 1) to insure an adequate 'baseline' conditions with which to compare future changes; 2) to reduce flood estimate uncertainty; 3) to maximize use of statistical information in circumstances where multiple weak predictions individually lack power, but collectively provide meaningful information; 4) to adjust multi-model consistency criteria when model biases are large; and 5) to explicitly consider the influence of the (model performance) stationarity assumption. Moreover, the analysis indicates that reducing shared model discrepancy is the key to further reduction of uncertainty in the flood frequency analysis. The findings are of value regarding how conclusions about changing exposure to flooding are drawn, and to flood frequency change attribution studies.
Application of hierarchical Bayesian unmixing models in river sediment source apportionment
NASA Astrophysics Data System (ADS)
Blake, Will; Smith, Hugh; Navas, Ana; Bodé, Samuel; Goddard, Rupert; Zou Kuzyk, Zou; Lennard, Amy; Lobb, David; Owens, Phil; Palazon, Leticia; Petticrew, Ellen; Gaspar, Leticia; Stock, Brian; Boeckx, Pacsal; Semmens, Brice
2016-04-01
Fingerprinting and unmixing concepts are used widely across environmental disciplines for forensic evaluation of pollutant sources. In aquatic and marine systems, this includes tracking the source of organic and inorganic pollutants in water and linking problem sediment to soil erosion and land use sources. It is, however, the particular complexity of ecological systems that has driven creation of the most sophisticated mixing models, primarily to (i) evaluate diet composition in complex ecological food webs, (ii) inform population structure and (iii) explore animal movement. In the context of the new hierarchical Bayesian unmixing model, MIXSIAR, developed to characterise intra-population niche variation in ecological systems, we evaluate the linkage between ecological 'prey' and 'consumer' concepts and river basin sediment 'source' and sediment 'mixtures' to exemplify the value of ecological modelling tools to river basin science. Recent studies have outlined advantages presented by Bayesian unmixing approaches in handling complex source and mixture datasets while dealing appropriately with uncertainty in parameter probability distributions. MixSIAR is unique in that it allows individual fixed and random effects associated with mixture hierarchy, i.e. factors that might exert an influence on model outcome for mixture groups, to be explored within the source-receptor framework. This offers new and powerful ways of interpreting river basin apportionment data. In this contribution, key components of the model are evaluated in the context of common experimental designs for sediment fingerprinting studies namely simple, nested and distributed catchment sampling programmes. Illustrative examples using geochemical and compound specific stable isotope datasets are presented and used to discuss best practice with specific attention to (1) the tracer selection process, (2) incorporation of fixed effects relating to sample timeframe and sediment type in the modelling
NASA Astrophysics Data System (ADS)
Cha, YoonKyung; Soon Park, Seok; Won Lee, Hye; Stow, Craig A.
2016-01-01
Modeling to accurately predict river phytoplankton distribution and abundance is important in water quality and resource management. Nevertheless, the complex nature of eutrophication processes in highly connected river systems makes the task challenging. To model dynamics of river phytoplankton, represented by chlorophyll a (Chl a) concentration, we propose a Bayesian hierarchical model that explicitly accommodates seasonality and upstream-downstream spatial gradient in the structure. The utility of our model is demonstrated with an application to the Nakdong River (South Korea), which is a eutrophic, intensively regulated river, but functions as an irreplaceable water source for more than 13 million people. Chl a is modeled with two manageable factors, river flow, and total phosphorus (TP) concentration. Our model results highlight the importance of taking seasonal and spatial context into account when describing flow regimes and phosphorus delivery in rivers. A contrasting positive Chl a-flow relationship across stations versus negative Chl a-flow slopes that arose when Chl a was modeled on a station-month basis is an illustration of Simpson's paradox, which necessitates modeling Chl a-flow relationships decomposed into seasonal and spatial components. Similar Chl a-TP slopes among stations and months suggest that, with the flow effect removed, positive TP effects on Chl a are uniform regardless of the season and station in the river. Our model prediction successfully captured the shift in the spatial and monthly patterns of Chl a.
Jin, Ick Hoon; Yuan, Ying; Bandyopadhyay, Dipankar
2016-01-01
Research in dental caries generates data with two levels of hierarchy: that of a tooth overall and that of the different surfaces of the tooth. The outcomes often exhibit spatial referencing among neighboring teeth and surfaces, i.e., the disease status of a tooth or surface might be influenced by the status of a set of proximal teeth/surfaces. Assessments of dental caries (tooth decay) at the tooth level yield binary outcomes indicating the presence/absence of teeth, and trinary outcomes at the surface level indicating healthy, decayed, or filled surfaces. The presence of these mixed discrete responses complicates the data analysis under a unified framework. To mitigate complications, we develop a Bayesian two-level hierarchical model under suitable (spatial) Markov random field assumptions that accommodates the natural hierarchy within the mixed responses. At the first level, we utilize an autologistic model to accommodate the spatial dependence for the tooth-level binary outcomes. For the second level and conditioned on a tooth being non-missing, we utilize a Potts model to accommodate the spatial referencing for the surface-level trinary outcomes. The regression models at both levels were controlled for plausible covariates (risk factors) of caries, and remain connected through shared parameters. To tackle the computational challenges in our Bayesian estimation scheme caused due to the doubly-intractable normalizing constant, we employ a double Metropolis-Hastings sampler. We compare and contrast our model performances to the standard non-spatial (naive) model using a small simulation study, and illustrate via an application to a clinical dataset on dental caries. PMID:27807470
Full Bayesian hierarchical light curve modeling of core-collapse supernova populations
NASA Astrophysics Data System (ADS)
Sanders, Nathan; Betancourt, Michael; Soderberg, Alicia Margarita
2016-06-01
While wide field surveys have yielded remarkable quantities of photometry of transient objects, including supernovae, light curves reconstructed from this data suffer from several characteristic problems. Because most transients are discovered near the detection limit, signal to noise is generally poor; because coverage is limited to the observing season, light curves are often incomplete; and because temporal sampling can be uneven across filters, these problems can be exacerbated at any one wavelength. While the prevailing approach of modeling individual light curves independently is successful at recovering inferences for the objects with the highest quality observations, it typically neglects a substantial portion of the data and can introduce systematic biases. Joint modeling of the light curves of transient populations enables direct inference on population-level characteristics as well as superior measurements for individual objects. We present a new hierarchical Bayesian model for supernova light curves, where information inferred from observations of every individual light curve in a sample is partially pooled across objects to constrain population-level hyperparameters. Using an efficient Hamiltonian Monte Carlo sampling technique, the model posterior can be explored to enable marginalization over weakly-identified hyperparameters through full Bayesian inference. We demonstrate our technique on the Pan-STARRS1 (PS1) Type IIP supernova light curve sample published by Sanders et al. (2015), consisting of nearly 20,000 individual photometric observations of more than 70 supernovae in five photometric filters. We discuss the Stan probabilistic programming language used to implement the model, computational challenges, and prospects for future work including generalization to multiple supernova types. We also discuss scientific results from the PS1 dataset including a new relation between the peak magnitude and decline rate of SNe IIP, a new perspective on the
Hierarchical Bayesian Approach to Locating Seismic Events
Johannesson, G; Myers, S C; Hanley, W G
2005-11-09
We propose a hierarchical Bayesian model for conducting inference on the location of multiple seismic events (earthquakes) given data on the arrival of various seismic phases to sensor locations. The model explicitly accounts for the uncertainty associated with a theoretical seismic-wave travel-time model used along with the uncertainty of the arrival data. Posterior inferences is carried out using Markov chain Monte Carlo (MCMC).
Jiménez, José; García, Emilio J; Llaneza, Luis; Palacios, Vicente; González, Luis Mariano; García-Domínguez, Francisco; Múñoz-Igualada, Jaime; López-Bao, José Vicente
2016-08-01
In many cases, the first step in large-carnivore management is to obtain objective, reliable, and cost-effective estimates of population parameters through procedures that are reproducible over time. However, monitoring predators over large areas is difficult, and the data have a high level of uncertainty. We devised a practical multimethod and multistate modeling approach based on Bayesian hierarchical-site-occupancy models that combined multiple survey methods to estimate different population states for use in monitoring large predators at a regional scale. We used wolves (Canis lupus) as our model species and generated reliable estimates of the number of sites with wolf reproduction (presence of pups). We used 2 wolf data sets from Spain (Western Galicia in 2013 and Asturias in 2004) to test the approach. Based on howling surveys, the naïve estimation (i.e., estimate based only on observations) of the number of sites with reproduction was 9 and 25 sites in Western Galicia and Asturias, respectively. Our model showed 33.4 (SD 9.6) and 34.4 (3.9) sites with wolf reproduction, respectively. The number of occupied sites with wolf reproduction was 0.67 (SD 0.19) and 0.76 (0.11), respectively. This approach can be used to design more cost-effective monitoring programs (i.e., to define the sampling effort needed per site). Our approach should inspire well-coordinated surveys across multiple administrative borders and populations and lead to improved decision making for management of large carnivores on a landscape level. The use of this Bayesian framework provides a simple way to visualize the degree of uncertainty around population-parameter estimates and thus provides managers and stakeholders an intuitive approach to interpreting monitoring results. Our approach can be widely applied to large spatial scales in wildlife monitoring where detection probabilities differ between population states and where several methods are being used to estimate different population
How does aging affect recognition-based inference? A hierarchical Bayesian modeling approach.
Horn, Sebastian S; Pachur, Thorsten; Mata, Rui
2015-01-01
The recognition heuristic (RH) is a simple strategy for probabilistic inference according to which recognized objects are judged to score higher on a criterion than unrecognized objects. In this article, a hierarchical Bayesian extension of the multinomial r-model is applied to measure use of the RH on the individual participant level and to re-evaluate differences between younger and older adults' strategy reliance across environments. Further, it is explored how individual r-model parameters relate to alternative measures of the use of recognition and other knowledge, such as adherence rates and indices from signal-detection theory (SDT). Both younger and older adults used the RH substantially more often in an environment with high than low recognition validity, reflecting adaptivity in strategy use across environments. In extension of previous analyses (based on adherence rates), hierarchical modeling revealed that in an environment with low recognition validity, (a) older adults had a stronger tendency than younger adults to rely on the RH and (b) variability in RH use between individuals was larger than in an environment with high recognition validity; variability did not differ between age groups. Further, the r-model parameters correlated moderately with an SDT measure expressing how well people can discriminate cases where the RH leads to a correct vs. incorrect inference; this suggests that the r-model and the SDT measures may offer complementary insights into the use of recognition in decision making. In conclusion, younger and older adults are largely adaptive in their application of the RH, but cognitive aging may be associated with an increased tendency to rely on this strategy.
Cruz-Marcelo, Alejandro; Ensor, Katherine B; Rosner, Gary L
2011-06-01
The term structure of interest rates is used to price defaultable bonds and credit derivatives, as well as to infer the quality of bonds for risk management purposes. We introduce a model that jointly estimates term structures by means of a Bayesian hierarchical model with a prior probability model based on Dirichlet process mixtures. The modeling methodology borrows strength across term structures for purposes of estimation. The main advantage of our framework is its ability to produce reliable estimators at the company level even when there are only a few bonds per company. After describing the proposed model, we discuss an empirical application in which the term structure of 197 individual companies is estimated. The sample of 197 consists of 143 companies with only one or two bonds. In-sample and out-of-sample tests are used to quantify the improvement in accuracy that results from approximating the term structure of corporate bonds with estimators by company rather than by credit rating, the latter being a popular choice in the financial literature. A complete description of a Markov chain Monte Carlo (MCMC) scheme for the proposed model is available as Supplementary Material.
Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models
NASA Astrophysics Data System (ADS)
Vakilzadeh, Majid K.; Huang, Yong; Beck, James L.; Abrahamsson, Thomas
2017-02-01
A new multi-level Markov Chain Monte Carlo algorithm for Approximate Bayesian Computation, ABC-SubSim, has recently appeared that exploits the Subset Simulation method for efficient rare-event simulation. ABC-SubSim adaptively creates a nested decreasing sequence of data-approximating regions in the output space that correspond to increasingly closer approximations of the observed output vector in this output space. At each level, multiple samples of the model parameter vector are generated by a component-wise Metropolis algorithm so that the predicted output corresponding to each parameter value falls in the current data-approximating region. Theoretically, if continued to the limit, the sequence of data-approximating regions would converge on to the observed output vector and the approximate posterior distributions, which are conditional on the data-approximation region, would become exact, but this is not practically feasible. In this paper we study the performance of the ABC-SubSim algorithm for Bayesian updating of the parameters of dynamical systems using a general hierarchical state-space model. We note that the ABC methodology gives an approximate posterior distribution that actually corresponds to an exact posterior where a uniformly distributed combined measurement and modeling error is added. We also note that ABC algorithms have a problem with learning the uncertain error variances in a stochastic state-space model and so we treat them as nuisance parameters and analytically integrate them out of the posterior distribution. In addition, the statistical efficiency of the original ABC-SubSim algorithm is improved by developing a novel strategy to regulate the proposal variance for the component-wise Metropolis algorithm at each level. We demonstrate that Self-regulated ABC-SubSim is well suited for Bayesian system identification by first applying it successfully to model updating of a two degree-of-freedom linear structure for three cases: globally
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
Huang, Yangxin; Wu, Hulin; Acosta, Edward P
2010-08-01
Studies on HIV dynamics in AIDS research are very important in understanding the pathogenesis of HIV-1 infection and also in assessing the effectiveness of antiretroviral (ARV) treatment. Viral dynamic models can be formulated through a system of nonlinear ordinary differential equations (ODE), but there has been only limited development of statistical methodologies for inference. This article, motivated by an AIDS clinical study, discusses a hierarchical Bayesian nonlinear mixed-effects modeling approach to dynamic ODE models without a closed-form solution. In this model, we fully integrate viral load, medication adherence, drug resistance, pharmacokinetics, baseline covariates and time-dependent drug efficacy into the data analysis for characterizing long-term virologic responses. Our method is implemented by a data set from an AIDS clinical study. The results suggest that modeling HIV dynamics and virologic responses with consideration of time-varying clinical factors as well as baseline characteristics may be important for HIV/AIDS studies in providing quantitative guidance to better understand the virologic responses to ARV treatment and to help the evaluation of clinical trial design in response to existing therapies.
A Bayesian Hierarchical Modeling Approach to Predicting Flow in Ungauged Basins
NASA Astrophysics Data System (ADS)
Gronewold, A.; Alameddine, I.; Anderson, R. M.
2009-12-01
Recent innovative approaches to identifying and applying regression-based relationships between land use patterns (such as increasing impervious surface area and decreasing vegetative cover) and rainfall-runoff model parameters represent novel and promising improvements to predicting flow from ungauged basins. In particular, these approaches allow for predicting flows under uncertain and potentially variable future conditions due to rapid land cover changes, variable climate conditions, and other factors. Despite the broad range of literature on estimating rainfall-runoff model parameters, however, the absence of a robust set of modeling tools for identifying and quantifying uncertainties in (and correlation between) rainfall-runoff model parameters represents a significant gap in current hydrological modeling research. Here, we build upon a series of recent publications promoting novel Bayesian and probabilistic modeling strategies for quantifying rainfall-runoff model parameter estimation uncertainty. Our approach applies alternative measures of rainfall-runoff model parameter joint likelihood (including Nash-Sutcliffe efficiency, among others) to simulate samples from the joint parameter posterior probability density function. We then use these correlated samples as response variables in a Bayesian hierarchical model with land use coverage data as predictor variables in order to develop a robust land use-based tool for forecasting flow in ungauged basins while accounting for, and explicitly acknowledging, parameter estimation uncertainty. We apply this modeling strategy to low-relief coastal watersheds of Eastern North Carolina, an area representative of coastal resource waters throughout the world because of its sensitive embayments and because of the abundant (but currently threatened) natural resources it hosts. Consequently, this area is the subject of several ongoing studies and large-scale planning initiatives, including those conducted through the United
2008-01-01
Background Marine allopatric speciation is an enigma because pelagic larval dispersal can potentially connect disjunct populations thereby preventing reproductive and morphological divergence. Here we present a new hierarchical approximate Bayesian computation model (HABC) that tests two hypotheses of marine allopatric speciation: 1.) "soft vicariance", where a speciation involves fragmentation of a large widespread ancestral species range that was previously connected by long distance gene flow; and 2.) peripatric colonization, where speciations in peripheral archipelagos emerge from sweepstakes colonizations from central source regions. The HABC approach analyzes all the phylogeographic datasets at once in order to make across taxon-pair inferences about biogeographic processes while explicitly allowing for uncertainty in the demographic differences within each taxon-pair. Our method uses comparative phylogeographic data that consists of single locus mtDNA sequences from multiple co-distributed taxa containing pairs of central and peripheral populations. We use the method on two comparative phylogeographic data sets consisting of cowrie gastropod endemics co-distributed in the Hawaiian (11 taxon-pairs) and Marquesan archipelagos (7 taxon-pairs). Results Given the Marquesan data, we find strong evidence of simultaneous colonization across all seven cowrie gastropod endemics co-distributed in the Marquesas. In contrast, the lower sample sizes in the Hawaiian data lead to greater uncertainty associated with the Hawaiian estimates. Although, the hyper-parameter estimates point to soft vicariance in a subset of the 11 Hawaiian taxon-pairs, the hyper-prior and hyper-posterior are too similar to make a definitive conclusion. Both results are not inconsistent with what is known about the geologic history of the archipelagos. Simulations verify that our method can successfully distinguish these two histories across a wide range of conditions given sufficient sampling
Hu, Yi; Ward, Michael P; Xia, Congcong; Li, Rui; Sun, Liqian; Lynn, Henry; Gao, Fenghua; Wang, Qizhi; Zhang, Shiqing; Xiong, Chenglong; Zhang, Zhijie; Jiang, Qingwu
2016-04-07
Schistosomiasis remains a major public health problem and causes substantial economic impact in east China, particularly along the Yangtze River Basin. Disease forecasting and surveillance can assist in the development and implementation of more effective intervention measures to control disease. In this study, we applied a Bayesian hierarchical spatio-temporal model to describe trends in schistosomiasis risk in Anhui Province, China, using annual parasitological and environmental data for the period 1997-2010. A computationally efficient approach-Integrated Nested Laplace Approximation-was used for model inference. A zero-inflated, negative binomial model best described the spatio-temporal dynamics of schistosomiasis risk. It predicted that the disease risk would generally be low and stable except for some specific, local areas during the period 2011-2014. High-risk counties were identified in the forecasting maps: three in which the risk remained high, and two in which risk would become high. The results indicated that schistosomiasis risk has been reduced to consistently low levels throughout much of this region of China; however, some counties were identified in which progress in schistosomiasis control was less than satisfactory. Whilst maintaining overall control, specific interventions in the future should focus on these refractive counties as part of a strategy to eliminate schistosomiasis from this region.
Hu, Yi; Ward, Michael P.; Xia, Congcong; Li, Rui; Sun, Liqian; Lynn, Henry; Gao, Fenghua; Wang, Qizhi; Zhang, Shiqing; Xiong, Chenglong; Zhang, Zhijie; Jiang, Qingwu
2016-01-01
Schistosomiasis remains a major public health problem and causes substantial economic impact in east China, particularly along the Yangtze River Basin. Disease forecasting and surveillance can assist in the development and implementation of more effective intervention measures to control disease. In this study, we applied a Bayesian hierarchical spatio-temporal model to describe trends in schistosomiasis risk in Anhui Province, China, using annual parasitological and environmental data for the period 1997–2010. A computationally efficient approach–Integrated Nested Laplace Approximation–was used for model inference. A zero-inflated, negative binomial model best described the spatio-temporal dynamics of schistosomiasis risk. It predicted that the disease risk would generally be low and stable except for some specific, local areas during the period 2011–2014. High-risk counties were identified in the forecasting maps: three in which the risk remained high, and two in which risk would become high. The results indicated that schistosomiasis risk has been reduced to consistently low levels throughout much of this region of China; however, some counties were identified in which progress in schistosomiasis control was less than satisfactory. Whilst maintaining overall control, specific interventions in the future should focus on these refractive counties as part of a strategy to eliminate schistosomiasis from this region. PMID:27053447
Multiple testing on standardized mortality ratios: a Bayesian hierarchical model for FDR estimation.
Ventrucci, Massimo; Scott, E Marian; Cocchi, Daniela
2011-01-01
The analysis of large data sets of standardized mortality ratios (SMRs), obtained by collecting observed and expected disease counts in a map of contiguous regions, is a first step in descriptive epidemiology to detect potential environmental risk factors. A common situation arises when counts are collected in small areas, that is, where the expected count is very low, and disease risks underlying the map are spatially correlated. Traditional p-value-based methods, which control the false discovery rate (FDR) by means of Poisson p-values, might achieve small sensitivity in identifying risk in small areas. This problem is the focus of the present work, where a Bayesian approach which performs a test to evaluate the null hypothesis of no risk over each SMR and controls the posterior FDR is proposed. A Bayesian hierarchical model including spatial random effects to allow for extra-Poisson variability is implemented providing estimates of the posterior probabilities that the null hypothesis of absence of risk is true. By means of such posterior probabilities, an estimate of the posterior FDR conditional on the data can be computed. A conservative estimation is needed to achieve the control which is checked by simulation. The availability of this estimate allows the practitioner to determine nonarbitrary FDR-based selection rules to identify high-risk areas according to a preset FDR level. Sensitivity and specificity of FDR-based rules are studied via simulation and a comparison with p-value-based rules is also shown. A real data set is analyzed using rules based on several FDR levels.
Bååth, Rasmus
2016-06-01
The sensorimotor synchronization paradigm is used when studying the coordination of rhythmic motor responses with a pacing stimulus and is an important paradigm in the study of human timing and time perception. Two measures of performance frequently calculated using sensorimotor synchronization data are the average offset and variability of the stimulus-to-response asynchronies-the offsets between the stimuli and the motor responses. Here it is shown that assuming that asynchronies are normally distributed when estimating these measures can result in considerable underestimation of both the average offset and variability. This is due to a tendency for the distribution of the asynchronies to be bimodal and left skewed when the interstimulus interval is longer than 2 s. It is argued that (1) this asymmetry is the result of the distribution of the asynchronies being a mixture of two types of responses-predictive and reactive-and (2) the main interest in a sensorimotor synchronization study is the predictive responses. A Bayesian hierarchical modeling approach is proposed in which sensorimotor synchronization data are modeled as coming from a right-censored normal distribution that effectively separates the predictive responses from the reactive responses. Evaluation using both simulated data and experimental data from a study by Repp and Doggett (2007) showed that the proposed approach produces more precise estimates of the average offset and variability, with considerably less underestimation.
Sillanpää, M J; Pikkuhookana, P; Abrahamsson, S; Knürr, T; Fries, A; Lerceteau, E; Waldmann, P; García-Gil, M R
2012-01-01
A novel hierarchical quantitative trait locus (QTL) mapping method using a polynomial growth function and a multiple-QTL model (with no dependence in time) in a multitrait framework is presented. The method considers a population-based sample where individuals have been phenotyped (over time) with respect to some dynamic trait and genotyped at a given set of loci. A specific feature of the proposed approach is that, instead of an average functional curve, each individual has its own functional curve. Moreover, each QTL can modify the dynamic characteristics of the trait value of an individual through its influence on one or more growth curve parameters. Apparent advantages of the approach include: (1) assumption of time-independent QTL and environmental effects, (2) alleviating the necessity for an autoregressive covariance structure for residuals and (3) the flexibility to use variable selection methods. As a by-product of the method, heritabilities and genetic correlations can also be estimated for individual growth curve parameters, which are considered as latent traits. For selecting trait-associated loci in the model, we use a modified version of the well-known Bayesian adaptive shrinkage technique. We illustrate our approach by analysing a sub sample of 500 individuals from the simulated QTLMAS 2009 data set, as well as simulation replicates and a real Scots pine (Pinus sylvestris) data set, using temporal measurements of height as dynamic trait of interest. PMID:21792229
Li, Yunfeng; Morrow, Jarrett; Raby, Benjamin; Tantisira, Kelan; Weiss, Scott T.; Huang, Wei
2017-01-01
Detecting disease-associated genomic outcomes is one of the key steps in precision medicine research. Cutting-edge high-throughput technologies enable researchers to unbiasedly test if genomic outcomes are associated with disease of interest. However, these technologies also include the challenges associated with the analysis of genome-wide data. Two big challenges are (1) how to reduce the effects of technical noise; and (2) how to handle the curse of dimensionality (i.e., number of variables are way larger than the number of samples). To tackle these challenges, we propose a constrained mixture of Bayesian hierarchical models (MBHM) for detecting disease-associated genomic outcomes for data obtained from paired/matched designs. Paired/matched designs can effectively reduce effects of confounding factors. MBHM does not involve multiple testing, hence does not have the problem of the curse of dimensionality. It also could borrow information across genes so that it can be used for whole genome data with small sample sizes. PMID:28358896
Bayesian hierarchical mixture modeling to assign copy number from a targeted CNV array.
Cardin, Niall; Holmes, Chris; Donnelly, Peter; Marchini, Jonathan
2011-09-01
Accurate assignment of copy number at known copy number variant (CNV) loci is important for both increasing understanding of the structural evolution of genomes as well as for carrying out association studies of copy number with disease. As with calling SNP genotypes, the task can be framed as a clustering problem but for a number of reasons assigning copy number is much more challenging. CNV assays have lower signal-to-noise ratios than SNP assays, often display heavy tailed and asymmetric intensity distributions, contain outlying observations and may exhibit systematic technical differences among different cohorts. In addition, the number of copy-number classes at a CNV in the population may be unknown a priori. Due to these complications, automatic and robust assignment of copy number from array data remains a challenging problem. We have developed a copy number assignment algorithm, CNVCALL, for a targeted CNV array, such as that used by the Wellcome Trust Case Control Consortium's recent CNV association study. We use a Bayesian hierarchical mixture model that robustly identifies both the number of different copy number classes at a specific locus as well as relative copy number for each individual in the sample. This approach is fully automated which is a critical requirement when analyzing large numbers of CNVs. We illustrate the methods performance using real data from the Wellcome Trust Case Control Consortium's CNV association study and using simulated data.
Huang, Susie Shih-Yin; Strathe, Anders Bjerring; Hung, Silas S O; Boston, Raymond C; Fadel, James G
2012-03-01
The biological function of selenium (Se) is determined by its form and concentration. Selenium is an essential micronutrient for all vertebrates, however, at environmental levels, it is a potent toxin. In the San Francisco Bay-Delta, Se pollution threatens top predatory fish, including white sturgeon. A multi-compartmental Bayesian hierarchical model was developed to estimate the fractional rates of absorption, disposition, and elimination of selenocompounds, in white sturgeon, from tissue measurements obtained in a previous study (Huang et al., 2012). This modeling methodology allows for a population based approach to estimate kinetic physiological parameters in white sturgeon. Briefly, thirty juvenile white sturgeon (five per treatment) were orally intubated with a control (no selenium) or a single dose of Se (500 μg Se/kg body weight) in the form of one inorganic (Selenite) or four organic selenocompounds: selenocystine (SeCys), l-selenomethionine (SeMet), Se-methylseleno-l-cysteine (MSeCys), or selenoyeast (SeYeast). Blood and urine Se were measured at intervals throughout the 48h post intubation period and eight tissues were sampled at 48 h. The model is composed of four state variables, conceptually the gut (Q1), blood (Q2), and tissue (Q3); and urine (Q0), all in units of μg Se. Six kinetics parameters were estimated: the fractional rates [1/h] of absorption, tissue disposition, tissue release, and urinary elimination (k12, k23, k32, and k20), the proportion of the absorbed dose eliminated through the urine (f20), and the distribution blood volume (V; percent body weight, BW). The parameter k12 was higher in sturgeon given the organic Se forms, in the descending order of MSeCys > SeMet > SeCys > Selenite > SeYeast. The parameters k23 and k32 followed similar patterns, and f20 was lowest in fish given MSeCys. Selenium form did not affect k20 or V. The parameter differences observed can be attributed to the different mechanisms of transmucosal transport
Wasson, Anton P; Chiu, Grace S; Zwart, Alexander B; Binns, Timothy R
2017-01-01
Ensuring future food security for a growing population while climate change and urban sprawl put pressure on agricultural land will require sustainable intensification of current farming practices. For the crop breeder this means producing higher crop yields with less resources due to greater environmental stresses. While easy gains in crop yield have been made mostly "above ground," little progress has been made "below ground"; and yet it is these root system traits that can improve productivity and resistance to drought stress. Wheat pre-breeders use soil coring and core-break counts to phenotype root architecture traits, with data collected on rooting density for hundreds of genotypes in small increments of depth. The measured densities are both large datasets and highly variable even within the same genotype, hence, any rigorous, comprehensive statistical analysis of such complex field data would be technically challenging. Traditionally, most attributes of the field data are therefore discarded in favor of simple numerical summary descriptors which retain much of the high variability exhibited by the raw data. This poses practical challenges: although plant scientists have established that root traits do drive resource capture in crops, traits that are more randomly (rather than genetically) determined are difficult to breed for. In this paper we develop a hierarchical nonlinear mixed modeling approach that utilizes the complete field data for wheat genotypes to fit, under the Bayesian paradigm, an "idealized" relative intensity function for the root distribution over depth. Our approach was used to determine heritability: how much of the variation between field samples was purely random vs. being mechanistically driven by the plant genetics? Based on the genotypic intensity functions, the overall heritability estimate was 0.62 (95% Bayesian confidence interval was 0.52 to 0.71). Despite root count profiles that were statistically very noisy, our approach led
Wasson, Anton P.; Chiu, Grace S.; Zwart, Alexander B.; Binns, Timothy R.
2017-01-01
Ensuring future food security for a growing population while climate change and urban sprawl put pressure on agricultural land will require sustainable intensification of current farming practices. For the crop breeder this means producing higher crop yields with less resources due to greater environmental stresses. While easy gains in crop yield have been made mostly “above ground,” little progress has been made “below ground”; and yet it is these root system traits that can improve productivity and resistance to drought stress. Wheat pre-breeders use soil coring and core-break counts to phenotype root architecture traits, with data collected on rooting density for hundreds of genotypes in small increments of depth. The measured densities are both large datasets and highly variable even within the same genotype, hence, any rigorous, comprehensive statistical analysis of such complex field data would be technically challenging. Traditionally, most attributes of the field data are therefore discarded in favor of simple numerical summary descriptors which retain much of the high variability exhibited by the raw data. This poses practical challenges: although plant scientists have established that root traits do drive resource capture in crops, traits that are more randomly (rather than genetically) determined are difficult to breed for. In this paper we develop a hierarchical nonlinear mixed modeling approach that utilizes the complete field data for wheat genotypes to fit, under the Bayesian paradigm, an “idealized” relative intensity function for the root distribution over depth. Our approach was used to determine heritability: how much of the variation between field samples was purely random vs. being mechanistically driven by the plant genetics? Based on the genotypic intensity functions, the overall heritability estimate was 0.62 (95% Bayesian confidence interval was 0.52 to 0.71). Despite root count profiles that were statistically very noisy, our
NASA Astrophysics Data System (ADS)
Werner, J. P.; Smerdon, J. E.; Luterbacher, J.
2011-12-01
A Pseudoproxy comparison is presented for two statistical methods used to derive annual climate field reconstructions (CFR) for europe. The employed methods use the canonical correlation analysis (CCA) procedure presented by Smerdon et al. (2010, J. Climate) and the Bayesian Hierarchical Model (BHM) based method adopted from Tingley and Huybers (2010a,b, J. Climate). Pseudoproxy experiments are constructed from modelled temperature data sampled from the 1250-year paleo-run of the NCAR CCSM 1.4 model (Ammann et al. 2007, PNAS). The pseudoproxies approximate the distribution of the Mann et al. (1998, Nature) multi-proxy network and use Gaussian white noise to mimic the combined signal and noise properties of real-world proxies. The derived CFRs are tested by comparing the mean temperature bias, the reconstructed temperature variability and two error measures: the cross correlation and the root mean square error. The results show that the BHM method performs much better than the CCA method in areas with good proxy coverage. The BHM method also delivers the added value over the more traditional CCA method by providing objective error estimates. Reconstructions of key years are also analysed. While CCA returns estimates for the full climate field even for areas with sparse data, the more flexible model used in the BHM method returns results that are closer to the target for most of the reconstruction area, albeit with higher uncertainties in data sparse regions. Based on the success of these current BHM results, the algorithm will be extended to make use of proxies with different temporal resolution (cf. Li et al. 2010) in order to reconstruct the temperature and precipitation fields over Europe and the Mediterranean covering much of the common-era period. Ammann, C. et al. (2007), PNAS 104, 3713--3718 Li, B. et al. (2010), J. Am. Stat. Assoc. 105, 883-911 Mann, M. et al. (1998), Nature 392, 779-787 Smerdon, J. et al. (2010), J. Climate 24, 1284-1309 Tingley, M. and
Zou, Kelly H.; O’Malley, A. James
2005-01-01
Receiver operating characteristic (ROC) analysis is a useful evaluative method of diagnostic accuracy. A Bayesian hierarchical nonlinear regression model for ROC analysis was developed. A validation analysis of diagnostic accuracy was conducted using prospective multi-center clinical trial prostate cancer biopsy data collected from three participating centers. The gold standard was based on radical prostatectomy to determine local and advanced disease. To evaluate the diagnostic performance of PSA level at fixed levels of Gleason score, a normality transformation was applied to the outcome data. A hierarchical regression analysis incorporating the effects of cluster (clinical center) and cancer risk (low, intermediate, and high) was performed, and the area under the ROC curve (AUC) was estimated. PMID:16161801
Rodhouse, T.J.; Irvine, K.M.; Vierling, K.T.; Vierling, L.A.
2011-01-01
Monitoring programs that evaluate restoration and inform adaptive management are important for addressing environmental degradation. These efforts may be well served by spatially explicit hierarchical approaches to modeling because of unavoidable spatial structure inherited from past land use patterns and other factors. We developed Bayesian hierarchical models to estimate trends from annual density counts observed in a spatially structured wetland forb (Camassia quamash [camas]) population following the cessation of grazing and mowing on the study area, and in a separate reference population of camas. The restoration site was bisected by roads and drainage ditches, resulting in distinct subpopulations ("zones") with different land use histories. We modeled this spatial structure by fitting zone-specific intercepts and slopes. We allowed spatial covariance parameters in the model to vary by zone, as in stratified kriging, accommodating anisotropy and improving computation and biological interpretation. Trend estimates provided evidence of a positive effect of passive restoration, and the strength of evidence was influenced by the amount of spatial structure in the model. Allowing trends to vary among zones and accounting for topographic heterogeneity increased precision of trend estimates. Accounting for spatial autocorrelation shifted parameter coefficients in ways that varied among zones depending on strength of statistical shrinkage, autocorrelation and topographic heterogeneity-a phenomenon not widely described. Spatially explicit estimates of trend from hierarchical models will generally be more useful to land managers than pooled regional estimates and provide more realistic assessments of uncertainty. The ability to grapple with historical contingency is an appealing benefit of this approach.
Mapping brucellosis increases relative to elk density using hierarchical Bayesian models
Cross, Paul C.; Heisey, Dennis M.; Scurlock, Brandon M.; Edwards, William H.; Brennan, Angela; Ebinger, Michael R.
2010-01-01
The relationship between host density and parasite transmission is central to the effectiveness of many disease management strategies. Few studies, however, have empirically estimated this relationship particularly in large mammals. We applied hierarchical Bayesian methods to a 19-year dataset of over 6400 brucellosis tests of adult female elk (Cervus elaphus) in northwestern Wyoming. Management captures that occurred from January to March were over two times more likely to be seropositive than hunted elk that were killed in September to December, while accounting for site and year effects. Areas with supplemental feeding grounds for elk had higher seroprevalence in 1991 than other regions, but by 2009 many areas distant from the feeding grounds were of comparable seroprevalence. The increases in brucellosis seroprevalence were correlated with elk densities at the elk management unit, or hunt area, scale (mean 2070 km2; range = [95–10237]). The data, however, could not differentiate among linear and non-linear effects of host density. Therefore, control efforts that focus on reducing elk densities at a broad spatial scale were only weakly supported. Additional research on how a few, large groups within a region may be driving disease dynamics is needed for more targeted and effective management interventions. Brucellosis appears to be expanding its range into new regions and elk populations, which is likely to further complicate the United States brucellosis eradication program. This study is an example of how the dynamics of host populations can affect their ability to serve as disease reservoirs.
Jatrana, Santosh; Richardson, Ken; Blakely, Tony; Dayal, Saira
2014-01-01
The aim of this paper was to see whether all-cause and cause-specific mortality rates vary between Asian ethnic subgroups, and whether overseas born Asian subgroup mortality rate ratios varied by nativity and duration of residence. We used hierarchical Bayesian methods to allow for sparse data in the analysis of linked census-mortality data for 25–75 year old New Zealanders. We found directly standardised posterior all-cause and cardiovascular mortality rates were highest for the Indian ethnic group, significantly so when compared with those of Chinese ethnicity. In contrast, cancer mortality rates were lowest for ethnic Indians. Asian overseas born subgroups have about 70% of the mortality rate of their New Zealand born Asian counterparts, a result that showed little variation by Asian subgroup or cause of death. Within the overseas born population, all-cause mortality rates for migrants living 0–9 years in New Zealand were about 60% of the mortality rate of those living more than 25 years in New Zealand regardless of ethnicity. The corresponding figure for cardiovascular mortality rates was 50%. However, while Chinese cancer mortality rates increased with duration of residence, Indian and Other Asian cancer mortality rates did not. Future research on the mechanisms of worsening of health with increased time spent in the host country is required to improve the understanding of the process, and would assist the policy-makers and health planners. PMID:25140523
Yang, Yuqing; Chen, Ning; Chen, Ting
2017-01-25
The inference of associations between environmental factors and microbes and among microbes is critical to interpreting metagenomic data, but compositional bias, indirect associations resulting from common factors, and variance within metagenomic sequencing data limit the discovery of associations. To account for these problems, we propose metagenomic Lognormal-Dirichlet-Multinomial (mLDM), a hierarchical Bayesian model with sparsity constraints, to estimate absolute microbial abundance and simultaneously infer both conditionally dependent associations among microbes and direct associations between microbes and environmental factors. We empirically show the effectiveness of the mLDM model using synthetic data, data from the TARA Oceans project, and a colorectal cancer dataset. Finally, we apply mLDM to 16S sequencing data from the western English Channel and report several associations. Our model can be used on both natural environmental and human metagenomic datasets, promoting the understanding of associations in the microbial community.
Bao, Le; Raftery, Adrian E; Reddy, Amala
2015-04-01
In most countries in the world outside of sub-Saharan Africa, HIV is largely concentrated in sub-populations whose behavior puts them at higher risk of contracting and transmitting HIV, such as people who inject drugs, sex workers and men who have sex with men. Estimating the size of these sub-populations is important for assessing overall HIV prevalence and designing effective interventions. We present a Bayesian hierarchical model for estimating the sizes of local and national HIV key affected populations. The model incorporates multiple commonly used data sources including mapping data, surveys, interventions, capture-recapture data, estimates or guesstimates from organizations, and expert opinion. The proposed model is used to estimate the numbers of people who inject drugs in Bangladesh.
Linden, Daniel W; Roloff, Gary J
2015-08-01
Pilot studies are often used to design short-term research projects and long-term ecological monitoring programs, but data are sometimes discarded when they do not match the eventual survey design. Bayesian hierarchical modeling provides a convenient framework for integrating multiple data sources while explicitly separating sample variation into observation and ecological state processes. Such an approach can better estimate state uncertainty and improve inferences from short-term studies in dynamic systems. We used a dynamic multistate occupancy model to estimate the probabilities of occurrence and nesting for white-headed woodpeckers Picoides albolarvatus in recent harvest units within managed forests of northern California, USA. Our objectives were to examine how occupancy states and state transitions were related to forest management practices, and how the probabilities changed over time. Using Gibbs variable selection, we made inferences using multiple model structures and generated model-averaged estimates. Probabilities of white-headed woodpecker occurrence and nesting were high in 2009 and 2010, and the probability that nesting persisted at a site was positively related to the snag density in harvest units. Prior-year nesting resulted in higher probabilities of subsequent occurrence and nesting. We demonstrate the benefit of forest management practices that increase the density of retained snags in harvest units for providing white-headed woodpecker nesting habitat. While including an additional year of data from our pilot study did not drastically alter management recommendations, it changed the interpretation of the mechanism behind the observed dynamics. Bayesian hierarchical modeling has the potential to maximize the utility of studies based on small sample sizes while fully accounting for measurement error and both estimation and model uncertainty, thereby improving the ability of observational data to inform conservation and management strategies.
Linden, Daniel W; Roloff, Gary J
2015-01-01
Pilot studies are often used to design short-term research projects and long-term ecological monitoring programs, but data are sometimes discarded when they do not match the eventual survey design. Bayesian hierarchical modeling provides a convenient framework for integrating multiple data sources while explicitly separating sample variation into observation and ecological state processes. Such an approach can better estimate state uncertainty and improve inferences from short-term studies in dynamic systems. We used a dynamic multistate occupancy model to estimate the probabilities of occurrence and nesting for white-headed woodpeckers Picoides albolarvatus in recent harvest units within managed forests of northern California, USA. Our objectives were to examine how occupancy states and state transitions were related to forest management practices, and how the probabilities changed over time. Using Gibbs variable selection, we made inferences using multiple model structures and generated model-averaged estimates. Probabilities of white-headed woodpecker occurrence and nesting were high in 2009 and 2010, and the probability that nesting persisted at a site was positively related to the snag density in harvest units. Prior-year nesting resulted in higher probabilities of subsequent occurrence and nesting. We demonstrate the benefit of forest management practices that increase the density of retained snags in harvest units for providing white-headed woodpecker nesting habitat. While including an additional year of data from our pilot study did not drastically alter management recommendations, it changed the interpretation of the mechanism behind the observed dynamics. Bayesian hierarchical modeling has the potential to maximize the utility of studies based on small sample sizes while fully accounting for measurement error and both estimation and model uncertainty, thereby improving the ability of observational data to inform conservation and management strategies
NASA Astrophysics Data System (ADS)
Yin, Ping; Mu, Lan; Madden, Marguerite; Vena, John E.
2014-10-01
Lung cancer is the second most commonly diagnosed cancer in both men and women in Georgia, USA. However, the spatio-temporal patterns of lung cancer risk in Georgia have not been fully studied. Hierarchical Bayesian models are used here to explore the spatio-temporal patterns of lung cancer incidence risk by race and gender in Georgia for the period of 2000-2007. With the census tract level as the spatial scale and the 2-year period aggregation as the temporal scale, we compare a total of seven Bayesian spatio-temporal models including two under a separate modeling framework and five under a joint modeling framework. One joint model outperforms others based on the deviance information criterion. Results show that the northwest region of Georgia has consistently high lung cancer incidence risk for all population groups during the study period. In addition, there are inverse relationships between the socioeconomic status and the lung cancer incidence risk among all Georgian population groups, and the relationships in males are stronger than those in females. By mapping more reliable variations in lung cancer incidence risk at a relatively fine spatio-temporal scale for different Georgian population groups, our study aims to better support healthcare performance assessment, etiological hypothesis generation, and health policy making.
NASA Astrophysics Data System (ADS)
Cahill, N.; Kemp, A.; Horton, B.; Parnell, A. C.
2015-12-01
We present a holistic Bayesian hierarchical model for reconstructing the continuous and dynamic evolution of relative sea-level change with fully quantified uncertainty. The reconstruction is produced from biological (foraminifera) and geochemical (δ13C) sea-level indicators preserved in dated cores of salt-marsh sediment. The model is comprised of three modules: (1) A Bayesian transfer function for the calibration of foraminifera into tidal elevation, which is flexible enough to formally accommodate additional proxies (in this case bulk-sediment δ13C values). (2) A chronology developed from a Bchron age-depth model. (3) An errors-in-variables integrated Gaussian process (EIV-IGP) model for estimating rates of sea-level change. We illustrate our approach using a case study of Common Era sea-level variability from New Jersey, USA. Results from our new Bayesian transfer function (B-TF), with and without the δ13C proxy, are compared to those from a widely-used weighted-averaging transfer function (WA-TF). The incorporation of secondary proxy information into the model in a formalized way results in smaller vertical uncertainties for reconstructed relative sea level. The vertical uncertainty from the multi proxy B-TF is ~30% smaller on average compared to the WA-TF. We evaluate the performance of both transfer functions by comparing reconstructed relative sea level to historic tide-gauge measurements. The multi proxy B-TF most accurately reconstructs the relative sea-level changes observed in the tide-gauge record. The holistic model provides a single, unifying framework for reconstructing and analysing sea level through time.
Bayesian hierarchical models suggest oldest known plant-visiting bat was omnivorous
Rojas, Danny; Gerstner, Beth E.; Simmons, Nancy B.
2015-01-01
The earliest record of plant visiting in bats dates to the Middle Miocene of La Venta, the world's most diverse tropical palaeocommunity. Palynephyllum antimaster is known from molars that indicate nectarivory. Skull length, an important indicator of key traits such as body size, bite force and trophic specialization, remains unknown. We developed Bayesian models to infer skull length based on dental measurements. These models account for variation within and between species, variation between clades, and phylogenetic error structure. Models relating skull length to trophic level for nectarivorous bats were then used to infer the diet of the fossil. The skull length estimate for Palynephyllum places it among the larger lonchophylline bats. The inferred diet suggests Palynephyllum fed on nectar and insects, similar to its living relatives. Omnivory has persisted since the mid-Miocene. This is the first study to corroborate with fossil data that highly specialized nectarivory in bats requires an omnivorous transition. PMID:26559512
Bayesian hierarchical models suggest oldest known plant-visiting bat was omnivorous.
Yohe, Laurel R; Velazco, Paúl M; Rojas, Danny; Gerstner, Beth E; Simmons, Nancy B; Dávalos, Liliana M
2015-11-01
The earliest record of plant visiting in bats dates to the Middle Miocene of La Venta, the world's most diverse tropical palaeocommunity. Palynephyllum antimaster is known from molars that indicate nectarivory. Skull length, an important indicator of key traits such as body size, bite force and trophic specialization, remains unknown. We developed Bayesian models to infer skull length based on dental measurements. These models account for variation within and between species, variation between clades, and phylogenetic error structure. Models relating skull length to trophic level for nectarivorous bats were then used to infer the diet of the fossil. The skull length estimate for Palynephyllum places it among the larger lonchophylline bats. The inferred diet suggests Palynephyllum fed on nectar and insects, similar to its living relatives. Omnivory has persisted since the mid-Miocene. This is the first study to corroborate with fossil data that highly specialized nectarivory in bats requires an omnivorous transition.
Bayesian Hierarchical Duration Model for Repeated Events : An Application to Behavioral Observations
Dagne, Getachew A.; Snyder, James
2009-01-01
This paper presents a continuous-time Bayesian model for analyzing durations of behavior displays in social interactions. Duration data of social interactions are often complex because of repeated behaviors (events) at individual or group (e.g., dyad) level, multiple behaviors (multistates), and several choices of exit from a current event (competing risks). A multilevel, multistate model is proposed to adequately characterize the behavioral processes. The model incorporates dyad-specific and transition-specific random effects to account for heterogeneity among dyads and interdependence among competing risks. The proposed method is applied to child-parent observational data derived from the School Transitions Project to assess the relation of emotional expression in child-parent interaction to risk for early and persisting child conduct problems. PMID:20209032
Rodhouse, Thomas J.; Irvine, Kathryn M.; Vierling, Kerri T.; Vierling, Lee A.
2011-01-01
Monitoring programs that evaluate restoration and inform adaptive management are important for addressing environmental degradation. These efforts may be well served by spatially explicit hierarchical approaches to modeling because of unavoidable spatial structure inherited from past land use patterns and other factors. We developed Bayesian hierarchical models to estimate trends from annual density counts observed in a spatially structured wetland forb (Camassia quamash [camas]) population following the cessation of grazing and mowing on the study area, and in a separate reference population of camas. The restoration site was bisected by roads and drainage ditches, resulting in distinct subpopulations (“zones”) with different land use histories. We modeled this spatial structure by fitting zone-specific intercepts and slopes. We allowed spatial covariance parameters in the model to vary by zone, as in stratified kriging, accommodating anisotropy and improving computation and biological interpretation. Trend estimates provided evidence of a positive effect of passive restoration, and the strength of evidence was influenced by the amount of spatial structure in the model. Allowing trends to vary among zones and accounting for topographic heterogeneity increased precision of trend estimates. Accounting for spatial autocorrelation shifted parameter coefficients in ways that varied among zones depending on strength of statistical shrinkage, autocorrelation and topographic heterogeneity—a phenomenon not widely described. Spatially explicit estimates of trend from hierarchical models will generally be more useful to land managers than pooled regional estimates and provide more realistic assessments of uncertainty. The ability to grapple with historical contingency is an appealing benefit of this approach. PMID:22163047
Semmens, Brice X; Ward, Eric J; Moore, Jonathan W; Darimont, Chris T
2009-07-09
Variability in resource use defines the width of a trophic niche occupied by a population. Intra-population variability in resource use may occur across hierarchical levels of population structure from individuals to subpopulations. Understanding how levels of population organization contribute to population niche width is critical to ecology and evolution. Here we describe a hierarchical stable isotope mixing model that can simultaneously estimate both the prey composition of a consumer diet and the diet variability among individuals and across levels of population organization. By explicitly estimating variance components for multiple scales, the model can deconstruct the niche width of a consumer population into relevant levels of population structure. We apply this new approach to stable isotope data from a population of gray wolves from coastal British Columbia, and show support for extensive intra-population niche variability among individuals, social groups, and geographically isolated subpopulations. The analytic method we describe improves mixing models by accounting for diet variability, and improves isotope niche width analysis by quantitatively assessing the contribution of levels of organization to the niche width of a population.
Scheuerell, Mark D; Buhle, Eric R; Semmens, Brice X; Ford, Michael J; Cooney, Tom; Carmichael, Richard W
2015-01-01
Myriad human activities increasingly threaten the existence of many species. A variety of conservation interventions such as habitat restoration, protected areas, and captive breeding have been used to prevent extinctions. Evaluating the effectiveness of these interventions requires appropriate statistical methods, given the quantity and quality of available data. Historically, analysis of variance has been used with some form of predetermined before-after control-impact design to estimate the effects of large-scale experiments or conservation interventions. However, ad hoc retrospective study designs or the presence of random effects at multiple scales may preclude the use of these tools. We evaluated the effects of a large-scale supplementation program on the density of adult Chinook salmon Oncorhynchus tshawytscha from the Snake River basin in the northwestern United States currently listed under the U.S. Endangered Species Act. We analyzed 43 years of data from 22 populations, accounting for random effects across time and space using a form of Bayesian hierarchical time-series model common in analyses of financial markets. We found that varying degrees of supplementation over a period of 25 years increased the density of natural-origin adults, on average, by 0–8% relative to nonsupplementation years. Thirty-nine of the 43 year effects were at least two times larger in magnitude than the mean supplementation effect, suggesting common environmental variables play a more important role in driving interannual variability in adult density. Additional residual variation in density varied considerably across the region, but there was no systematic difference between supplemented and reference populations. Our results demonstrate the power of hierarchical Bayesian models to detect the diffuse effects of management interventions and to quantitatively describe the variability of intervention success. Nevertheless, our study could not address whether ecological
Hierarchical Bayesian inference in the visual cortex
NASA Astrophysics Data System (ADS)
Lee, Tai Sing; Mumford, David
2003-07-01
Traditional views of visual processing suggest that early visual neurons in areas V1 and V2 are static spatiotemporal filters that extract local features from a visual scene. The extracted information is then channeled through a feedforward chain of modules in successively higher visual areas for further analysis. Recent electrophysiological recordings from early visual neurons in awake behaving monkeys reveal that there are many levels of complexity in the information processing of the early visual cortex, as seen in the long-latency responses of its neurons. These new findings suggest that activity in the early visual cortex is tightly coupled and highly interactive with the rest of the visual system. They lead us to propose a new theoretical setting based on the mathematical framework of hierarchical Bayesian inference for reasoning about the visual system. In this framework, the recurrent feedforward/feedback loops in the cortex serve to integrate top-down contextual priors and bottom-up observations so as to implement concurrent probabilistic inference along the visual hierarchy. We suggest that the algorithms of particle filtering and Bayesian-belief propagation might model these interactive cortical computations. We review some recent neurophysiological evidences that support the plausibility of these ideas. 2003 Optical Society of America
Manual hierarchical clustering of regional geochemical data using a Bayesian finite mixture model
Ellefsen, Karl J.; Smith, David
2016-01-01
Interpretation of regional scale, multivariate geochemical data is aided by a statistical technique called “clustering.” We investigate a particular clustering procedure by applying it to geochemical data collected in the State of Colorado, United States of America. The clustering procedure partitions the field samples for the entire survey area into two clusters. The field samples in each cluster are partitioned again to create two subclusters, and so on. This manual procedure generates a hierarchy of clusters, and the different levels of the hierarchy show geochemical and geological processes occurring at different spatial scales. Although there are many different clustering methods, we use Bayesian finite mixture modeling with two probability distributions, which yields two clusters. The model parameters are estimated with Hamiltonian Monte Carlo sampling of the posterior probability density function, which usually has multiple modes. Each mode has its own set of model parameters; each set is checked to ensure that it is consistent both with the data and with independent geologic knowledge. The set of model parameters that is most consistent with the independent geologic knowledge is selected for detailed interpretation and partitioning of the field samples.
A BAYESIAN HIERARCHICAL SPATIAL POINT PROCESS MODEL FOR MULTI-TYPE NEUROIMAGING META-ANALYSIS
Kang, Jian; Nichols, Thomas E.; Wager, Tor D.; Johnson, Timothy D.
2014-01-01
Neuroimaging meta-analysis is an important tool for finding consistent effects over studies that each usually have 20 or fewer subjects. Interest in meta-analysis in brain mapping is also driven by a recent focus on so-called “reverse inference”: where as traditional “forward inference” identifies the regions of the brain involved in a task, a reverse inference identifies the cognitive processes that a task engages. Such reverse inferences, however, requires a set of meta-analysis, one for each possible cognitive domain. However, existing methods for neuroimaging meta-analysis have significant limitations. Commonly used methods for neuroimaging meta-analysis are not model based, do not provide interpretable parameter estimates, and only produce null hypothesis inferences; further, they are generally designed for a single group of studies and cannot produce reverse inferences. In this work we address these limitations by adopting a non-parametric Bayesian approach for meta analysis data from multiple classes or types of studies. In particular, foci from each type of study are modeled as a cluster process driven by a random intensity function that is modeled as a kernel convolution of a gamma random field. The type-specific gamma random fields are linked and modeled as a realization of a common gamma random field, shared by all types, that induces correlation between study types and mimics the behavior of a univariate mixed effects model. We illustrate our model on simulation studies and a meta analysis of five emotions from 219 studies and check model fit by a posterior predictive assessment. In addition, we implement reverse inference by using the model to predict study type from a newly presented study. We evaluate this predictive performance via leave-one-out cross validation that is efficiently implemented using importance sampling techniques. PMID:25426185
NASA Astrophysics Data System (ADS)
Zarekarizi, M.; Moradkhani, H.
2015-12-01
Extreme events are proven to be affected by climate change, influencing hydrologic simulations for which stationarity is usually a main assumption. Studies have discussed that this assumption would lead to large bias in model estimations and higher flood hazard consequently. Getting inspired by the importance of non-stationarity, we determined how the exceedance probabilities have changed over time in Johnson Creek River, Oregon. This could help estimate the probability of failure of a structure that was primarily designed to resist less likely floods according to common practice. Therefore, we built a climate informed Bayesian hierarchical model and non-stationarity was considered in modeling framework. Principle component analysis shows that North Atlantic Oscillation (NAO), Western Pacific Index (WPI) and Eastern Asia (EA) are mostly affecting stream flow in this river. We modeled flood extremes using peaks over threshold (POT) method rather than conventional annual maximum flood (AMF) mainly because it is possible to base the model on more information. We used available threshold selection methods to select a suitable threshold for the study area. Accounting for non-stationarity, model parameters vary through time with climate indices. We developed a couple of model scenarios and chose one which could best explain the variation in data based on performance measures. We also estimated return periods under non-stationarity condition. Results show that ignoring stationarity could increase the flood hazard up to four times which could increase the probability of an in-stream structure being overtopped.
Bayesian Hierarchical Model Characterization of Model Error in Ocean Data Assimilation and Forecasts
2013-09-30
discrepancy between the two models M̃ and M. We work under the assumption that model M̃ can be explored efficiently via Markov - Chain Monte Carlo (MCMC... methods and that model M can be explored via parallel computing. We derive a Monte Carlo estimate of H which requires the following components: (i) A...MCMC exploration of model M̃ ; Assume θ1,θ2, . . . θB represents a Markov chain which explores the target p(θ |Ỹ ). (ii) An evaluation of the un
Bayesian Hierarchical Model Characterization of Model Error in Ocean Data Assimilation and Forecasts
2013-09-30
under the assumption that model M̃ can be explored efficiently via Markov - Chain Monte Carlo (MCMC) methods and that model M can be explored via...distribution – a Monte Carlo approach” in preparation. Wikle, C.K., R.F. Milliff, R. Herbei and W.B. Leeds, 2013: “Modern Statistical Methods in...parallel computing. We derive a Monte Carlo estimate of H which requires the following components: (i) A MCMC exploration of model M̃ ; Assume θ1,θ2
Bayesian Hierarchical Model Characterization of Model Error in Ocean Data Assimilation and Forecasts
2012-09-28
potential benefits from allowing switching between different process models in this setting. This will be greatly facilitated by the emulator approach...of sea surface height (SSH), SST, and phytoplankton ( chlorophyll ) data from 1998, 1999, 2000, and 2001. We then used remotely sensed SeaWiFS ocean
Chen, Cong; Zhang, Guohui; Tian, Zong; Bogus, Susan M; Yang, Yin
2015-12-01
Traffic crashes occurring on rural roadways induce more severe injuries and fatalities than those in urban areas, especially when there are trucks involved. Truck drivers are found to suffer higher potential of crash injuries compared with other occupational labors. Besides, unobserved heterogeneity in crash data analysis is a critical issue that needs to be carefully addressed. In this study, a hierarchical Bayesian random intercept model decomposing cross-level interaction effects as unobserved heterogeneity is developed to examine the posterior probabilities of truck driver injuries in rural truck-involved crashes. The interaction effects contributing to truck driver injury outcomes are investigated based on two-year rural truck-involved crashes in New Mexico from 2010 to 2011. The analysis results indicate that the cross-level interaction effects play an important role in predicting truck driver injury severities, and the proposed model produces comparable performance with the traditional random intercept model and the mixed logit model even after penalization by high model complexity. It is revealed that factors including road grade, number of vehicles involved in a crash, maximum vehicle damage in a crash, vehicle actions, driver age, seatbelt use, and driver under alcohol or drug influence, as well as a portion of their cross-level interaction effects with other variables are significantly associated with truck driver incapacitating injuries and fatalities. These findings are helpful to understand the respective or joint impacts of these attributes on truck driver injury patterns in rural truck-involved crashes.
Bayesian Hierarchical Model Characterization of Model Error in Ocean Data Assimilation and Forecasts
2012-07-01
in projects led by PI Milliff in the first full year of funding. First year results were also presented at a project workshop held at the Courant ...Institute for Mathematical Sciences, New York University, in November 2011. Objectives addressed in this annual report focus on extensions of a time- and...year of the ONR model error project demonstrates practical methods to add time- and space-dependence to error process and error covariance
Ishigami, Hideaki
2016-01-01
Relative age effect (RAE) in sports has been well documented. Recent studies investigate the effect of birthplace in addition to the RAE. The first objective of this study was to show the magnitude of the RAE in two major professional sports in Japan, baseball and soccer. Second, we examined the birthplace effect and compared its magnitude with that of the RAE. The effect sizes were estimated using a Bayesian hierarchical Poisson model with the number of players as dependent variable. The RAEs were 9.0% and 7.7% per month for soccer and baseball, respectively. These estimates imply that children born in the first month of a school year have about three times greater chance of becoming a professional player than those born in the last month of the year. Over half of the difference in likelihoods of becoming a professional player between birthplaces was accounted for by weather conditions, with the likelihood decreasing by 1% per snow day. An effect of population size was not detected in the data. By investigating different samples, we demonstrated that using quarterly data leads to underestimation and that the age range of sampled athletes should be set carefully.
Hiruki-Raring, Lisa M; Ver Hoef, Jay M; Boveng, Peter L; Bengtson, John L
2012-03-01
We created a Bayesian hierarchical model (BHM) to investigate ecosystem relationships between the physical ecosystem (sea ice extent), a prey measure (krill density), predator behaviors (diving and foraging effort of female Antarctic fur seals, Arctocephalus gazella, with pups) and predator characteristics (mass of maternal fur seals and pups). We collected data on Antarctic fur seals from 1987/1988 to 1994/1995 at Seal Island, Antarctica. The BHM allowed us to link together predators and prey into a model that uses all the data efficiently and accounts for major sources of uncertainty. Based on the literature, we made hypotheses about the relationships in the model, which we compared with the model outcome after fitting the BHM. For each BHM parameter, we calculated the mean of the posterior density and the 95% credible interval. Our model confirmed others' findings that increased sea ice was related to increased krill density. Higher krill density led to reduced dive intensity of maternal fur seals, as measured by dive depth and duration, and to less time spent foraging by maternal fur seals. Heavier maternal fur seals and lower maternal foraging effort resulted in heavier pups at 22 d. No relationship was found between krill density and maternal mass, or between maternal mass and foraging effort on pup growth rates between 22 and 85 days of age. Maternal mass may have reflected environmental conditions prior to the pup provisioning season, rather than summer prey densities. Maternal mass and foraging effort were not related to pup growth rates between 22 and 85 d, possibly indicating that food was not limiting, food sources other than krill were being used, or differences occurred before pups reached age 22 d.
Hierarchical Bayesian modeling and Markov chain Monte Carlo sampling for tuning-curve analysis.
Cronin, Beau; Stevenson, Ian H; Sur, Mriganka; Körding, Konrad P
2010-01-01
A central theme of systems neuroscience is to characterize the tuning of neural responses to sensory stimuli or the production of movement. Statistically, we often want to estimate the parameters of the tuning curve, such as preferred direction, as well as the associated degree of uncertainty, characterized by error bars. Here we present a new sampling-based, Bayesian method that allows the estimation of tuning-curve parameters, the estimation of error bars, and hypothesis testing. This method also provides a useful way of visualizing which tuning curves are compatible with the recorded data. We demonstrate the utility of this approach using recordings of orientation and direction tuning in primary visual cortex, direction of motion tuning in primary motor cortex, and simulated data.
Yu, Rongjie; Abdel-Aty, Mohamed
2014-01-01
Severe crashes are causing serious social and economic loss, and because of this, reducing crash injury severity has become one of the key objectives of the high speed facilities' (freeway and expressway) management. Traditional crash injury severity analysis utilized data mainly from crash reports concerning the crash occurrence information, drivers' characteristics and roadway geometric related variables. In this study, real-time traffic and weather data were introduced to analyze the crash injury severity. The space mean speeds captured by the Automatic Vehicle Identification (AVI) system on the two roadways were used as explanatory variables in this study; and data from a mountainous freeway (I-70 in Colorado) and an urban expressway (State Road 408 in Orlando) have been used to identify the analysis result's consistence. Binary probit (BP) models were estimated to classify the non-severe (property damage only) crashes and severe (injury and fatality) crashes. Firstly, Bayesian BP models' results were compared to the results from Maximum Likelihood Estimation BP models and it was concluded that Bayesian inference was superior with more significant variables. Then different levels of hierarchical Bayesian BP models were developed with random effects accounting for the unobserved heterogeneity at segment level and crash individual level, respectively. Modeling results from both studied locations demonstrate that large variations of speed prior to the crash occurrence would increase the likelihood of severe crash occurrence. Moreover, with considering unobserved heterogeneity in the Bayesian BP models, the model goodness-of-fit has improved substantially. Finally, possible future applications of the model results and the hierarchical Bayesian probit models were discussed.
Wu, Zhen; Liu, Yong; Liang, Zhongyao; Wu, Sifeng; Guo, Huaicheng
2017-03-19
Lake eutrophication is associated with excessive anthropogenic nutrients (mainly nitrogen (N) and phosphorus (P)) and unobserved internal nutrient cycling. Despite the advances in understanding the role of external loadings, the contribution of internal nutrient cycling is still an open question. A dynamic mass-balance model was developed to simulate and measure the contributions of internal cycling and external loading. It was based on the temporal Bayesian Hierarchical Framework (BHM), where we explored the seasonal patterns in the dynamics of nutrient cycling processes and the limitation of N and P on phytoplankton growth in hyper-eutrophic Lake Dianchi, China. The dynamic patterns of the five state variables (Chla, TP, ammonia, nitrate and organic N) were simulated based on the model. Five parameters (algae growth rate, sediment exchange rate of N and P, nitrification rate and denitrification rate) were estimated based on BHM. The model provided a good fit to observations. Our model results highlighted the role of internal cycling of N and P in Lake Dianchi. The internal cycling processes contributed more than external loading to the N and P changes in the water column. Further insights into the nutrient limitation analysis indicated that the sediment exchange of P determined the P limitation. Allowing for the contribution of denitrification to N removal, N was the more limiting nutrient in most of the time, however, P was the more important nutrient for eutrophication management. For Lake Dianchi, it would not be possible to recover solely by reducing the external watershed nutrient load; the mechanisms of internal cycling should also be considered as an approach to inhibit the release of sediments and to enhance denitrification.
Crépet, Amélie; Stahl, Valérie; Carlin, Frédéric
2009-05-31
The optimal growth rate mu(opt) of Listeria monocytogenes in minimally processed (MP) fresh leafy salads was estimated with a hierarchical Bayesian model at (mean+/-standard deviation) 0.33+/-0.16 h(-1). This mu(opt) value was much lower on average than that in nutrient broth, liquid dairy, meat and seafood products (0.7-1.3 h(-1)), and of the same order of magnitude as in cheese. Cardinal temperatures T(min), T(opt) and T(max) were determined at -4.5+/-1.3 degrees C, 37.1+/-1.3 degrees C and 45.4+/-1.2 degrees C respectively. These parameters were determined from 206 growth curves of L. monocytogenes in MP fresh leafy salads (lettuce including iceberg lettuce, broad leaf endive, curly leaf endive, lamb's lettuce, and mixtures of them) selected in the scientific literature and in technical reports. The adequacy of the model was evaluated by comparing observed data (bacterial concentrations at each experimental time for the completion of the 206 growth curves, mean log(10) increase at selected times and temperatures, L. monocytogenes concentrations in naturally contaminated MP iceberg lettuce) with the distribution of the predicted data generated by the model. The sensitivity of the model to assumptions about the prior values also was tested. The observed values mostly fell into the 95% credible interval of the distribution of predicted values. The mu(opt) and its uncertainty determined in this work could be used in quantitative microbial risk assessment for L. monocytogenes in minimally processed fresh leafy salads.
Correlation Between Hierarchical Bayesian and Aerosol ...
Tools to estimate PM2.5 mass have expanded in recent years, and now include: 1) stationary monitor readings, 2) Community Multi-Scale Air Quality (CMAQ) model estimates, 3) Hierarchical Bayesian (HB) estimates from combined stationary monitor readings and CMAQ model output; and, 4) calibrated Aerosol Optical Depth (AOD) readings from two Moderate Resolution Imaging Spetroradiometer (MODIS) units on National Aeronautics and Space Administration’s (NASA) Terra and Aqua satellites. Case-crossover design and conditional logistic regression were used to determine concentration response (CR) functions for three different PM2.5 levels on asthma emergency department (ED) visits and acute myocardial infarction (MI) inpatient hospitalizations in ninety-nine, 12 km2 grids in Baltimore, MD (2005 data). HB analyses for asthma ED visits produced significant results at 3-day lags for the main effect (OR=1.002, 95% CI=1.000-1.005), and two effect modifiers for females (OR=1.003, 95% CI=1.000-1.006), and non-Caucasian/non-African American persons (OR=1.010, 95% CI=1.001-1.019). HB analyses for acute MI inpatient hospitalizations also consistently produced a significant outcome for persons of other race (OR=1.031, 95% CI=1.006-1.056). Correlation coefficients computed between stationary monitor and satellite AOD PM2.5 values were significant for both asthma (rxy=0.944) and acute MI (rxy=0.940). Both monitor and AOD PM2.5 values were higher in February and June through Aug
2012-01-01
Background The EU Regulation No 2160/2003 imposes a reduction in the prevalence of Salmonella in pigs. The efficiency of control programmes for Salmonella in pigs, reported among the EU Member States, varies and definitive eradication seems very difficult. Control measures currently recommended for Salmonella are not serotype-specific. Is it possible that the risk factors for different Salmonella serotypes are different? The aim of this study was to investigate potential risk factors for two groups of Salmonella sp serotypes using pen faecal samples from breeding pig holdings representative of the Portuguese pig sector. Methods The data used come from the Baseline Survey for the Prevalence of Salmonella in breeding pigs in Portugal. A total of 1670 pen faecal samples from 167 herds were tested, and 170 samples were positive for Salmonella. The presence of Salmonella in each sample (outcome variable) was classified in three categories: i) no Salmonella, ii) Salmonella Typhimurium or S. Typhimurium-like strains with the antigenic formula: 1,4,5,12:i:-, , and iii) other serotypes. Along with the sample collection, a questionnaire concerning herd management and potential risk factors was utilised. The data have a “natural” hierarchical structure so a categorical multilevel analysis of the dataset was carried out using a Bayesian hierarchical model. The model was estimated using Markov Chain Monte Carlo methods, implemented in the software WinBUGS. Results The significant associations found (when compared to category “no Salmonella”), for category “serotype Typhimurium or S. Typhimurium-like strains with the antigenic formula: 1,4,5,12:i:-” were: age of breeding sows, size of the herd, number of pigs/pen and source of semen. For the category “other serotypes” the significant associations found were: control of rodents, region of the country, source of semen, breeding sector room and source of feed. Conclusions The risk factors significantly associated
Guo, Ying; DuBois Bowman, F; Kilts, Clinton
2008-09-01
In vivo functional neuroimaging, including functional magnetic resonance imaging (fMRI) and positron emission tomography (PET), is becoming increasingly important in defining the pathophysiology of psychiatric disorders such as schizophrenia, major depression, and Alzheimer's disease. Furthermore, recent studies have begun to investigate the possibility of using functional neuroimaging to guide treatment selection for individual patients. By studying the changes between a patient's pre- and post-treatment brain activity, investigators are gaining insights into the impact of treatment on behavior-related neural processing traits associated with particular psychiatric disorders. Furthermore, these studies may shed light on the neural basis of response and nonresponse to specific treatments. The practical limitation of such studies is that the post-treatment scans offer little guidance to treatment selection in clinical settings, since treatment decisions precede the availability of post-treatment brain scans. This shortcoming represents the impetus for developing statistical methodology that would provide clinicians with predictive information concerning the effect of treatment on brain activity and, ultimately, symptom-related behaviors. We present a prediction algorithm that uses a patient's pretreatment scans, coupled with relevant patient characteristics, to forecast the patient's brain activity following a specified treatment regimen. We derive our predictive method from a Bayesian hierarchical model constructed on the pre- and post-treatment scans of designated training data. We perform estimation using the expectation-maximization algorithm. We evaluate the accuracy of our proposed prediction method using K-fold cross-validation, quantifying the error using two new measures that we propose for neuroimaging data. The proposed method is applicable to both PET and fMRI studies. We illustrate its use with a PET study of working memory in patients with
Bertram, Douglas F; Drever, Mark C; McAllister, Murdoch K; Schroeder, Bernard K; Lindsay, David J; Faust, Deborah A
2015-01-01
Species at risk with secretive breeding behaviours, low densities, and wide geographic range pose a significant challenge to conservation actions because population trends are difficult to detect. Such is the case with the Marbled Murrelet (Brachyramphus marmoratus), a seabird listed as 'Threatened' by the Species at Risk Act in Canada largely due to the loss of its old growth forest nesting habitat. We report the first estimates of population trend of Marbled Murrelets in Canada derived from a monitoring program that uses marine radar to detect birds as they enter forest watersheds during 923 dawn surveys at 58 radar monitoring stations within the six Marbled Murrelet Conservation Regions on coastal British Columbia, Canada, 1996-2013. Temporal trends in radar counts were analyzed with a hierarchical Bayesian multivariate modeling approach that controlled for variation in tilt of the radar unit and day of year, included year-specific deviations from the overall trend ('year effects'), and allowed for trends to be estimated at three spatial scales. A negative overall trend of -1.6%/yr (95% credibility interval: -3.2%, 0.01%) indicated moderate evidence for a coast-wide decline, although trends varied strongly among the six conservation regions. Negative annual trends were detected in East Vancouver Island (-9%/yr) and South Mainland Coast (-3%/yr) Conservation Regions. Over a quarter of the year effects were significantly different from zero, and the estimated standard deviation in common-shared year effects between sites within each region was about 50% per year. This large common-shared interannual variation in counts may have been caused by regional movements of birds related to changes in marine conditions that affect the availability of prey.
Schroeder, Bernard K.; Lindsay, David J.; Faust, Deborah A.
2015-01-01
Species at risk with secretive breeding behaviours, low densities, and wide geographic range pose a significant challenge to conservation actions because population trends are difficult to detect. Such is the case with the Marbled Murrelet (Brachyramphus marmoratus), a seabird listed as ‘Threatened’ by the Species at Risk Act in Canada largely due to the loss of its old growth forest nesting habitat. We report the first estimates of population trend of Marbled Murrelets in Canada derived from a monitoring program that uses marine radar to detect birds as they enter forest watersheds during 923 dawn surveys at 58 radar monitoring stations within the six Marbled Murrelet Conservation Regions on coastal British Columbia, Canada, 1996–2013. Temporal trends in radar counts were analyzed with a hierarchical Bayesian multivariate modeling approach that controlled for variation in tilt of the radar unit and day of year, included year-specific deviations from the overall trend (‘year effects’), and allowed for trends to be estimated at three spatial scales. A negative overall trend of -1.6%/yr (95% credibility interval: -3.2%, 0.01%) indicated moderate evidence for a coast-wide decline, although trends varied strongly among the six conservation regions. Negative annual trends were detected in East Vancouver Island (-9%/yr) and South Mainland Coast (-3%/yr) Conservation Regions. Over a quarter of the year effects were significantly different from zero, and the estimated standard deviation in common-shared year effects between sites within each region was about 50% per year. This large common-shared interannual variation in counts may have been caused by regional movements of birds related to changes in marine conditions that affect the availability of prey. PMID:26258803
Giovanini, Jack; Kroll, Andrew J; Jones, Jay E; Altman, Bob; Arnett, Edward B
2013-01-01
As human demand for ecosystem products increases, management intervention may become more frequent after environmental disturbances. Evaluations of ecological responses to cumulative effects of management interventions and natural disturbances provide critical decision-support tools for managers who strive to balance environmental conservation and economic development. We conducted an experiment to evaluate the effects of salvage logging on avian community composition in lodgepole pine (Pinus contorta) forests affected by beetle outbreaks in Oregon, USA, 1996-1998. Treatments consisted of the removal of lodgepole pine snags only, and live trees were not harvested. We used a bayesian hierarchical model to quantify occupancy dynamics for 27 breeding species, while accounting for variation in the detection process. We examined how magnitude and precision of treatment effects varied when incorporating prior information from a separate intervention study that occurred in a similar ecological system. Regardless of which prior we evaluated, we found no evidence that the harvest treatment had a negative impact on species richness, with an estimated average of 0.2-2.2 more species in harvested stands than unharvested stands. Estimated average similarity between control and treatment stands ranged from 0.82-0.87 (1 indicating complete similarity between a pair of stands) and suggested that treatment stands did not contain novel assemblies of species responding to the harvesting prescription. Estimated treatment effects were positive for twenty-four (90%) of the species, although the credible intervals contained 0 in all cases. These results suggest that, unlike most post-fire salvage logging prescriptions, selective harvesting after beetle outbreaks may meet multiple management objectives, including the maintenance of avian community richness comparable to what is found in unharvested stands. Our results provide managers with prescription alternatives to respond to severe
ERIC Educational Resources Information Center
Song, Xin-Yuan; Lee, Sik-Yum
2008-01-01
Structural equation models are widely appreciated in behavioral, social, and psychological research to model relations between latent constructs and manifest variables, and to control for measurement errors. Most applications of structural equation models are based on fully observed data that are independently distributed. However, hierarchical…
A Survey of Model Evaluation Approaches with a Tutorial on Hierarchical Bayesian Methods
ERIC Educational Resources Information Center
Shiffrin, Richard M.; Lee, Michael D.; Kim, Woojae; Wagenmakers, Eric-Jan
2008-01-01
This article reviews current methods for evaluating models in the cognitive sciences, including theoretically based approaches, such as Bayes factors and minimum description length measures; simulation approaches, including model mimicry evaluations; and practical approaches, such as validation and generalization measures. This article argues…
Bayesian Data Analysis with the Bivariate Hierarchical Ornstein-Uhlenbeck Process Model.
Oravecz, Zita; Tuerlinckx, Francis; Vandekerckhove, Joachim
2016-01-01
In this paper, we propose a multilevel process modeling approach to describing individual differences in within-person changes over time. To characterize changes within an individual, repeated measures over time are modeled in terms of three person-specific parameters: a baseline level, intraindividual variation around the baseline, and regulatory mechanisms adjusting toward baseline. Variation due to measurement error is separated from meaningful intraindividual variation. The proposed model allows for the simultaneous analysis of longitudinal measurements of two linked variables (bivariate longitudinal modeling) and captures their relationship via two person-specific parameters. Relationships between explanatory variables and model parameters can be studied in a one-stage analysis, meaning that model parameters and regression coefficients are estimated simultaneously. Mathematical details of the approach, including a description of the core process model-the Ornstein-Uhlenbeck model-are provided. We also describe a user friendly, freely accessible software program that provides a straightforward graphical interface to carry out parameter estimation and inference. The proposed approach is illustrated by analyzing data collected via self-reports on affective states.
A Bayesian Hierarchical Modeling Approach to Predicting Flow in Ungauged Basins
Recent innovative approaches to identifying and applying regression-based relationships between land use patterns (such as increasing impervious surface area and decreasing vegetative cover) and rainfall-runoff model parameters represent novel and promising improvements to predic...
Cassese, Alberto; Guindani, Michele; Tadesse, Mahlet G.; Falciani, Francesco; Vannucci, Marina
2014-01-01
A number of statistical models have been successfully developed for the analysis of high-throughput data from a single source, but few methods are available for integrating data from different sources. Here we focus on integrating gene expression levels with comparative genomic hybridization (CGH) array measurements collected on the same subjects. We specify a measurement error model that relates the gene expression levels to latent copy number states which, in turn, are related to the observed surrogate CGH measurements via a hidden Markov model. We employ selection priors that exploit the dependencies across adjacent copy number states and investigate MCMC stochastic search techniques for posterior inference. Our approach results in a unified modeling framework for simultaneously inferring copy number variants (CNV) and identifying their significant associations with mRNA transcripts abundance. We show performance on simulated data and illustrate an application to data from a genomic study on human cancer cell lines. PMID:24834139
Paddock, Susan M; Savitsky, Terrance D
2013-06-01
There are several challenges to testing the effectiveness of group therapy-based interventions in alcohol and other drug use (AOD) treatment settings. Enrollment into AOD therapy groups typically occurs on an open (rolling) basis. Changes in therapy group membership induce a complex correlation structure among client outcomes, with relatively small numbers of clients attending each therapy group session. Primary outcomes are measured post-treatment, so each datum reflects the effect of all sessions attended by a client. The number of post-treatment outcomes assessments is typically very limited. The first feature of our modeling approach relaxes the assumption of independent random effects in the standard multiple membership model by employing conditional autoregression (CAR) to model correlation in random therapy group session effects associated with clients' attendance of common group therapy sessions. A second feature specifies a longitudinal growth model under which the posterior distribution of client-specific random effects, or growth parameters, is modeled non-parametrically. The Dirichlet process prior helps to overcome limitations of standard parametric growth models given limited numbers of longitudinal assessments. We motivate and illustrate our approach with a data set from a study of group cognitive behavioral therapy to reduce depressive symptoms among residential AOD treatment clients.
NASA Astrophysics Data System (ADS)
Mandel, Kaisey; Scolnic, Daniel; Shariff, Hikmatali; Foley, Ryan; Kirshner, Robert
2017-01-01
Inferring peak optical absolute magnitudes of Type Ia supernovae (SN Ia) from distance-independent measures such as their light curve shapes and colors underpins the evidence for cosmic acceleration. SN Ia with broader, slower declining optical light curves are more luminous (“broader-brighter”) and those with redder colors are dimmer. But the “redder-dimmer” color-luminosity relation widely used in cosmological SN Ia analyses confounds its two separate physical origins. An intrinsic correlation arises from the physics of exploding white dwarfs, while interstellar dust in the host galaxy also makes SN Ia appear dimmer and redder. Conventional 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 (MB vs. B-V) slope βint differs from the host galaxy dust law RB, this convolution results in a specific curve of mean extinguished absolute magnitude vs. apparent color. The derivative of this curve smoothly transitions from βint in the blue tail to RB 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 βapp between βint and RB. We incorporate these effects into a hierarchical Bayesian statistical model for SN Ia light curve measurements, and analyze a dataset of SALT2 optical light curve fits of 277 nearby SN Ia at z < 0.10. The conventional linear fit obtains βapp ≈ 3. Our model finds a βint = 2.2 ± 0.3 and a distinct dust law of RB = 3.7 ± 0
MacNab, Ying C
2007-11-20
This paper presents a Bayesian disability-adjusted life year (DALY) methodology for spatial and spatiotemporal analyses of disease and/or injury burden. A Bayesian disease mapping model framework, which blends together spatial modelling, shared-component modelling (SCM), temporal modelling, ecological modelling, and non-linear modelling, is developed for small-area DALY estimation and inference. In particular, we develop a model framework that enables SCM as well as multivariate CAR modelling of non-fatal and fatal disease or injury rates and facilitates spline smoothing for non-linear modelling of temporal rate and risk trends. Using British Columbia (Canada) hospital admission-separation data and vital statistics mortality data on non-fatal and fatal road traffic injuries to male population age 20-39 for year 1991-2000 and for 84 local health areas and 16 health service delivery areas, spatial and spatiotemporal estimation and inference on years of life lost due to premature death, years lived with disability, and DALYs are presented. Fully Bayesian estimation and inference, with Markov chain Monte Carlo implementation, are illustrated. We present a methodological framework within which the DALY and the Bayesian disease mapping methodologies interface and intersect. Its development brings the relative importance of premature mortality and disability into the assessment of community health and health needs in order to provide reliable information and evidence for community-based public health surveillance and evaluation, disease and injury prevention, and resource provision.
Bayesian Hierarchical Air-Sea Interaction Modeling: Application to the Labrador Sea
NASA Technical Reports Server (NTRS)
Niiler, Pearn P.
2002-01-01
The objectives are to: 1) Organize data from 26 MINIMET drifters in the Labrador Sea, including sensor calibration and error checking of ARGOS transmissions. 2) Produce wind direction, barometer, and sea surface temperature time series. In addition, provide data from historical file of 150 SHARP drifters in the Labrador Sea. 3) Work with data interpretation and data-modeling assimilation issues.
Savitsky, Terrance D; Paddock, Susan M
2013-06-01
We develop a dependent Dirichlet process (DDP) model for repeated measures multiple membership (MM) data. This data structure arises in studies under which an intervention is delivered to each client through a sequence of elements which overlap with those of other clients on different occasions. Our interest concentrates on study designs for which the overlaps of sequences occur for clients who receive an intervention in a shared or grouped fashion whose memberships may change over multiple treatment events. Our motivating application focuses on evaluation of the effectiveness of a group therapy intervention with treatment delivered through a sequence of cognitive behavioral therapy session blocks, called modules. An open-enrollment protocol permits entry of clients at the beginning of any new module in a manner that may produce unique MM sequences across clients. We begin with a model that composes an addition of client and multiple membership module random effect terms, which are assumed independent. Our MM DDP model relaxes the assumption of conditionally independent client and module random effects by specifying a collection of random distributions for the client effect parameters that are indexed by the unique set of module attendances. We demonstrate how this construction facilitates examining heterogeneity in the relative effectiveness of group therapy modules over repeated measurement occasions.
NASA Astrophysics Data System (ADS)
Kim, Jang-Gyeong; Kwon, Hyun-Han; Kim, Dongkyun
2017-01-01
Poisson cluster stochastic rainfall generators (e.g., modified Bartlett-Lewis rectangular pulse, MBLRP) have been widely applied to generate synthetic sub-daily rainfall sequences. The MBLRP model reproduces the underlying distribution of the rainfall generating process. The existing optimization techniques are typically based on individual parameter estimates that treat each parameter as independent. However, parameter estimates sometimes compensate for the estimates of other parameters, which can cause high variability in the results if the covariance structure is not formally considered. Moreover, uncertainty associated with model parameters in the MBLRP rainfall generator is not usually addressed properly. Here, we develop a hierarchical Bayesian model (HBM)-based MBLRP model to jointly estimate parameters across weather stations and explicitly consider the covariance and uncertainty through a Bayesian framework. The model is tested using weather stations in South Korea. The HBM-based MBLRP model improves the identification of parameters with better reproduction of rainfall statistics at various temporal scales. Additionally, the spatial variability of the parameters across weather stations is substantially reduced compared to that of other methods.
Bayesian hierarchical models for network meta-analysis incorporating nonignorable missingness.
Zhang, Jing; Chu, Haitao; Hong, Hwanhee; Virnig, Beth A; Carlin, Bradley P
2015-07-28
Network meta-analysis expands the scope of a conventional pairwise meta-analysis to simultaneously compare multiple treatments, synthesizing both direct and indirect information and thus strengthening inference. Since most of trials only compare two treatments, a typical data set in a network meta-analysis managed as a trial-by-treatment matrix is extremely sparse, like an incomplete block structure with significant missing data. Zhang et al. proposed an arm-based method accounting for correlations among different treatments within the same trial and assuming that absent arms are missing at random. However, in randomized controlled trials, nonignorable missingness or missingness not at random may occur due to deliberate choices of treatments at the design stage. In addition, those undertaking a network meta-analysis may selectively choose treatments to include in the analysis, which may also lead to missingness not at random. In this paper, we extend our previous work to incorporate missingness not at random using selection models. The proposed method is then applied to two network meta-analyses and evaluated through extensive simulation studies. We also provide comprehensive comparisons of a commonly used contrast-based method and the arm-based method via simulations in a technical appendix under missing completely at random and missing at random.
Bayesian hierarchical analysis of within-units variances in repeated measures experiments.
Ten Have, T R; Chinchilli, V M
1994-09-30
We develop hierarchical Bayesian models for biomedical data that consist of multiple measurements on each individual under each of several conditions. The focus is on investigating differences in within-subject variation between conditions. We present both population-level and individual-level comparisons. We extend the partial likelihood models of Chinchilli et al. with a unique Bayesian hierarchical framework for variance components and associated degrees of freedom. We use the Gibbs sampler to estimate posterior marginal distributions for the parameters of the Bayesian hierarchical models. The application involves a comparison of two cholesterol analysers each applied repeatedly to a sample of subjects. Both the partial likelihood and Bayesian approaches yield similar results, although confidence limits tend to be wider under the Bayesian models.
Song, Hae-Ryoung; Lawson, Andrew; D'Agostino, Ralph B; Liese, Angela D
2011-03-01
Sparse count data violate assumptions of traditional Poisson models due to the excessive amount of zeros, and modeling sparse data becomes challenging. However, since aggregation to reduce sparseness may result in biased estimates of risk, solutions need to be found at the level of disaggregated data. We investigated different statistical approaches within a Bayesian hierarchical framework for modeling sparse data without aggregation of data. We compared our proposed models with the traditional Poisson model and the zero-inflated model based on simulated data. We applied statistical models to type 1 and type 2 diabetes in youth 10-19 years known as rare diseases, and compared models using the inference results and various model diagnostic tools. We showed that one of the models we proposed, a sparse Poisson convolution model, performed better than other models in the simulation and application based on the deviance information criterion (DIC) and the mean squared prediction error.
Wan, Rongrong; Cai, Shanshan; Li, Hengpeng; Yang, Guishan; Li, Zhaofu; Nie, Xiaofei
2014-01-15
Lake eutrophication has become a very serious environmental problem in China. If water pollution is to be controlled and ultimately eliminated, it is essential to understand how human activities affect surface water quality. A recently developed technique using the Bayesian hierarchical linear regression model revealed the effects of land use and land cover (LULC) on stream water quality at a watershed scale. Six LULC categories combined with watershed characteristics, including size, slope, and permeability were the variables that were studied. The pollutants of concern were nutrient concentrations of total nitrogen (TN) and total phosphorus (TP), common pollutants found in eutrophication. The monthly monitoring data at 41 sites in the Xitiaoxi Watershed, China during 2009-2010 were used for model demonstration. The results showed that the relationships between LULC and stream water quality are so complicated that the effects are varied over large areas. The models suggested that urban and agricultural land are important sources of TN and TP concentrations, while rural residential land is one of the major sources of TN. Certain agricultural practices (excessive fertilizer application) result in greater concentrations of nutrients in paddy fields, artificial grasslands, and artificial woodlands. This study suggests that Bayesian hierarchical modeling is a powerful tool for examining the complicated relationships between land use and water quality on different scales, and for developing land use and water management policies.
NASA Astrophysics Data System (ADS)
Chen, J.; Hubbard, S. S.; Williams, K. H.; Tuglus, C.; Flores-Orozco, A.; Kemna, A.
2010-12-01
Although in-situ bioremediation is often considered as a key approach for subsurface environmental remediation, monitoring induced biogeochemical processes, needed to evaluate the efficacy of the treatments, is challenging over field relevant scales. In this study, we develop a hierarchical Bayesian model that builds on our previous framework for estimating biogeochemical transformations using geochemical and geophysical data obtained from laboratory column experiments. The new Bayesian model treats the induced biogeochemical transformations as both spatial and temporal (rather than just temporal) processes and combines time-lapse borehole ‘point’ geochemical measurements with inverted surface- or crosshole-based spectral induced polarization (SIP) data. This model consists of three levels of statistical sub-models: (1) data model (or likelihood function), which provides links between the biogeochemical end-products and geophysical attributes, (2) process model, which describes the spatial and temporal variability of biogeochemical properties in the disturbed subsurface systems, and (3) parameter model, which describes the prior distributions of various parameters and initial conditions. The joint posterior probability distribution is explored using Markov Chain Monte Carlo sampling methods to obtain the spatial and temporal distribution of the hidden parameters. We apply the developed Bayesian model to the datasets collected from the uranium-contaminated DOE Rifle site for estimating the spatial and temporal distribution of remediation-induced end products. The datasets consist of time-lapse wellbore aqueous geochemical parameters (including Fe(II), sulfate, sulfide, acetate, uranium, chloride, and bromide concentrations) and surface SIP data collected over 13 frequencies (ranging from 0.065Hz to 256Hz). We first perform statistical analysis on the multivariate data to identify possible patterns (or ‘diagnostic signatures’) of bioremediation, and then we
A Bayesian Hierarchical Approach to Regional Frequency Analysis of Extremes
NASA Astrophysics Data System (ADS)
Renard, B.
2010-12-01
Rainfall and runoff frequency analysis is a major issue for the hydrological community. The distribution of hydrological extremes varies in space and possibly in time. Describing and understanding this spatiotemporal variability are primary challenges to improve hazard quantification and risk assessment. This presentation proposes a general approach based on a Bayesian hierarchical model, following previous work by Cooley et al. [2007], Micevski [2007], Aryal et al. [2009] or Lima and Lall [2009; 2010]. Such a hierarchical model is made up of two levels: (1) a data level modeling the distribution of observations, and (2) a process level describing the fluctuation of the distribution parameters in space and possibly in time. At the first level of the model, at-site data (e.g., annual maxima series) are modeled with a chosen distribution (e.g., a GEV distribution). Since data from several sites are considered, the joint distribution of a vector of (spatial) observations needs to be derived. This is challenging because data are in general not spatially independent, especially for nearby sites. An elliptical copula is therefore used to formally account for spatial dependence between at-site data. This choice might be questionable in the context of extreme value distributions. However, it is motivated by its applicability in spatial highly dimensional problems, where the joint pdf of a vector of n observations is required to derive the likelihood function (with n possibly amounting to hundreds of sites). At the second level of the model, parameters of the chosen at-site distribution are then modeled by a Gaussian spatial process, whose mean may depend on covariates (e.g. elevation, distance to sea, weather pattern, time). In particular, this spatial process allows estimating parameters at ungauged sites, and deriving the predictive distribution of rainfall/runoff at every pixel/catchment of the studied domain. An application to extreme rainfall series from the French
Carroll, Carlos; Johnson, Devin S
2008-08-01
Regional conservation planning increasingly draws on habitat suitability models to support decisions regarding land allocation and management. Nevertheless, statistical techniques commonly used for developing such models may give misleading results because they fail to account for 3 factors common in data sets of species distribution: spatial autocorrelation, the large number of sites where the species is absent (zero inflation), and uneven survey effort. We used spatial autoregressive models fit with Bayesian Markov Chain Monte Carlo techniques to assess the relationship between older coniferous forest and the abundance of Northern Spotted Owl nest and activity sites throughout the species' range. The spatial random-effect term incorporated in the autoregressive models successfully accounted for zero inflation and reduced the effect of survey bias on estimates of species-habitat associations. Our results support the hypothesis that the relationship between owl distribution and older forest varies with latitude. A quadratic relationship between owl abundance and older forest was evident in the southern portion of the range, and a pseudothreshold relationship was evident in the northern portion of the range. Our results suggest that proposed changes to the network of owl habitat reserves would reduce the proportion of the population protected by up to one-third, and that proposed guidelines for forest management within reserves underestimate the proportion of older forest associated with maximum owl abundance and inappropriately generalize threshold relationships among subregions. Bayesian spatial models can greatly enhance the utility of habitat analysis for conservation planning because they add the statistical flexibility necessary for analyzing regional survey data while retaining the interpretability of simpler models.
Lucka, Felix; Pursiainen, Sampsa; Burger, Martin; Wolters, Carsten H
2012-07-16
The estimation of the activity-related ion currents by measuring the induced electromagnetic fields at the head surface is a challenging and severely ill-posed inverse problem. This is especially true in the recovery of brain networks involving deep-lying sources by means of EEG/MEG recordings which is still a challenging task for any inverse method. Recently, hierarchical Bayesian modeling (HBM) emerged as a unifying framework for current density reconstruction (CDR) approaches comprising most established methods as well as offering promising new methods. Our work examines the performance of fully-Bayesian inference methods for HBM for source configurations consisting of few, focal sources when used with realistic, high-resolution finite element (FE) head models. The main foci of interest are the correct depth localization, a well-known source of systematic error of many CDR methods, and the separation of single sources in multiple-source scenarios. Both aspects are very important in the analysis of neurophysiological data and in clinical applications. For these tasks, HBM provides a promising framework and is able to improve upon established CDR methods such as minimum norm estimation (MNE) or sLORETA in many aspects. For challenging multiple-source scenarios where the established methods show crucial errors, promising results are attained. Additionally, we introduce Wasserstein distances as performance measures for the validation of inverse methods in complex source scenarios.
Bayesian Hierarchical Grouping: perceptual grouping as mixture estimation
Froyen, Vicky; Feldman, Jacob; Singh, Manish
2015-01-01
We propose a novel framework for perceptual grouping based on the idea of mixture models, called Bayesian Hierarchical Grouping (BHG). In BHG we assume that the configuration of image elements is generated by a mixture of distinct objects, each of which generates image elements according to some generative assumptions. Grouping, in this framework, means estimating the number and the parameters of the mixture components that generated the image, including estimating which image elements are “owned” by which objects. We present a tractable implementation of the framework, based on the hierarchical clustering approach of Heller and Ghahramani (2005). We illustrate it with examples drawn from a number of classical perceptual grouping problems, including dot clustering, contour integration, and part decomposition. Our approach yields an intuitive hierarchical representation of image elements, giving an explicit decomposition of the image into mixture components, along with estimates of the probability of various candidate decompositions. We show that BHG accounts well for a diverse range of empirical data drawn from the literature. Because BHG provides a principled quantification of the plausibility of grouping interpretations over a wide range of grouping problems, we argue that it provides an appealing unifying account of the elusive Gestalt notion of Prägnanz. PMID:26322548
Pham, Lisa M; Carvalho, Luis; Schaus, Scott; Kolaczyk, Eric D
Cellular response to a perturbation is the result of a dynamic system of biological variables linked in a complex network. A major challenge in drug and disease studies is identifying the key factors of a biological network that are essential in determining the cell's fate. Here our goal is the identification of perturbed pathways from high-throughput gene expression data. We develop a three-level hierarchical model, where (i) the first level captures the relationship between gene expression and biological pathways using confirmatory factor analysis, (ii) the second level models the behavior within an underlying network of pathways induced by an unknown perturbation using a conditional autoregressive model, and (iii) the third level is a spike-and-slab prior on the perturbations. We then identify perturbations through posterior-based variable selection. We illustrate our approach using gene transcription drug perturbation profiles from the DREAM7 drug sensitivity predication challenge data set. Our proposed method identified regulatory pathways that are known to play a causative role and that were not readily resolved using gene set enrichment analysis or exploratory factor models. Simulation results are presented assessing the performance of this model relative to a network-free variant and its robustness to inaccuracies in biological databases.
Poor-data and data-poor species stock assessment using a Bayesian hierarchical approach.
Jiao, Yan; Cortés, Enric; Andrews, Kate; Guo, Feng
2011-10-01
Appropriate inference for stocks or species with low-quality data (poor data) or limited data (data poor) is extremely important. Hierarchical Bayesian methods are especially applicable to small-area, small-sample-size estimation problems because they allow poor-data species to borrow strength from species with good-quality data. We used a hammerhead shark complex as an example to investigate the advantages of using hierarchical Bayesian models in assessing the status of poor-data and data-poor exploited species. The hammerhead shark complex (Sphyrna spp.) along the Atlantic and Gulf of Mexico coasts of the United States is composed of three species: the scalloped hammerhead (S. lewini), the great hammerhead (S. mokarran), and the smooth hammerhead (S. zygaena) sharks. The scalloped hammerhead comprises 70-80% of the catch and has catch and relative abundance data of good quality, whereas great and smooth hammerheads have relative abundance indices that are both limited and of low quality presumably because of low stock density and limited sampling. Four hierarchical Bayesian state-space surplus production models were developed to simulate variability in population growth rates, carrying capacity, and catchability of the species. The results from the hierarchical Bayesian models were considerably more robust than those of the nonhierarchical models. The hierarchical Bayesian approach represents an intermediate strategy between traditional models that assume different population parameters for each species and those that assume all species share identical parameters. Use of the hierarchical Bayesian approach is suggested for future hammerhead shark stock assessments and for modeling fish complexes with species-specific data, because the poor-data species can borrow strength from the species with good data, making the estimation more stable and robust.
NASA Astrophysics Data System (ADS)
Lall, U.; Zamora, M. R.; Cook, E.; Gelman, A.; Sperry, E.
2003-12-01
Reconstruction of annual or seasonal streamflow at multiple locations or of multiple climatic indices (e.g., PDSI at many locations, or ENSO, PDO, NAO) is sometimes of interest using an array of common paleo predictors. The predictands may be correlated with each other, and the form of each regression between predictand and predictors may also be very similar. Principal or Canonical Component Methods have been used to address this regression problem, after transformation of the data sets to be approximately Normally distributed. An alternative to such methods is presented here. A hierarchical model considers that the regression coefficients are random variables, and seeks to make inferences about the parameters (e.g., they may be Normally distributed, with a certain vector of means and a covariance matrix) of a model that describes the distribution of these variables. Further, the parameters of such a model may in turn be considered to be random variables and one can seek a model that describes them, leading to a multilevel modeling approach. Generally, a diffuse prior distribution is assumed for the parameters at the end of the hierarchy, and a Markov Chain Monte Carlo approach is used to learn or estimate the parameters of the distribution at each level of the hierarchy. Here, we use such an approach in a Generalized Linear Modeling framework - the distribution of the predictand is directly considered to correspond to a parametric family, instead of using transformations to Normality, and a set of basis functions (not necessarily linear) is used to relate the predictors to the predictands. An uncertainty distribution of parameters and hence of estimates is derived automatically as part of the model learning process. We present examples of the applications of these methods and contrast the results with those obtained using PCA/CCA.
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
Swallow, Ben; Buckland, Stephen T; King, Ruth; Toms, Mike P
2016-03-01
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.
Ma, Xiaoye; Chen, Yong; Cole, Stephen R; Chu, Haitao
2016-12-01
To account for between-study heterogeneity in meta-analysis of diagnostic accuracy studies, bivariate random effects models have been recommended to jointly model the sensitivities and specificities. As study design and population vary, the definition of disease status or severity could differ across studies. Consequently, sensitivity and specificity may be correlated with disease prevalence. To account for this dependence, a trivariate random effects model had been proposed. However, the proposed approach can only include cohort studies with information estimating study-specific disease prevalence. In addition, some diagnostic accuracy studies only select a subset of samples to be verified by the reference test. It is known that ignoring unverified subjects may lead to partial verification bias in the estimation of prevalence, sensitivities, and specificities in a single study. However, the impact of this bias on a meta-analysis has not been investigated. In this paper, we propose a novel hybrid Bayesian hierarchical model combining cohort and case-control studies and correcting partial verification bias at the same time. We investigate the performance of the proposed methods through a set of simulation studies. Two case studies on assessing the diagnostic accuracy of gadolinium-enhanced magnetic resonance imaging in detecting lymph node metastases and of adrenal fluorine-18 fluorodeoxyglucose positron emission tomography in characterizing adrenal masses are presented.
UNSUPERVISED TRANSIENT LIGHT CURVE ANALYSIS VIA HIERARCHICAL BAYESIAN INFERENCE
Sanders, N. E.; Soderberg, A. M.; Betancourt, M.
2015-02-10
Historically, light curve studies of supernovae (SNe) and other transient classes have focused on individual objects with copious and high signal-to-noise observations. In the nascent era of wide field transient searches, objects with detailed observations are decreasing as a fraction of the overall known SN population, and this strategy sacrifices the majority of the information contained in the data about the underlying population of transients. A population level modeling approach, simultaneously fitting all available observations of objects in a transient sub-class of interest, fully mines the data to infer the properties of the population and avoids certain systematic biases. We present a novel hierarchical Bayesian statistical model for population level modeling of transient light curves, and discuss its implementation using an efficient Hamiltonian Monte Carlo technique. As a test case, we apply this model to the Type IIP SN sample from the Pan-STARRS1 Medium Deep Survey, consisting of 18,837 photometric observations of 76 SNe, corresponding to a joint posterior distribution with 9176 parameters under our model. Our hierarchical model fits provide improved constraints on light curve parameters relevant to the physical properties of their progenitor stars relative to modeling individual light curves alone. Moreover, we directly evaluate the probability for occurrence rates of unseen light curve characteristics from the model hyperparameters, addressing observational biases in survey methodology. We view this modeling framework as an unsupervised machine learning technique with the ability to maximize scientific returns from data to be collected by future wide field transient searches like LSST.
Coggins, Lewis G.; Bacheler, Nathan M.; Gwinn, Daniel C.
2014-01-01
Occupancy models using incidence data collected repeatedly at sites across the range of a population are increasingly employed to infer patterns and processes influencing population distribution and dynamics. While such work is common in terrestrial systems, fewer examples exist in marine applications. This disparity likely exists because the replicate samples required by these models to account for imperfect detection are often impractical to obtain when surveying aquatic organisms, particularly fishes. We employ simultaneous sampling using fish traps and novel underwater camera observations to generate the requisite replicate samples for occupancy models of red snapper, a reef fish species. Since the replicate samples are collected simultaneously by multiple sampling devices, many typical problems encountered when obtaining replicate observations are avoided. Our results suggest that augmenting traditional fish trap sampling with camera observations not only doubled the probability of detecting red snapper in reef habitats off the Southeast coast of the United States, but supplied the necessary observations to infer factors influencing population distribution and abundance while accounting for imperfect detection. We found that detection probabilities tended to be higher for camera traps than traditional fish traps. Furthermore, camera trap detections were influenced by the current direction and turbidity of the water, indicating that collecting data on these variables is important for future monitoring. These models indicate that the distribution and abundance of this species is more heavily influenced by latitude and depth than by micro-scale reef characteristics lending credence to previous characterizations of red snapper as a reef habitat generalist. This study demonstrates the utility of simultaneous sampling devices, including camera traps, in aquatic environments to inform occupancy models and account for imperfect detection when describing factors
Stewart, David R.; Long, James M.
2015-01-01
Species distribution models are useful tools to evaluate habitat relationships of fishes. We used hierarchical Bayesian multispecies mixture models to evaluate the relationships of both detection and abundance with habitat of reservoir fishes caught using tandem hoop nets. A total of 7,212 fish from 12 species were captured, and the majority of the catch was composed of Channel Catfish Ictalurus punctatus (46%), Bluegill Lepomis macrochirus(25%), and White Crappie Pomoxis annularis (14%). Detection estimates ranged from 8% to 69%, and modeling results suggested that fishes were primarily influenced by reservoir size and context, water clarity and temperature, and land-use types. Species were differentially abundant within and among habitat types, and some fishes were found to be more abundant in turbid, less impacted (e.g., by urbanization and agriculture) reservoirs with longer shoreline lengths; whereas, other species were found more often in clear, nutrient-rich impoundments that had generally shorter shoreline length and were surrounded by a higher percentage of agricultural land. Our results demonstrated that habitat and reservoir characteristics may differentially benefit species and assemblage structure. This study provides a useful framework for evaluating capture efficiency for not only hoop nets but other gear types used to sample fishes in reservoirs.
Tan, M; Qu, Y; Mascha, E; Schubert, A
1999-08-15
Oral practice examinations (OPEs) are used in many anaesthesiology programmes to familiarize anaesthesiology residents with the format of the oral examination administered by the American Board of Anesthesiology. The OPE outcome (final grade) consists of 'Definite Not Pass', 'Probable Not Pass', 'Probable Pass' and 'Definite Pass'. In our study to assess the validity of the OPE, residents took an average of two (ranging from one to six) OPEs, each of which was evaluated by two board certified anaesthesiologists randomly selected from a pool of 12. A key question of interest was to identify factors, for example, the length of training, didactic experience and other characteristics, that most influence OPE outcome. In addition, we were interested in assessing the reliability of the final grade, that is, the covariance parameters are of interest as well. However, estimating variance components in multi-level data with an unequal number of repeated ordinal outcomes presents several statistical challenges, such as how to estimate high dimensional random effects parameters, especially for ordinal outcomes. We propose a Bayesian hierarchical proportional odds model for data with such complexity. The flexibility of such a model allows us to make inference on the association of OPE outcomes with other factors and to estimate the variance components as well.
Spatial Hierarchical Bayesian Analysis of the Historical Extreme Streamflow
NASA Astrophysics Data System (ADS)
Najafi, M. R.; Moradkhani, H.
2012-04-01
Analysis of the climate change impact on extreme hydro-climatic events is crucial for future hydrologic/hydraulic designs and water resources decision making. The purpose of this study is to investigate the changes of the extreme value distribution parameters with respect to time to reflect upon the impact of climate change. We develop a statistical model using the observed streamflow data of the Columbia River Basin in USA to estimate the changes of high flows as a function of time as well as other variables. Generalized Pareto Distribution (GPD) is used to model the upper 95% flows during December through March for 31 gauge stations. In the process layer of the model the covariates including time, latitude, longitude, elevation and basin area are considered to assess the sensitivity of the model to each variable. Markov Chain Monte Carlo (MCMC) method is used to estimate the parameters. The Spatial Hierarchical Bayesian technique models the GPD parameters spatially and borrows strength from other locations by pooling data together, while providing an explicit estimation of the uncertainties in all stages of modeling.
Seichter, Felicia; Vogt, Josef; Radermacher, Peter; Mizaikoff, Boris
2017-01-25
The calibration of analytical systems is time-consuming and the effort for daily calibration routines should therefore be minimized, while maintaining the analytical accuracy and precision. The 'calibration transfer' approach proposes to combine calibration data already recorded with actual calibrations measurements. However, this strategy was developed for the multivariate, linear analysis of spectroscopic data, and thus, cannot be applied to sensors with a single response channel and/or a non-linear relationship between signal and desired analytical concentration. To fill this gap for a non-linear calibration equation, we assume that the coefficients for the equation, collected over several calibration runs, are normally distributed. Considering that coefficients of an actual calibration are a sample of this distribution, only a few standards are needed for a complete calibration data set. The resulting calibration transfer approach is demonstrated for a fluorescence oxygen sensor and implemented as a hierarchical Bayesian model, combined with a Lagrange Multipliers technique and Monte-Carlo Markov-Chain sampling. The latter provides realistic estimates for coefficients and prediction together with accurate error bounds by simulating known measurement errors and system fluctuations. Performance criteria for validation and optimal selection of a reduced set of calibration samples were developed and lead to a setup which maintains the analytical performance of a full calibration. Strategies for a rapid determination of problems occurring in a daily calibration routine, are proposed, thereby opening the possibility of correcting the problem just in time.
Recent global methane trends: an investigation using hierarchical Bayesian methods
NASA Astrophysics Data System (ADS)
Rigby, M. L.; Stavert, A.; Ganesan, A.; Lunt, M. F.
2014-12-01
Following a decade with little growth, methane concentrations began to increase across the globe in 2007, and have continued to rise ever since. The reasons for this renewed growth are currently the subject of much debate. Here, we discuss the recent observed trends, and highlight some of the strengths and weaknesses in current "inverse" methods for quantifying fluxes using observations. In particular, we focus on the outstanding problems of accurately quantifying uncertainties in inverse frameworks. We examine to what extent the recent methane changes can be explained by the current generation of flux models and inventories. We examine the major modes of variability in wetland models along with the Global Fire Emissions Database (GFED) and the Emissions Database for Global Atmospheric Research (EDGAR). Using the Model for Ozone and Related Tracers (MOZART), we determine whether the spatial and temporal atmospheric trends predicted using these emissions can be brought into consistency with in situ atmospheric observations. We use a novel hierarchical Bayesian methodology in which scaling factors applied to the principal components of the flux fields are estimated simultaneously with the uncertainties associated with the a priori fluxes and with model representations of the observations. Using this method, we examine the predictive power of methane flux models for explaining recent fluctuations.
Hierarchical Theme and Topic Modeling.
Chien, Jen-Tzung
2016-03-01
Considering the hierarchical data groupings in text corpus, e.g., words, sentences, and documents, we conduct the structural learning and infer the latent themes and topics for sentences and words from a collection of documents, respectively. The relation between themes and topics under different data groupings is explored through an unsupervised procedure without limiting the number of clusters. A tree stick-breaking process is presented to draw theme proportions for different sentences. We build a hierarchical theme and topic model, which flexibly represents the heterogeneous documents using Bayesian nonparametrics. Thematic sentences and topical words are extracted. In the experiments, the proposed method is evaluated to be effective to build semantic tree structure for sentences and the corresponding words. The superiority of using tree model for selection of expressive sentences for document summarization is illustrated.
2009-01-01
Background Assessing agreement in method comparison studies depends on two fundamentally important components; validity (the between method agreement) and reproducibility (the within method agreement). The Bland-Altman limits of agreement technique is one of the favoured approaches in medical literature for assessing between method validity. However, few researchers have adopted this approach for the assessment of both validity and reproducibility. This may be partly due to a lack of a flexible, easily implemented and readily available statistical machinery to analyse repeated measurement method comparison data. Methods Adopting the Bland-Altman framework, but using Bayesian methods, we present this statistical machinery. Two multivariate hierarchical Bayesian models are advocated, one which assumes that the underlying values for subjects remain static (exchangeable replicates) and one which assumes that the underlying values can change between repeated measurements (non-exchangeable replicates). Results We illustrate the salient advantages of these models using two separate datasets that have been previously analysed and presented; (i) assuming static underlying values analysed using both multivariate hierarchical Bayesian models, and (ii) assuming each subject's underlying value is continually changing quantity and analysed using the non-exchangeable replicate multivariate hierarchical Bayesian model. Conclusion These easily implemented models allow for full parameter uncertainty, simultaneous method comparison, handle unbalanced or missing data, and provide estimates and credible regions for all the parameters of interest. Computer code for the analyses in also presented, provided in the freely available and currently cost free software package WinBUGS. PMID:19161599
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…
Finley, Andrew O.; Banerjee, Sudipto; Cook, Bruce D.; Bradford, John B.
2013-01-01
In this paper we detail a multivariate spatial regression model that couples LiDAR, hyperspectral and forest inventory data to predict forest outcome variables at a high spatial resolution. The proposed model is used to analyze forest inventory data collected on the US Forest Service Penobscot Experimental Forest (PEF), ME, USA. In addition to helping meet the regression model's assumptions, results from the PEF analysis suggest that the addition of multivariate spatial random effects improves model fit and predictive ability, compared with two commonly applied modeling approaches. This improvement results from explicitly modeling the covariation among forest outcome variables and spatial dependence among observations through the random effects. Direct application of such multivariate models to even moderately large datasets is often computationally infeasible because of cubic order matrix algorithms involved in estimation. We apply a spatial dimension reduction technique to help overcome this computational hurdle without sacrificing richness in modeling.
A hierarchical Bayesian framework for force field selection in molecular dynamics simulations.
Wu, S; Angelikopoulos, P; Papadimitriou, C; Moser, R; Koumoutsakos, P
2016-02-13
We present a hierarchical Bayesian framework for the selection of force fields in molecular dynamics (MD) simulations. The framework associates the variability of the optimal parameters of the MD potentials under different environmental conditions with the corresponding variability in experimental data. The high computational cost associated with the hierarchical Bayesian framework is reduced by orders of magnitude through a parallelized Transitional Markov Chain Monte Carlo method combined with the Laplace Asymptotic Approximation. The suitability of the hierarchical approach is demonstrated by performing MD simulations with prescribed parameters to obtain data for transport coefficients under different conditions, which are then used to infer and evaluate the parameters of the MD model. We demonstrate the selection of MD models based on experimental data and verify that the hierarchical model can accurately quantify the uncertainty across experiments; improve the posterior probability density function estimation of the parameters, thus, improve predictions on future experiments; identify the most plausible force field to describe the underlying structure of a given dataset. The framework and associated software are applicable to a wide range of nanoscale simulations associated with experimental data with a hierarchical structure.
Marrelec, Guillaume; Messé, Arnaud; Bellec, Pierre
2015-01-01
The use of mutual information as a similarity measure in agglomerative hierarchical clustering (AHC) raises an important issue: some correction needs to be applied for the dimensionality of variables. In this work, we formulate the decision of merging dependent multivariate normal variables in an AHC procedure as a Bayesian model comparison. We found that the Bayesian formulation naturally shrinks the empirical covariance matrix towards a matrix set a priori (e.g., the identity), provides an automated stopping rule, and corrects for dimensionality using a term that scales up the measure as a function of the dimensionality of the variables. Also, the resulting log Bayes factor is asymptotically proportional to the plug-in estimate of mutual information, with an additive correction for dimensionality in agreement with the Bayesian information criterion. We investigated the behavior of these Bayesian alternatives (in exact and asymptotic forms) to mutual information on simulated and real data. An encouraging result was first derived on simulations: the hierarchical clustering based on the log Bayes factor outperformed off-the-shelf clustering techniques as well as raw and normalized mutual information in terms of classification accuracy. On a toy example, we found that the Bayesian approaches led to results that were similar to those of mutual information clustering techniques, with the advantage of an automated thresholding. On real functional magnetic resonance imaging (fMRI) datasets measuring brain activity, it identified clusters consistent with the established outcome of standard procedures. On this application, normalized mutual information had a highly atypical behavior, in the sense that it systematically favored very large clusters. These initial experiments suggest that the proposed Bayesian alternatives to mutual information are a useful new tool for hierarchical clustering. PMID:26406245
Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon
2017-04-10
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.
NASA Astrophysics Data System (ADS)
Eadie, Gwendolyn M.; Springford, Aaron; Harris, William E.
2017-02-01
We present a hierarchical Bayesian method for estimating the total mass and mass profile of the Milky Way Galaxy. The new hierarchical Bayesian approach further improves the framework presented by Eadie et al. and Eadie and Harris and builds upon the preliminary reports by Eadie et al. The method uses a distribution function f({ E },L) to model the Galaxy and kinematic data from satellite objects, such as globular clusters (GCs), to trace the Galaxy’s gravitational potential. A major advantage of the method is that it not only includes complete and incomplete data simultaneously in the analysis, but also incorporates measurement uncertainties in a coherent and meaningful way. We first test the hierarchical Bayesian framework, which includes measurement uncertainties, using the same data and power-law model assumed in Eadie and Harris and find the results are similar but more strongly constrained. Next, we take advantage of the new statistical framework and incorporate all possible GC data, finding a cumulative mass profile with Bayesian credible regions. This profile implies a mass within 125 kpc of 4.8× {10}11{M}ȯ with a 95% Bayesian credible region of (4.0{--}5.8)× {10}11{M}ȯ . Our results also provide estimates of the true specific energies of all the GCs. By comparing these estimated energies to the measured energies of GCs with complete velocity measurements, we observe that (the few) remote tracers with complete measurements may play a large role in determining a total mass estimate of the Galaxy. Thus, our study stresses the need for more remote tracers with complete velocity measurements.
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.
Tools to estimate PM2.5 mass have expanded in recent years, and now include: 1) stationary monitor readings, 2) Community Multi-Scale Air Quality (CMAQ) model estimates, 3) Hierarchical Bayesian (HB) estimates from combined stationary monitor readings and CMAQ model output; and, ...
Risk Assessment for Mobile Systems Through a Multilayered Hierarchical Bayesian Network.
Li, Shancang; Tryfonas, Theo; Russell, Gordon; Andriotis, Panagiotis
2016-08-01
Mobile systems are facing a number of application vulnerabilities that can be combined together and utilized to penetrate systems with devastating impact. When assessing the overall security of a mobile system, it is important to assess the security risks posed by each mobile applications (apps), thus gaining a stronger understanding of any vulnerabilities present. This paper aims at developing a three-layer framework that assesses the potential risks which apps introduce within the Android mobile systems. A Bayesian risk graphical model is proposed to evaluate risk propagation in a layered risk architecture. By integrating static analysis, dynamic analysis, and behavior analysis in a hierarchical framework, the risks and their propagation through each layer are well modeled by the Bayesian risk graph, which can quantitatively analyze risks faced to both apps and mobile systems. The proposed hierarchical Bayesian risk graph model offers a novel way to investigate the security risks in mobile environment and enables users and administrators to evaluate the potential risks. This strategy allows to strengthen both app security as well as the security of the entire system.
Sensitivity Analysis of Hierarchical Models for the Ages of Galactic Halo White Dwarfs
NASA Astrophysics Data System (ADS)
Si, S.; van Dyk, D. A.; von Hippel, T.
2017-03-01
The ages of white dwarfs are of great importance in stellar evolution. Si et al. developed a novel approach to increase the precision of such estimates by combining multiple white dwarfs in a Bayesian hierarchical model. In this paper, we further investigate the robustness of the Bayesian hierarchical model by performing a simulation study.
Hierarchical Bayesian inference for ion channel screening dose-response data
2016-01-01
Dose-response (or ‘concentration-effect’) relationships commonly occur in biological and pharmacological systems and are well characterised by Hill curves. These curves are described by an equation with two parameters: the inhibitory concentration 50% (IC50); and the Hill coefficient. Typically just the ‘best fit’ parameter values are reported in the literature. Here we introduce a Python-based software tool, PyHillFit, and describe the underlying Bayesian inference methods that it uses, to infer probability distributions for these parameters as well as the level of experimental observation noise. The tool also allows for hierarchical fitting, characterising the effect of inter-experiment variability. We demonstrate the use of the tool on a recently published dataset on multiple ion channel inhibition by multiple drug compounds. We compare the maximum likelihood, Bayesian and hierarchical Bayesian approaches. We then show how uncertainty in dose-response inputs can be characterised and propagated into a cardiac action potential simulation to give a probability distribution on model outputs. PMID:27918599
Hierarchical Bayesian inference for ion channel screening dose-response data.
Johnstone, Ross H; Bardenet, Rémi; Gavaghan, David J; Mirams, Gary R
2016-01-01
Dose-response (or 'concentration-effect') relationships commonly occur in biological and pharmacological systems and are well characterised by Hill curves. These curves are described by an equation with two parameters: the inhibitory concentration 50% (IC50); and the Hill coefficient. Typically just the 'best fit' parameter values are reported in the literature. Here we introduce a Python-based software tool, PyHillFit , and describe the underlying Bayesian inference methods that it uses, to infer probability distributions for these parameters as well as the level of experimental observation noise. The tool also allows for hierarchical fitting, characterising the effect of inter-experiment variability. We demonstrate the use of the tool on a recently published dataset on multiple ion channel inhibition by multiple drug compounds. We compare the maximum likelihood, Bayesian and hierarchical Bayesian approaches. We then show how uncertainty in dose-response inputs can be characterised and propagated into a cardiac action potential simulation to give a probability distribution on model outputs.
Shao, Kan; Allen, Bruce C; Wheeler, Matthew W
2016-12-29
Human variability is a very important factor considered in human health risk assessment for protecting sensitive populations from chemical exposure. Traditionally, to account for this variability, an interhuman uncertainty factor is applied to lower the exposure limit. However, using a fixed uncertainty factor rather than probabilistically accounting for human variability can hardly support probabilistic risk assessment advocated by a number of researchers; new methods are needed to probabilistically quantify human population variability. We propose a Bayesian hierarchical model to quantify variability among different populations. This approach jointly characterizes the distribution of risk at background exposure and the sensitivity of response to exposure, which are commonly represented by model parameters. We demonstrate, through both an application to real data and a simulation study, that using the proposed hierarchical structure adequately characterizes variability across different populations.
Determining the Bayesian optimal sampling strategy in a hierarchical system.
Grace, Matthew D.; Ringland, James T.; Boggs, Paul T.; Pebay, Philippe Pierre
2010-09-01
Consider a classic hierarchy tree as a basic model of a 'system-of-systems' network, where each node represents a component system (which may itself consist of a set of sub-systems). For this general composite system, we present a technique for computing the optimal testing strategy, which is based on Bayesian decision analysis. In previous work, we developed a Bayesian approach for computing the distribution of the reliability of a system-of-systems structure that uses test data and prior information. This allows for the determination of both an estimate of the reliability and a quantification of confidence in the estimate. Improving the accuracy of the reliability estimate and increasing the corresponding confidence require the collection of additional data. However, testing all possible sub-systems may not be cost-effective, feasible, or even necessary to achieve an improvement in the reliability estimate. To address this sampling issue, we formulate a Bayesian methodology that systematically determines the optimal sampling strategy under specified constraints and costs that will maximally improve the reliability estimate of the composite system, e.g., by reducing the variance of the reliability distribution. This methodology involves calculating the 'Bayes risk of a decision rule' for each available sampling strategy, where risk quantifies the relative effect that each sampling strategy could have on the reliability estimate. A general numerical algorithm is developed and tested using an example multicomponent system. The results show that the procedure scales linearly with the number of components available for testing.
Gu, Hairong; Kim, Woojae; Hou, Fang; Lesmes, Luis Andres; Pitt, Mark A.; Lu, Zhong-Lin; Myung, Jay I.
2016-01-01
Measurement efficiency is of concern when a large number of observations are required to obtain reliable estimates for parametric models of vision. The standard entropy-based Bayesian adaptive testing procedures addressed the issue by selecting the most informative stimulus in sequential experimental trials. Noninformative, diffuse priors were commonly used in those tests. Hierarchical adaptive design optimization (HADO; Kim, Pitt, Lu, Steyvers, & Myung, 2014) further improves the efficiency of the standard Bayesian adaptive testing procedures by constructing an informative prior using data from observers who have already participated in the experiment. The present study represents an empirical validation of HADO in estimating the human contrast sensitivity function. The results show that HADO significantly improves the accuracy and precision of parameter estimates, and therefore requires many fewer observations to obtain reliable inference about contrast sensitivity, compared to the method of quick contrast sensitivity function (Lesmes, Lu, Baek, & Albright, 2010), which uses the standard Bayesian procedure. The improvement with HADO was maintained even when the prior was constructed from heterogeneous populations or a relatively small number of observers. These results of this case study support the conclusion that HADO can be used in Bayesian adaptive testing by replacing noninformative, diffuse priors with statistically justified informative priors without introducing unwanted bias. PMID:27105061
Hierarchical models of animal abundance and occurrence
Royle, J. Andrew; Dorazio, R.M.
2006-01-01
Much of animal ecology is devoted to studies of abundance and occurrence of species, based on surveys of spatially referenced sample units. These surveys frequently yield sparse counts that are contaminated by imperfect detection, making direct inference about abundance or occurrence based on observational data infeasible. This article describes a flexible hierarchical modeling framework for estimation and inference about animal abundance and occurrence from survey data that are subject to imperfect detection. Within this framework, we specify models of abundance and detectability of animals at the level of the local populations defined by the sample units. Information at the level of the local population is aggregated by specifying models that describe variation in abundance and detection among sites. We describe likelihood-based and Bayesian methods for estimation and inference under the resulting hierarchical model. We provide two examples of the application of hierarchical models to animal survey data, the first based on removal counts of stream fish and the second based on avian quadrat counts. For both examples, we provide a Bayesian analysis of the models using the software WinBUGS.
A Coalescence-Guided Hierarchical Bayesian Method for Haplotype Inference
Zhang, Yu; Niu, Tianhua; Liu, Jun S.
2006-01-01
Haplotype inference from phase-ambiguous multilocus genotype data is an important task for both disease-gene mapping and studies of human evolution. We report a novel haplotype-inference method based on a coalescence-guided hierarchical Bayes model. In this model, a hierarchical structure is imposed on the prior haplotype frequency distributions to capture the similarities among modern-day haplotypes attributable to their common ancestry. As a consequence, the model both allows distinct haplotypes to have different a priori probabilities according to the inferred hierarchical ancestral structure and results in a proper joint posterior distribution for all the parameters of interest. A Markov chain–Monte Carlo scheme is designed to draw from this posterior distribution. By using coalescence-based simulation and empirically generated data sets (Whitehead Institute’s inflammatory bowel disease data sets and HapMap data sets), we demonstrate the merits of the new method in comparison with HAPLOTYPER and PHASE, with or without the presence of recombination hotspots and missing genotypes. PMID:16826521
Zhang, Lin; Baladandayuthapani, Veerabhadran; Mallick, Bani K; Manyam, Ganiraju C; Thompson, Patricia A; Bondy, Melissa L; Do, Kim-Anh
2014-08-01
The analysis of alterations that may occur in nature when segments of chromosomes are copied (known as copy number alterations) has been a focus of research to identify genetic markers of cancer. One high-throughput technique recently adopted is the use of molecular inversion probes (MIPs) to measure probe copy number changes. The resulting data consist of high-dimensional copy number profiles that can be used to ascertain probe-specific copy number alterations in correlative studies with patient outcomes to guide risk stratification and future treatment. We propose a novel Bayesian variable selection method, the hierarchical structured variable selection (HSVS) method, which accounts for the natural gene and probe-within-gene architecture to identify important genes and probes associated with clinically relevant outcomes. We propose the HSVS model for grouped variable selection, where simultaneous selection of both groups and within-group variables is of interest. The HSVS model utilizes a discrete mixture prior distribution for group selection and group-specific Bayesian lasso hierarchies for variable selection within groups. We provide methods for accounting for serial correlations within groups that incorporate Bayesian fused lasso methods for within-group selection. Through simulations we establish that our method results in lower model errors than other methods when a natural grouping structure exists. We apply our method to an MIP study of breast cancer and show that it identifies genes and probes that are significantly associated with clinically relevant subtypes of breast cancer.
Zhang, Lin; Baladandayuthapani, Veerabhadran; Mallick, Bani K.; Manyam, Ganiraju C.; Thompson, Patricia A.; Bondy, Melissa L.; Do, Kim-Anh
2015-01-01
Summary The analysis of alterations that may occur in nature when segments of chromosomes are copied (known as copy number alterations) has been a focus of research to identify genetic markers of cancer. One high-throughput technique recently adopted is the use of molecular inversion probes (MIPs) to measure probe copy number changes. The resulting data consist of high-dimensional copy number profiles that can be used to ascertain probe-specific copy number alterations in correlative studies with patient outcomes to guide risk stratification and future treatment. We propose a novel Bayesian variable selection method, the hierarchical structured variable selection (HSVS) method, which accounts for the natural gene and probe-within-gene architecture to identify important genes and probes associated with clinically relevant outcomes. We propose the HSVS model for grouped variable selection, where simultaneous selection of both groups and within-group variables is of interest. The HSVS model utilizes a discrete mixture prior distribution for group selection and group-specific Bayesian lasso hierarchies for variable selection within groups. We provide methods for accounting for serial correlations within groups that incorporate Bayesian fused lasso methods for within-group selection. Through simulations we establish that our method results in lower model errors than other methods when a natural grouping structure exists. We apply our method to an MIP study of breast cancer and show that it identifies genes and probes that are significantly associated with clinically relevant subtypes of breast cancer. PMID:25705056
A hierarchical Bayesian-MAP approach to inverse problems in imaging
NASA Astrophysics Data System (ADS)
Raj, Raghu G.
2016-07-01
We present a novel approach to inverse problems in imaging based on a hierarchical Bayesian-MAP (HB-MAP) formulation. In this paper we specifically focus on the difficult and basic inverse problem of multi-sensor (tomographic) imaging wherein the source object of interest is viewed from multiple directions by independent sensors. Given the measurements recorded by these sensors, the problem is to reconstruct the image (of the object) with a high degree of fidelity. We employ a probabilistic graphical modeling extension of the compound Gaussian distribution as a global image prior into a hierarchical Bayesian inference procedure. Since the prior employed by our HB-MAP algorithm is general enough to subsume a wide class of priors including those typically employed in compressive sensing (CS) algorithms, HB-MAP algorithm offers a vehicle to extend the capabilities of current CS algorithms to include truly global priors. After rigorously deriving the regression algorithm for solving our inverse problem from first principles, we demonstrate the performance of the HB-MAP algorithm on Monte Carlo trials and on real empirical data (natural scenes). In all cases we find that our algorithm outperforms previous approaches in the literature including filtered back-projection and a variety of state-of-the-art CS algorithms. We conclude with directions of future research emanating from this work.
Hierarchical Bayesian Logistic Regression to forecast metabolic control in type 2 DM patients.
Dagliati, Arianna; Malovini, Alberto; Decata, Pasquale; Cogni, Giulia; Teliti, Marsida; Sacchi, Lucia; Cerra, Carlo; Chiovato, Luca; Bellazzi, Riccardo
2016-01-01
In this work we present our efforts in building a model able to forecast patients' changes in clinical conditions when repeated measurements are available. In this case the available risk calculators are typically not applicable. We propose a Hierarchical Bayesian Logistic Regression model, which allows taking into account individual and population variability in model parameters estimate. The model is used to predict metabolic control and its variation in type 2 diabetes mellitus. In particular we have analyzed a population of more than 1000 Italian type 2 diabetic patients, collected within the European project Mosaic. The results obtained in terms of Matthews Correlation Coefficient are significantly better than the ones gathered with standard logistic regression model, based on data pooling.
Hierarchical Bayesian Logistic Regression to forecast metabolic control in type 2 DM patients
Dagliati, Arianna; Malovini, Alberto; Decata, Pasquale; Cogni, Giulia; Teliti, Marsida; Sacchi, Lucia; Cerra, Carlo; Chiovato, Luca; Bellazzi, Riccardo
2016-01-01
In this work we present our efforts in building a model able to forecast patients’ changes in clinical conditions when repeated measurements are available. In this case the available risk calculators are typically not applicable. We propose a Hierarchical Bayesian Logistic Regression model, which allows taking into account individual and population variability in model parameters estimate. The model is used to predict metabolic control and its variation in type 2 diabetes mellitus. In particular we have analyzed a population of more than 1000 Italian type 2 diabetic patients, collected within the European project Mosaic. The results obtained in terms of Matthews Correlation Coefficient are significantly better than the ones gathered with standard logistic regression model, based on data pooling. PMID:28269842
Joint Lung CT Image Segmentation: A Hierarchical Bayesian Approach
Cheng, Wenjun; Ma, Luyao; Yang, Tiejun; Liang, Jiali
2016-01-01
Accurate lung CT image segmentation is of great clinical value, especially when it comes to delineate pathological regions including lung tumor. In this paper, we present a novel framework that jointly segments multiple lung computed tomography (CT) images via hierarchical Dirichlet process (HDP). In specifics, based on the assumption that lung CT images from different patients share similar image structure (organ sets and relative positioning), we derive a mathematical model to segment them simultaneously so that shared information across patients could be utilized to regularize each individual segmentation. Moreover, compared to many conventional models, the algorithm requires little manual involvement due to the nonparametric nature of Dirichlet process (DP). We validated proposed model upon clinical data consisting of healthy and abnormal (lung cancer) patients. We demonstrate that, because of the joint segmentation fashion, more accurate and consistent segmentations could be obtained. PMID:27611188
A Hierarchical Bayesian Approach to Ecological Count Data: A Flexible Tool for Ecologists
Fordyce, James A.; Gompert, Zachariah; Forister, Matthew L.; Nice, Chris C.
2011-01-01
Many ecological studies use the analysis of count data to arrive at biologically meaningful inferences. Here, we introduce a hierarchical Bayesian approach to count data. This approach has the advantage over traditional approaches in that it directly estimates the parameters of interest at both the individual-level and population-level, appropriately models uncertainty, and allows for comparisons among models, including those that exceed the complexity of many traditional approaches, such as ANOVA or non-parametric analogs. As an example, we apply this method to oviposition preference data for butterflies in the genus Lycaeides. Using this method, we estimate the parameters that describe preference for each population, compare the preference hierarchies among populations, and explore various models that group populations that share the same preference hierarchy. PMID:22132077
Wu, Wei; Chen, Zhe; Gao, Shangkai; Brown, Emery N.
2011-01-01
Multichannel electroencephalography (EEG) offers a non-invasive tool to explore spatio-temporal dynamics of brain activity. With EEG recordings consisting of multiple trials, traditional signal processing approaches that ignore inter-trial variability in the data may fail to accurately estimate the underlying spatio-temporal brain patterns. Moreover, precise characterization of such inter-trial variability per se can be of high scientific value in establishing the relationship between brain activity and behavior. In this paper, a statistical modeling framework is introduced for learning spatiotemporal decomposition of multiple-trial EEG data recorded under two contrasting experimental conditions. By modeling the variance of source signals as random variables varying across trials, the proposed two-stage hierarchical Bayesian model is able to capture inter-trial amplitude variability in the data in a sparse way where a parsimonious representation of the data can be obtained. A variational Bayesian (VB) algorithm is developed for statistical inference of the hierarchical model. The efficacy of the proposed modeling framework is validated with the analysis of both synthetic and real EEG data. In the simulation study we show that even at low signal-to-noise ratios our approach is able to recover with high precision the underlying spatiotemporal patterns and the evolution of source amplitude across trials; on two brain-computer interface (BCI) data sets we show that our VB algorithm can extract physiologically meaningful spatio-temporal patterns and make more accurate predictions than other two widely used algorithms: the common spatial patterns (CSP) algorithm and the Infomax algorithm for independent component analysis (ICA). The results demonstrate that our statistical modeling framework can serve as a powerful tool for extracting brain patterns, characterizing trial-to-trial brain dynamics, and decoding brain states by exploiting useful structures in the data. PMID
Back to basics for Bayesian model building in genomic selection.
Kärkkäinen, Hanni P; Sillanpää, Mikko J
2012-07-01
Numerous Bayesian methods of phenotype prediction and genomic breeding value estimation based on multilocus association models have been proposed. Computationally the methods have been based either on Markov chain Monte Carlo or on faster maximum a posteriori estimation. The demand for more accurate and more efficient estimation has led to the rapid emergence of workable methods, unfortunately at the expense of well-defined principles for Bayesian model building. In this article we go back to the basics and build a Bayesian multilocus association model for quantitative and binary traits with carefully defined hierarchical parameterization of Student's t and Laplace priors. In this treatment we consider alternative model structures, using indicator variables and polygenic terms. We make the most of the conjugate analysis, enabled by the hierarchical formulation of the prior densities, by deriving the fully conditional posterior densities of the parameters and using the acquired known distributions in building fast generalized expectation-maximization estimation algorithms.
NASA Astrophysics Data System (ADS)
Devineni, N.; Lall, U.; Cook, E.; Pederson, N.
2011-12-01
We present the application of a linear model in a Hierarchical Bayesian Regression (HBR) framework for reconstructing the summer seasonal averaged streamflow at five stations in the Delaware River Basin using eight newly developed regional tree ring chronologies. This technique directly provides estimates of the posterior probability distribution of each reconstructed streamflow value, considering model parameter uncertainty. The methodology also allows us to shrink the model parameters towards a common mean to incorporate the predictive ability of each tree chronology on multiple stations. We present the results from HBR analysis along with the results from traditional Point by Point Regression (PPR) analysis to demonstrate the benefits of developing the reconstructions under a Bayesian modeling framework. Further, we also present the comparative results of the model validation using various performance evaluation metrics such as reduction in error (RE) and coefficient of efficiency (CE). The reconstructed streamflow at various stations can be utilized to examine the frequency and recurrence attributes of extreme droughts in the region and their potential connections to known low frequency climate modes.
NASA Astrophysics Data System (ADS)
Dries, M.; Trager, S. C.; Koopmans, L. V. E.
2016-11-01
Recent studies based on the integrated light of distant galaxies suggest that the initial mass function (IMF) might not be universal. Variations of the IMF with galaxy type and/or formation time may have important consequences for our understanding of galaxy evolution. We have developed a new stellar population synthesis (SPS) code specifically designed to reconstruct the IMF. We implement a novel approach combining regularization with hierarchical Bayesian inference. Within this approach, we use a parametrized IMF prior to regulate a direct inference of the IMF. This direct inference gives more freedom to the IMF and allows the model to deviate from parametrized models when demanded by the data. We use Markov chain Monte Carlo sampling techniques to reconstruct the best parameters for the IMF prior, the age and the metallicity of a single stellar population. We present our code and apply our model to a number of mock single stellar populations with different ages, metallicities and IMFs. When systematic uncertainties are not significant, we are able to reconstruct the input parameters that were used to create the mock populations. Our results show that if systematic uncertainties do play a role, this may introduce a bias on the results. Therefore, it is important to objectively compare different ingredients of SPS models. Through its Bayesian framework, our model is well suited for this.
Bayesian Model Selection for Group Studies
Stephan, Klaas Enno; Penny, Will D.; Daunizeau, Jean; Moran, Rosalyn J.; Friston, Karl J.
2009-01-01
Bayesian model selection (BMS) is a powerful method for determining the most likely among a set of competing hypotheses about the mechanisms that generated observed data. BMS has recently found widespread application in neuroimaging, particularly in the context of dynamic causal modelling (DCM). However, so far, combining BMS results from several subjects has relied on simple (fixed effects) metrics, e.g. the group Bayes factor (GBF), that do not account for group heterogeneity or outliers. In this paper, we compare the GBF with two random effects methods for BMS at the between-subject or group level. These methods provide inference on model-space using a classical and Bayesian perspective respectively. First, a classical (frequentist) approach uses the log model evidence as a subject-specific summary statistic. This enables one to use analysis of variance to test for differences in log-evidences over models, relative to inter-subject differences. We then consider the same problem in Bayesian terms and describe a novel hierarchical model, which is optimised to furnish a probability density on the models themselves. This new variational Bayes method rests on treating the model as a random variable and estimating the parameters of a Dirichlet distribution which describes the probabilities for all models considered. These probabilities then define a multinomial distribution over model space, allowing one to compute how likely it is that a specific model generated the data of a randomly chosen subject as well as the exceedance probability of one model being more likely than any other model. Using empirical and synthetic data, we show that optimising a conditional density of the model probabilities, given the log-evidences for each model over subjects, is more informative and appropriate than both the GBF and frequentist tests of the log-evidences. In particular, we found that the hierarchical Bayesian approach is considerably more robust than either of the other
Type Ia Supernova Light-Curve Inference: Hierarchical Bayesian Analysis in the Near-Infrared
NASA Astrophysics Data System (ADS)
Mandel, Kaisey S.; Wood-Vasey, W. Michael; Friedman, Andrew S.; Kirshner, Robert P.
2009-10-01
We present a comprehensive statistical analysis of the properties of Type Ia supernova (SN Ia) light curves in the near-infrared using recent data from Peters Automated InfraRed Imaging TELescope and the literature. We construct a hierarchical Bayesian framework, incorporating several uncertainties including photometric error, peculiar velocities, dust extinction, and intrinsic variations, for principled and coherent statistical inference. SN Ia light-curve inferences are drawn from the global posterior probability of parameters describing both individual supernovae and the population conditioned on the entire SN Ia NIR data set. The logical structure of the hierarchical model is represented by a directed acyclic graph. Fully Bayesian analysis of the model and data is enabled by an efficient Markov Chain Monte Carlo algorithm exploiting the conditional probabilistic structure using Gibbs sampling. We apply this framework to the JHKs SN Ia light-curve data. A new light-curve model captures the observed J-band light-curve shape variations. The marginal intrinsic variances in peak absolute magnitudes are σ(MJ ) = 0.17 ± 0.03, σ(MH ) = 0.11 ± 0.03, and σ(MKs ) = 0.19 ± 0.04. We describe the first quantitative evidence for correlations between the NIR absolute magnitudes and J-band light-curve shapes, and demonstrate their utility for distance estimation. The average residual in the Hubble diagram for the training set SNe at cz > 2000kms-1 is 0.10 mag. The new application of bootstrap cross-validation to SN Ia light-curve inference tests the sensitivity of the statistical model fit to the finite sample and estimates the prediction error at 0.15 mag. These results demonstrate that SN Ia NIR light curves are as effective as corrected optical light curves, and, because they are less vulnerable to dust absorption, they have great potential as precise and accurate cosmological distance indicators.
He, Ji X.; Bence, James R.; Roseman, Edward F.; Fielder, David G.; Ebener, Mark P.
2015-01-01
We evaluated the ecosystem regime shift in the main basin of Lake Huron that was indicated by the 2003 collapse of alewives, and dramatic declines in Chinook salmon abundance thereafter. We found that the period of 1995-2002 should be considered as the early phase of the final regime shift. We developed two Bayesian hierarchical models to describe time-varying growth based on the von Bertalanffy growth function and the length-mass relationship. We used asymptotic length as an index of growth potential, and predicted body mass at a given length as an index of body condition. Modeling fits to length and body mass at age of lake trout, Chinook salmon, and walleye were excellent. Based on posterior distributions, we evaluated the shifts in among-year geometric means of the growth potential and body condition. For a given top piscivore, one of the two indices responded to the regime shift much earlier than the 2003 collapse of alewives, the other corresponded to the 2003 changes, and which index provided the early signal differed among the three top piscivores.
NASA Astrophysics Data System (ADS)
Feeney, Stephen M.; Johnson, Matthew C.; McEwen, Jason D.; Mortlock, Daniel J.; Peiris, Hiranya V.
2013-08-01
A number of theoretically well-motivated additions to the standard cosmological model predict weak signatures in the form of spatially localized sources embedded in the cosmic microwave background (CMB) fluctuations. We present a hierarchical Bayesian statistical formalism and a complete data analysis pipeline for testing such scenarios. We derive an accurate approximation to the full posterior probability distribution over the parameters defining any theory that predicts sources embedded in the CMB, and perform an extensive set of tests in order to establish its validity. The approximation is implemented using a modular algorithm, designed to avoid a posteriori selection effects, which combines a candidate-detection stage with a full Bayesian model-selection and parameter-estimation analysis. We apply this pipeline to theories that predict cosmic textures and bubble collisions, extending previous analyses by using: (1) adaptive-resolution techniques, allowing us to probe features of arbitrary size, and (2) optimal filters, which provide the best possible sensitivity for detecting candidate signatures. We conclude that the WMAP 7-year data do not favor the addition of either cosmic textures or bubble collisions to ΛCDM, and place robust constraints on the predicted number of such sources. The expected numbers of bubble collisions and cosmic textures on the CMB sky within our detection thresholds are constrained to be fewer than 4.0 and 5.2 at 95% confidence, respectively.
What are hierarchical models and how do we analyze them?
Royle, Andy
2016-01-01
In this chapter we provide a basic definition of hierarchical models and introduce the two canonical hierarchical models in this book: site occupancy and N-mixture models. The former is a hierarchical extension of logistic regression and the latter is a hierarchical extension of Poisson regression. We introduce basic concepts of probability modeling and statistical inference including likelihood and Bayesian perspectives. We go through the mechanics of maximizing the likelihood and characterizing the posterior distribution by Markov chain Monte Carlo (MCMC) methods. We give a general perspective on topics such as model selection and assessment of model fit, although we demonstrate these topics in practice in later chapters (especially Chapters 5, 6, 7, and 10 Chapter 5 Chapter 6 Chapter 7 Chapter 10)
A Hierarchical Bayesian Procedure for Two-Mode Cluster Analysis
ERIC Educational Resources Information Center
DeSarbo, Wayne S.; Fong, Duncan K. H.; Liechty, John; Saxton, M. Kim
2004-01-01
This manuscript introduces a new Bayesian finite mixture methodology for the joint clustering of row and column stimuli/objects associated with two-mode asymmetric proximity, dominance, or profile data. That is, common clusters are derived which partition both the row and column stimuli/objects simultaneously into the same derived set of clusters.…
Busschaert, P; Geeraerd, A H; Uyttendaele, M; Van Impe, J F
2011-06-01
Microbiological contamination data often is censored because of the presence of non-detects or because measurement outcomes are known only to be smaller than, greater than, or between certain boundary values imposed by the laboratory procedures. Therefore, it is not straightforward to fit distributions that summarize contamination data for use in quantitative microbiological risk assessment, especially when variability and uncertainty are to be characterized separately. In this paper, distributions are fit using Bayesian analysis, and results are compared to results obtained with a methodology based on maximum likelihood estimation and the non-parametric bootstrap method. The Bayesian model is also extended hierarchically to estimate the effects of the individual elements of a covariate such as, for example, on a national level, the food processing company where the analyzed food samples were processed, or, on an international level, the geographical origin of contamination data. Including this extra information allows a risk assessor to differentiate between several scenario's and increase the specificity of the estimate of risk of illness, or compare different scenario's to each other. Furthermore, inference is made on the predictive importance of several different covariates while taking into account uncertainty, allowing to indicate which covariates are influential factors determining contamination.
Leaché, Adam D; Crews, Sarah C; Hickerson, Michael J
2007-12-22
Many species inhabiting the Peninsular Desert of Baja California demonstrate a phylogeographic break at the mid-peninsula, and previous researchers have attributed this shared pattern to a single vicariant event, a mid-peninsular seaway. However, previous studies have not explicitly considered the inherent stochasticity associated with the gene-tree coalescence for species preceding the time of the putative mid-peninsular divergence. We use a Bayesian analysis of a hierarchical model to test for simultaneous vicariance across co-distributed sister lineages sharing a genealogical break at the mid-peninsula. This Bayesian method is advantageous over traditional phylogenetic interpretations of biogeography because it considers the genetic variance associated with the coalescent and mutational processes, as well as the among-lineage demographic differences that affect gene-tree coalescent patterns. Mitochondrial DNA data from six small mammals and six squamate reptiles do not support the perception of a shared vicariant history among lineages exhibiting a north-south divergence at the mid-peninsula, and instead support two events differentially structuring genetic diversity in this region.
Bayesian Model Averaging for Propensity Score Analysis
ERIC Educational Resources Information Center
Kaplan, David; Chen, Jianshen
2013-01-01
The purpose of this study is to explore Bayesian model averaging in the propensity score context. Previous research on Bayesian propensity score analysis does not take into account model uncertainty. In this regard, an internally consistent Bayesian framework for model building and estimation must also account for model uncertainty. The…
Hierarchical Bayesian analysis of the velocity power spectrum in supersonic turbulence
NASA Astrophysics Data System (ADS)
Konstandin, L.; Shetty, R.; Girichidis, P.; Klessen, R. S.
2015-01-01
Turbulence is a dominant feature operating in gaseous flows across nearly all scales in astrophysical environments. Accordingly, accurately estimating the statistical properties of such flows is necessary for developing a comprehensive understanding of turbulence. We develop and employ a hierarchical Bayesian fitting method to estimate the parameters describing the scaling relationships of the velocity power spectra of supersonic turbulence. We demonstrate the accuracy and other advantages of this technique compared with ordinary linear regression methods. Using synthetic power spectra, we show that the Bayesian method provides accurate parameter and error estimates. Commonly used normal linear regression methods can provide estimates that fail to recover the underlying slopes, up to 70 per cent of the instances, even when considering the 2σ uncertainties. Additionally, we apply the Bayesian methods to analyse the statistical properties of compressible turbulence in three-dimensional numerical simulations. We model driven, isothermal, turbulence with root-mean-square Mach numbers in the highly supersonic regime {M}≈ 15. We study the influence of purely solenoidal (divergence-free) and purely compressive (curl-free) forcing on the scaling exponent of the power spectrum. In simulations with solenoidal forcing and 10243 resolution, our results indicate that there is no extended inertial range with a constant scaling exponent. The bottleneck effect results in a curved power spectrum at all wave numbers and is more pronounced in the transversal modes compared with the longitudinal modes. Therefore, this effect is stronger in stationary turbulent flows driven by solenoidal forcing compared to the compressive one. The longitudinal spectrum driven with compressive forcing is the only spectrum with constant scaling exponent ζ = -1.94 ± 0.01, corresponding to slightly shallower slopes than the Burger prediction.
Bayesian Inference for Nonnegative Matrix Factorisation Models
Cemgil, Ali Taylan
2009-01-01
We describe nonnegative matrix factorisation (NMF) with a Kullback-Leibler (KL) error measure in a statistical framework, with a hierarchical generative model consisting of an observation and a prior component. Omitting the prior leads to the standard KL-NMF algorithms as special cases, where maximum likelihood parameter estimation is carried out via the Expectation-Maximisation (EM) algorithm. Starting from this view, we develop full Bayesian inference via variational Bayes or Monte Carlo. Our construction retains conjugacy and enables us to develop more powerful models while retaining attractive features of standard NMF such as monotonic convergence and easy implementation. We illustrate our approach on model order selection and image reconstruction. PMID:19536273
Bayesian stable isotope mixing models
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 methods for estimating the reliability in complex hierarchical networks (interim report).
Marzouk, Youssef M.; Zurn, Rena M.; Boggs, Paul T.; Diegert, Kathleen V.; Red-Horse, John Robert; Pebay, Philippe Pierre
2007-05-01
Current work on the Integrated Stockpile Evaluation (ISE) project is evidence of Sandia's commitment to maintaining the integrity of the nuclear weapons stockpile. In this report, we undertake a key element in that process: development of an analytical framework for determining the reliability of the stockpile in a realistic environment of time-variance, inherent uncertainty, and sparse available information. This framework is probabilistic in nature and is founded on a novel combination of classical and computational Bayesian analysis, Bayesian networks, and polynomial chaos expansions. We note that, while the focus of the effort is stockpile-related, it is applicable to any reasonably-structured hierarchical system, including systems with feedback.
Bridging Inter- and Intraspecific Trait Evolution with a Hierarchical Bayesian Approach.
Kostikova, Anna; Silvestro, Daniele; Pearman, Peter B; Salamin, Nicolas
2016-05-01
The evolution of organisms is crucially dependent on the evolution of intraspecific variation. Its interactions with selective agents in the biotic and abiotic environments underlie many processes, such as intraspecific competition, resource partitioning and, eventually, species formation. Nevertheless, comparative models of trait evolution neither allow explicit testing of hypotheses related to the evolution of intraspecific variation nor do they simultaneously estimate rates of trait evolution by accounting for both trait mean and variance. Here, we present a model of phenotypic trait evolution using a hierarchical Bayesian approach that simultaneously incorporates interspecific and intraspecific variation. We assume that species-specific trait means evolve under a simple Brownian motion process, whereas species-specific trait variances are modeled with Brownian or Ornstein-Uhlenbeck processes. After evaluating the power of the method through simulations, we examine whether life-history traits impact evolution of intraspecific variation in the Eriogonoideae (buckwheat family, Polygonaceae). Our model is readily extendible to more complex scenarios of the evolution of inter- and intraspecific variation and presents a step toward more comprehensive comparative models for macroevolutionary studies.
Composite behavior analysis for video surveillance using hierarchical dynamic Bayesian networks
NASA Astrophysics Data System (ADS)
Cheng, Huanhuan; Shan, Yong; Wang, Runsheng
2011-03-01
Analyzing composite behaviors involving objects from multiple categories in surveillance videos is a challenging task due to the complicated relationships among human and objects. This paper presents a novel behavior analysis framework using a hierarchical dynamic Bayesian network (DBN) for video surveillance systems. The model is built for extracting objects' behaviors and their relationships by representing behaviors using spatial-temporal characteristics. The recognition of object behaviors is processed by the DBN at multiple levels: features of objects at low level, objects and their relationships at middle level, and event at high level, where event refers to behaviors of a single type object as well as behaviors consisting of several types of objects such as ``a person getting in a car.'' Furthermore, to reduce the complexity, a simple model selection criterion is addressed, by which the appropriated model is picked out from a pool of candidate models. Experiments are shown to demonstrate that the proposed framework could efficiently recognize and semantically describe composite object and human activities in surveillance videos.
Bayesian Model Averaging for Propensity Score Analysis.
Kaplan, David; Chen, Jianshen
2014-01-01
This article considers Bayesian model averaging as a means of addressing uncertainty in the selection of variables in the propensity score equation. We investigate an approximate Bayesian model averaging approach based on the model-averaged propensity score estimates produced by the R package BMA but that ignores uncertainty in the propensity score. We also provide a fully Bayesian model averaging approach via Markov chain Monte Carlo sampling (MCMC) to account for uncertainty in both parameters and models. A detailed study of our approach examines the differences in the causal estimate when incorporating noninformative versus informative priors in the model averaging stage. We examine these approaches under common methods of propensity score implementation. In addition, we evaluate the impact of changing the size of Occam's window used to narrow down the range of possible models. We also assess the predictive performance of both Bayesian model averaging propensity score approaches and compare it with the case without Bayesian model averaging. Overall, results show that both Bayesian model averaging propensity score approaches recover the treatment effect estimates well and generally provide larger uncertainty estimates, as expected. Both Bayesian model averaging approaches offer slightly better prediction of the propensity score compared with the Bayesian approach with a single propensity score equation. Covariate balance checks for the case study show that both Bayesian model averaging approaches offer good balance. The fully Bayesian model averaging approach also provides posterior probability intervals of the balance indices.
A method of spherical harmonic analysis in the geosciences via hierarchical Bayesian inference
NASA Astrophysics Data System (ADS)
Muir, J. B.; Tkalčić, H.
2015-11-01
The problem of decomposing irregular data on the sphere into a set of spherical harmonics is common in many fields of geosciences where it is necessary to build a quantitative understanding of a globally varying field. For example, in global seismology, a compressional or shear wave speed that emerges from tomographic images is used to interpret current state and composition of the mantle, and in geomagnetism, secular variation of magnetic field intensity measured at the surface is studied to better understand the changes in the Earth's core. Optimization methods are widely used for spherical harmonic analysis of irregular data, but they typically do not treat the dependence of the uncertainty estimates on the imposed regularization. This can cause significant difficulties in interpretation, especially when the best-fit model requires more variables as a result of underestimating data noise. Here, with the above limitations in mind, the problem of spherical harmonic expansion of irregular data is treated within the hierarchical Bayesian framework. The hierarchical approach significantly simplifies the problem by removing the need for regularization terms and user-supplied noise estimates. The use of the corrected Akaike Information Criterion for picking the optimal maximum degree of spherical harmonic expansion and the resulting spherical harmonic analyses are first illustrated on a noisy synthetic data set. Subsequently, the method is applied to two global data sets sensitive to the Earth's inner core and lowermost mantle, consisting of PKPab-df and PcP-P differential traveltime residuals relative to a spherically symmetric Earth model. The posterior probability distributions for each spherical harmonic coefficient are calculated via Markov Chain Monte Carlo sampling; the uncertainty obtained for the coefficients thus reflects the noise present in the real data and the imperfections in the spherical harmonic expansion.
NASA Astrophysics Data System (ADS)
Tashiro, Tohru
2014-03-01
We propose a new model about diffusion of a product which includes a memory of how many adopters or advertisements a non-adopter met, where (non-)adopters mean people (not) possessing the product. This effect is lacking in the Bass model. As an application, we utilize the model to fit the iPod sales data, and so the better agreement is obtained than the Bass model.
Wilson, Chris H; Caughlin, T Trevor; Civitello, David J; Flory, S Luke
2015-04-01
Invasive plant fecundity underlies propagule pressure and ultimately range expansion. Predicting fecundity across large spatial scales, from regions to landscapes, is critical for understanding invasion dynamics and optimizing management. However, to accurately predict fecundity and other demographic processes, improved models that scale individual plant responses to abiotic drivers across heterogeneous environments are needed. Here we combine two experimental data sets to predict fecundity of a widespread and problematic invasive grass over large spatial scales. First, we analyzed seed production as a function of plant biomass in a small-scale mesocosm experiment with manipulated light levels. Then, in a field introduction experiment, we tracked plant performance across 21 common garden sites that differed widely in available light and other factors. We jointly analyzed these data using a Bayesian hierarchical model (BHM) framework to predict fecundity as a function of light in the field. Our analysis reveals that the invasive species is likely to produce sufficient seed to overwhelm establishment resistance, even in deeply shaded environments, and is likely seed-limited across much of its range. Finally, we extend this framework to address the general problem of how to scale up plant demographic processes and analyze the factors that control plant distribution and abundance at large scales.
Baladandayuthapani, Veerabhadran; Mallick, Bani K.; Hong, Mee Young; Lupton, Joanne R.; Turner, Nancy D.; Carroll, Raymond J.
2009-01-01
Summary In this article, we present new methods to analyze data from an experiment using rodent models to investigate the role of p27, an important cell-cycle mediator, in early colon carcinogenesis. The responses modeled here are essentially functions nested within a two-stage hierarchy. Standard functional data analysis literature focuses on a single stage of hierarchy and conditionally independent functions with near white noise. However, in our experiment, there is substantial biological motivation for the existence of spatial correlation among the functions, which arise from the locations of biological structures called colonic crypts: this possible functional correlation is a phenomenon we term crypt signaling. Thus, as a point of general methodology, we require an analysis that allows for functions to be correlated at the deepest level of the hierarchy. Our approach is fully Bayesian and uses Markov chain Monte Carlo methods for inference and estimation. Analysis of this data set gives new insights into the structure of p27 expression in early colon carcinogenesis and suggests the existence of significant crypt signaling. Our methodology uses regression splines, and because of the hierarchical nature of the data, dimension reduction of the covariance matrix of the spline coefficients is important: we suggest simple methods for overcoming this problem. PMID:17608780
Bayesian Networks for Social Modeling
Whitney, Paul D.; White, Amanda M.; Walsh, Stephen J.; Dalton, Angela C.; Brothers, Alan J.
2011-03-28
This paper describes a body of work developed over the past five years. The work addresses the use of Bayesian network (BN) models for representing and predicting social/organizational behaviors. The topics covered include model construction, validation, and use. These topics show the bulk of the lifetime of such model, beginning with construction, moving to validation and other aspects of model ‘critiquing’, and finally demonstrating how the modeling approach might be used to inform policy analysis. To conclude, we discuss limitations of using BN for this activity and suggest remedies to address those limitations. The primary benefits of using a well-developed computational, mathematical, and statistical modeling structure, such as BN, are 1) there are significant computational, theoretical and capability bases on which to build 2) ability to empirically critique the model, and potentially evaluate competing models for a social/behavioral phenomena.
Hierarchical Molecular Modelling with Ellipsoids
Max, N
2004-03-29
Protein and DNA structures are represented at varying levels of details using ellipsoidal RGBA textured splats. The splat texture at each level is generated by rendering its children in a hierarchical model, from a distribution of viewing directions, and averaging the result. For rendering, the ellipsoids to be used are chosen adaptively, depending on the distance to the viewpoint. This technique is applied to visualize DNA coiling around nucleosomes in chromosomes.
Reasons for Hierarchical Linear Modeling: A Reminder.
ERIC Educational Resources Information Center
Wang, Jianjun
1999-01-01
Uses examples of hierarchical linear modeling (HLM) at local and national levels to illustrate proper applications of HLM and dummy variable regression. Raises cautions about the circumstances under which hierarchical data do not need HLM. (SLD)
NASA Astrophysics Data System (ADS)
Jomelli, Vincent; Pavlova, Irina; Eckert, Nicolas; Grancher, Delphine; Brunstein, Daniel
2015-12-01
How can debris flow occurrences be modelled at regional scale and take both environmental and climatic conditions into account? And, of the two, which has the most influence on debris flow activity? In this paper, we try to answer these questions with an innovative Bayesian hierarchical probabilistic model that simultaneously accounts for how debris flows respond to environmental and climatic variables. In it, full decomposition of space and time effects in occurrence probabilities is assumed, revealing an environmental and a climatic trend shared by all years/catchments, respectively, clearly distinguished from residual "random" effects. The resulting regional and annual occurrence probabilities evaluated as functions of the covariates make it possible to weight the respective contribution of the different terms and, more generally, to check the model performances at different spatio-temporal scales. After suitable validation, the model can be used to make predictions at undocumented sites and could be used in further studies for predictions under future climate conditions. Also, the Bayesian paradigm easily copes with missing data, thus making it possible to account for events that may have been missed during surveys. As a case study, we extract 124 debris flow event triggered between 1970 and 2005 in 27 catchments located in the French Alps from the French national natural hazard survey and model their variability of occurrence considering environmental and climatic predictors at the same time. We document the environmental characteristics of each debris flow catchment (morphometry, lithology, land cover, and the presence of permafrost). We also compute 15 climate variables including mean temperature and precipitation between May and October and the number of rainy days with daily cumulative rainfall greater than 10/15/20/25/30/40 mm day- 1. Application of our model shows that the combination of environmental and climatic predictors explained 77% of the overall
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…
Bayesian model updating using incomplete modal data without mode matching
NASA Astrophysics Data System (ADS)
Sun, Hao; Büyüköztürk, Oral
2016-04-01
This study investigates a new probabilistic strategy for model updating using incomplete modal data. A hierarchical Bayesian inference is employed to model the updating problem. A Markov chain Monte Carlo technique with adaptive random-work steps is used to draw parameter samples for uncertainty quantification. Mode matching between measured and predicted modal quantities is not required through model reduction. We employ an iterated improved reduced system technique for model reduction. The reduced model retains the dynamic features as close as possible to those of the model before reduction. The proposed algorithm is finally validated by an experimental example.
Bayesian Models of Individual Differences
Powell, Georgie; Meredith, Zoe; McMillin, Rebecca; Freeman, Tom C. A.
2016-01-01
According to Bayesian models, perception and cognition depend on the optimal combination of noisy incoming evidence with prior knowledge of the world. Individual differences in perception should therefore be jointly determined by a person’s sensitivity to incoming evidence and his or her prior expectations. It has been proposed that individuals with autism have flatter prior distributions than do nonautistic individuals, which suggests that prior variance is linked to the degree of autistic traits in the general population. We tested this idea by studying how perceived speed changes during pursuit eye movement and at low contrast. We found that individual differences in these two motion phenomena were predicted by differences in thresholds and autistic traits when combined in a quantitative Bayesian model. Our findings therefore support the flatter-prior hypothesis and suggest that individual differences in prior expectations are more systematic than previously thought. In order to be revealed, however, individual differences in sensitivity must also be taken into account. PMID:27770059
Weber, Stephanie A; Insaf, Tabassum Z; Hall, Eric S; Talbot, Thomas O; Huff, Amy K
2016-11-01
An enhanced research paradigm is presented to address the spatial and temporal gaps in fine particulate matter (PM2.5) measurements and generate realistic and representative concentration fields for use in epidemiological studies of human exposure to ambient air particulate concentrations. The general approach for research designed to analyze health impacts of exposure to PM2.5 is to use concentration data from the nearest ground-based air quality monitor(s), which typically have missing data on the temporal and spatial scales due to filter sampling schedules and monitor placement, respectively. To circumvent these data gaps, this research project uses a Hierarchical Bayesian Model (HBM) to generate estimates of PM2.5 in areas with and without air quality monitors by combining PM2.5 concentrations measured by monitors, PM2.5 concentration estimates derived from satellite aerosol optical depth (AOD) data, and Community-Multiscale Air Quality (CMAQ) model predictions of PM2.5 concentrations. This methodology represents a substantial step forward in the approach for developing representative PM2.5 concentration datasets to correlate with inpatient hospitalizations and emergency room visits data for asthma and inpatient hospitalizations for myocardial infarction (MI) and heart failure (HF) using case-crossover analysis. There were two key objective of this current study. First was to show that the inputs to the HBM could be expanded to include AOD data in addition to data from PM2.5 monitors and predictions from CMAQ. The second objective was to determine if inclusion of AOD surfaces in HBM model algorithms results in PM2.5 air pollutant concentration surfaces which more accurately predict hospital admittance and emergency room visits for MI, asthma, and HF. This study focuses on the New York City, NY metropolitan and surrounding areas during the 2004-2006 time period, in order to compare the health outcome impacts with those from previous studies and focus on any
ESTIMATION OF FAILURE RATES OF DIGITAL COMPONENTS USING A HIERARCHICAL BAYESIAN METHOD.
YUE, M.; CHU, T.L.
2006-01-30
One of the greatest challenges in evaluating reliability of digital I&C systems is how to obtain better failure rate estimates of digital components. A common practice of the digital component failure rate estimation is attempting to use empirical formulae to capture the impacts of various factors on the failure rates. The applicability of an empirical formula is questionable because it is not based on laws of physics and requires good data, which is scarce in general. In this study, the concept of population variability of the Hierarchical Bayesian Method (HBM) is applied to estimating the failure rate of a digital component using available data. Markov Chain Monte Carlo (MCMC) simulation is used to implement the HBM. Results are analyzed and compared by selecting different distribution types and priors distributions. Inspired by the sensitivity calculations and based on review of analytic derivations, it seems reasonable to suggest avoiding the use of gamma distribution in two-stage Bayesian analysis and HBM analysis.
NASA Astrophysics Data System (ADS)
Alsing, Justin; Heavens, Alan; Jaffe, Andrew H.
2017-04-01
We apply two Bayesian hierarchical inference schemes to infer shear power spectra, shear maps and cosmological parameters from the Canada-France-Hawaii Telescope (CFHTLenS) weak lensing survey - the first application of this method to data. In the first approach, we sample the joint posterior distribution of the shear maps and power spectra by Gibbs sampling, with minimal model assumptions. In the second approach, we sample the joint posterior of the shear maps and cosmological parameters, providing a new, accurate and principled approach to cosmological parameter inference from cosmic shear data. As a first demonstration on data, we perform a two-bin tomographic analysis to constrain cosmological parameters and investigate the possibility of photometric redshift bias in the CFHTLenS data. Under the baseline ΛCDM (Λ cold dark matter) model, we constrain S_8 = σ _8(Ω _m/0.3)^{0.5} = 0.67+0.03-0.03 (68 per cent), consistent with previous CFHTLenS analyses but in tension with Planck. Adding neutrino mass as a free parameter, we are able to constrain ∑mν < 4.6 eV (95 per cent) using CFHTLenS data alone. Including a linear redshift-dependent photo-z bias Δz = p2(z - p1), we find p_1=-0.25+0.53-0.60 and p_2 = -0.15+0.17-0.15, and tension with Planck is only alleviated under very conservative prior assumptions. Neither the non-minimal neutrino mass nor photo-z bias models are significantly preferred by the CFHTLenS (two-bin tomography) data.
NASA Astrophysics Data System (ADS)
Alameddine, Ibrahim; Karmakar, Subhankar; Qian, Song S.; Paerl, Hans W.; Reckhow, Kenneth H.
2013-10-01
The total maximum daily load program aims to monitor more than 40,000 standard violations in around 20,000 impaired water bodies across the United States. Given resource limitations, future monitoring efforts have to be hedged against the uncertainties in the monitored system, while taking into account existing knowledge. In that respect, we have developed a hierarchical spatiotemporal Bayesian model that can be used to optimize an existing monitoring network by retaining stations that provide the maximum amount of information, while identifying locations that would benefit from the addition of new stations. The model assumes the water quality parameters are adequately described by a joint matrix normal distribution. The adopted approach allows for a reduction in redundancies, while emphasizing information richness rather than data richness. The developed approach incorporates the concept of entropy to account for the associated uncertainties. Three different entropy-based criteria are adopted: total system entropy, chlorophyll-a standard violation entropy, and dissolved oxygen standard violation entropy. A multiple attribute decision making framework is adopted to integrate the competing design criteria and to generate a single optimal design. The approach is implemented on the water quality monitoring system of the Neuse River Estuary in North Carolina, USA. The model results indicate that the high priority monitoring areas identified by the total system entropy and the dissolved oxygen violation entropy criteria are largely coincident. The monitoring design based on the chlorophyll-a standard violation entropy proved to be less informative, given the low probabilities of violating the water quality standard in the estuary.
Hierarchical spatiotemporal matrix models for characterizing invasions
Hooten, M.B.; Wikle, C.K.; Dorazio, R.M.; Royle, J. Andrew
2007-01-01
The growth and dispersal of biotic organisms is an important subject in ecology. Ecologists are able to accurately describe survival and fecundity in plant and animal populations and have developed quantitative approaches to study the dynamics of dispersal and population size. Of particular interest are the dynamics of invasive species. Such nonindigenous animals and plants can levy significant impacts on native biotic communities. Effective models for relative abundance have been developed; however, a better understanding of the dynamics of actual population size (as opposed to relative abundance) in an invasion would be beneficial to all branches of ecology. In this article, we adopt a hierarchical Bayesian framework for modeling the invasion of such species while addressing the discrete nature of the data and uncertainty associated with the probability of detection. The nonlinear dynamics between discrete time points are intuitively modeled through an embedded deterministic population model with density-dependent growth and dispersal components. Additionally, we illustrate the importance of accommodating spatially varying dispersal rates. The method is applied to the specific case of the Eurasian Collared-Dove, an invasive species at mid-invasion in the United States at the time of this writing. ?? 2006, The International Biometric Society.
Hierarchical spatiotemporal matrix models for characterizing invasions
Hooten, Mevin B.; Wikle, Christopher K.; Dorazio, Robert M.; Royle, J. Andrew
2007-01-01
The growth and dispersal of biotic organisms is an important subject in ecology. Ecologists are able to accurately describe survival and fecundity in plant and animal populations and have developed quantitative approaches to study the dynamics of dispersal and population size. Of particular interest are the dynamics of invasive species. Such nonindigenous animals and plants can levy significant impacts on native biotic communities. Effective models for relative abundance have been developed; however, a better understanding of the dynamics of actual population size (as opposed to relative abundance) in an invasion would be beneficial to all branches of ecology. In this article, we adopt a hierarchical Bayesian framework for modeling the invasion of such species while addressing the discrete nature of the data and uncertainty associated with the probability of detection. The nonlinear dynamics between discrete time points are intuitively modeled through an embedded deterministic population model with density-dependent growth and dispersal components. Additionally, we illustrate the importance of accommodating spatially varying dispersal rates. The method is applied to the specific case of the Eurasian Collared-Dove, an invasive species at mid-invasion in the United States at the time of this writing.
ERIC Educational Resources Information Center
Zhou, Bo; Konstorum, Anna; Duong, Thao; Tieu, Kinh H.; Wells, William M.; Brown, Gregory G.; Stern, Hal S.; Shahbaba, Babak
2013-01-01
We propose a hierarchical Bayesian model for analyzing multi-site experimental fMRI studies. Our method takes the hierarchical structure of the data (subjects are nested within sites, and there are multiple observations per subject) into account and allows for modeling between-site variation. Using posterior predictive model checking and model…
A hierarchical model for spatial capture-recapture data
Royle, J. Andrew; Young, K.V.
2008-01-01
Estimating density is a fundamental objective of many animal population studies. Application of methods for estimating population size from ostensibly closed populations is widespread, but ineffective for estimating absolute density because most populations are subject to short-term movements or so-called temporary emigration. This phenomenon invalidates the resulting estimates because the effective sample area is unknown. A number of methods involving the adjustment of estimates based on heuristic considerations are in widespread use. In this paper, a hierarchical model of spatially indexed capture recapture data is proposed for sampling based on area searches of spatial sample units subject to uniform sampling intensity. The hierarchical model contains explicit models for the distribution of individuals and their movements, in addition to an observation model that is conditional on the location of individuals during sampling. Bayesian analysis of the hierarchical model is achieved by the use of data augmentation, which allows for a straightforward implementation in the freely available software WinBUGS. We present results of a simulation study that was carried out to evaluate the operating characteristics of the Bayesian estimator under variable densities and movement patterns of individuals. An application of the model is presented for survey data on the flat-tailed horned lizard (Phrynosoma mcallii) in Arizona, USA.
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…
Siwek, M; Finocchiaro, R; Curik, I; Portolano, B
2011-02-01
Genetic structure and relationship amongst the main goat populations in Sicily (Girgentana, Derivata di Siria, Maltese and Messinese) were analysed using information from 19 microsatellite markers genotyped on 173 individuals. A posterior Bayesian approach implemented in the program STRUCTURE revealed a hierarchical structure with two clusters at the first level (Girgentana vs. Messinese, Derivata di Siria and Maltese), explaining 4.8% of variation (amovaФ(ST) estimate). Seven clusters nested within these first two clusters (further differentiations of Girgentana, Derivata di Siria and Maltese), explaining 8.5% of variation (amovaФ(SC) estimate). The analyses and methods applied in this study indicate their power to detect subtle population structure.
Bayesian Variable Selection on Model Spaces Constrained by Heredity Conditions.
Taylor-Rodriguez, Daniel; Womack, Andrew; Bliznyuk, Nikolay
2016-01-01
This paper investigates Bayesian variable selection when there is a hierarchical dependence structure on the inclusion of predictors in the model. In particular, we study the type of dependence found in polynomial response surfaces of orders two and higher, whose model spaces are required to satisfy weak or strong heredity conditions. These conditions restrict the inclusion of higher-order terms depending upon the inclusion of lower-order parent terms. We develop classes of priors on the model space, investigate their theoretical and finite sample properties, and provide a Metropolis-Hastings algorithm for searching the space of models. The tools proposed allow fast and thorough exploration of model spaces that account for hierarchical polynomial structure in the predictors and provide control of the inclusion of false positives in high posterior probability models.
Mandel, Kaisey S.; Kirshner, Robert P.; Foley, Ryan J.
2014-12-20
We investigate the statistical dependence of the peak intrinsic colors of Type Ia supernovae (SNe Ia) on their expansion velocities at maximum light, measured from the Si II λ6355 spectral feature. We construct a new hierarchical Bayesian regression model, accounting for the random effects of intrinsic scatter, measurement error, and reddening by host galaxy dust, and implement a Gibbs sampler and deviance information criteria to estimate the correlation. The method is applied to the apparent colors from BVRI light curves and Si II velocity data for 79 nearby SNe Ia. The apparent color distributions of high-velocity (HV) and normal velocity (NV) supernovae exhibit significant discrepancies for B – V and B – R, but not other colors. Hence, they are likely due to intrinsic color differences originating in the B band, rather than dust reddening. The mean intrinsic B – V and B – R color differences between HV and NV groups are 0.06 ± 0.02 and 0.09 ± 0.02 mag, respectively. A linear model finds significant slopes of –0.021 ± 0.006 and –0.030 ± 0.009 mag (10{sup 3} km s{sup –1}){sup –1} for intrinsic B – V and B – R colors versus velocity, respectively. Because the ejecta velocity distribution is skewed toward high velocities, these effects imply non-Gaussian intrinsic color distributions with skewness up to +0.3. Accounting for the intrinsic-color-velocity correlation results in corrections to A{sub V} extinction estimates as large as –0.12 mag for HV SNe Ia and +0.06 mag for NV events. Velocity measurements from SN Ia spectra have the potential to diminish systematic errors from the confounding of intrinsic colors and dust reddening affecting supernova distances.
NASA Astrophysics Data System (ADS)
Mandel, Kaisey S.; Foley, Ryan J.; Kirshner, Robert P.
2014-12-01
We investigate the statistical dependence of the peak intrinsic colors of Type Ia supernovae (SNe Ia) on their expansion velocities at maximum light, measured from the Si II λ6355 spectral feature. We construct a new hierarchical Bayesian regression model, accounting for the random effects of intrinsic scatter, measurement error, and reddening by host galaxy dust, and implement a Gibbs sampler and deviance information criteria to estimate the correlation. The method is applied to the apparent colors from BVRI light curves and Si II velocity data for 79 nearby SNe Ia. The apparent color distributions of high-velocity (HV) and normal velocity (NV) supernovae exhibit significant discrepancies for B - V and B - R, but not other colors. Hence, they are likely due to intrinsic color differences originating in the B band, rather than dust reddening. The mean intrinsic B - V and B - R color differences between HV and NV groups are 0.06 ± 0.02 and 0.09 ± 0.02 mag, respectively. A linear model finds significant slopes of -0.021 ± 0.006 and -0.030 ± 0.009 mag (103 km s-1)-1 for intrinsic B - V and B - R colors versus velocity, respectively. Because the ejecta velocity distribution is skewed toward high velocities, these effects imply non-Gaussian intrinsic color distributions with skewness up to +0.3. Accounting for the intrinsic-color-velocity correlation results in corrections to AV extinction estimates as large as -0.12 mag for HV SNe Ia and +0.06 mag for NV events. Velocity measurements from SN Ia spectra have the potential to diminish systematic errors from the confounding of intrinsic colors and dust reddening affecting supernova distances.
Modeling abundance using hierarchical distance sampling
Royle, Andy; Kery, Marc
2016-01-01
In this chapter, we provide an introduction to classical distance sampling ideas for point and line transect data, and for continuous and binned distance data. We introduce the conditional and the full likelihood, and we discuss Bayesian analysis of these models in BUGS using the idea of data augmentation, which we discussed in Chapter 7. We then extend the basic ideas to the problem of hierarchical distance sampling (HDS), where we have multiple point or transect sample units in space (or possibly in time). The benefit of HDS in practice is that it allows us to directly model spatial variation in population size among these sample units. This is a preeminent concern of most field studies that use distance sampling methods, but it is not a problem that has received much attention in the literature. We show how to analyze HDS models in both the unmarked package and in the BUGS language for point and line transects, and for continuous and binned distance data. We provide a case study of HDS applied to a survey of the island scrub-jay on Santa Cruz Island, California.
Bayesian inference for OPC modeling
NASA Astrophysics Data System (ADS)
Burbine, Andrew; Sturtevant, John; Fryer, David; Smith, Bruce W.
2016-03-01
The use of optical proximity correction (OPC) demands increasingly accurate models of the photolithographic process. Model building and inference techniques in the data science community have seen great strides in the past two decades which make better use of available information. This paper aims to demonstrate the predictive power of Bayesian inference as a method for parameter selection in lithographic models by quantifying the uncertainty associated with model inputs and wafer data. Specifically, the method combines the model builder's prior information about each modelling assumption with the maximization of each observation's likelihood as a Student's t-distributed random variable. Through the use of a Markov chain Monte Carlo (MCMC) algorithm, a model's parameter space is explored to find the most credible parameter values. During parameter exploration, the parameters' posterior distributions are generated by applying Bayes' rule, using a likelihood function and the a priori knowledge supplied. The MCMC algorithm used, an affine invariant ensemble sampler (AIES), is implemented by initializing many walkers which semiindependently explore the space. The convergence of these walkers to global maxima of the likelihood volume determine the parameter values' highest density intervals (HDI) to reveal champion models. We show that this method of parameter selection provides insights into the data that traditional methods do not and outline continued experiments to vet the method.
Hierarchical modeling for image classification
NASA Technical Reports Server (NTRS)
Likens, W.; Maw, K.
1982-01-01
As part of the California Integrated Remote Sensing System's (CIRSS) San Bernardino County Project, the use of data layers from a geographic information system (GIS) as an integral part of the Landsat image classification process was investigated. Through a hierarchical modeling technique, elevation, aspect, land use, vegetation, and growth management data from the project's data base were used to guide class labeling decisions in a 1976 Landsat MSS land cover classification. A similar model, incorporating 1976-1979 Landsat spectral change data in addition to other data base elements, was used in the classification of a 1979 Landsat image. The resultant Landsat products were integrated as additional layers into the data base for use in growth management, fire hazard, and hydrological modeling.
Hierarchical modeling of protein interactions.
Kurcinski, Mateusz; Kolinski, Andrzej
2007-07-01
A novel approach to hierarchical peptide-protein and protein-protein docking is described and evaluated. Modeling procedure starts from a reduced space representation of proteins and peptides. Polypeptide chains are represented by strings of alpha-carbon beads restricted to a fine-mesh cubic lattice. Side chains are represented by up to two centers of interactions, corresponding to beta-carbons and the centers of mass of the remaining portions of the side groups, respectively. Additional pseudoatoms are located in the centers of the virtual bonds connecting consecutive alpha carbons. These pseudoatoms support a model of main-chain hydrogen bonds. Docking starts from a collection of random configurations of modeled molecules. Interacting molecules are flexible; however, higher accuracy models are obtained when the conformational freedom of one (the larger one) of the assembling molecules is limited by a set of weak distance restraints extracted from the experimental (or theoretically predicted) structures. Sampling is done by means of Replica Exchange Monte Carlo method. Afterwards, the set of obtained structures is subject to a hierarchical clustering. Then, the centroids of the resulting clusters are used as scaffolds for the reconstruction of the atomic details. Finally, the all-atom models are energy minimized and scored using classical tools of molecular mechanics. The method is tested on a set of macromolecular assemblies consisting of proteins and peptides. It is demonstrated that the proposed approach to the flexible docking could be successfully applied to prediction of protein-peptide and protein-protein interactions. The obtained models are almost always qualitatively correct, although usually of relatively low (or moderate) resolution. In spite of this limitation, the proposed method opens new possibilities of computational studies of macromolecular recognition and mechanisms of assembly of macromolecular complexes.
Bayesian Calibration of Microsimulation Models.
Rutter, Carolyn M; Miglioretti, Diana L; Savarino, James E
2009-12-01
Microsimulation models that describe disease processes synthesize information from multiple sources and can be used to estimate the effects of screening and treatment on cancer incidence and mortality at a population level. These models are characterized by simulation of individual event histories for an idealized population of interest. Microsimulation models are complex and invariably include parameters that are not well informed by existing data. Therefore, a key component of model development is the choice of parameter values. Microsimulation model parameter values are selected to reproduce expected or known results though the process of model calibration. Calibration may be done by perturbing model parameters one at a time or by using a search algorithm. As an alternative, we propose a Bayesian method to calibrate microsimulation models that uses Markov chain Monte Carlo. We show that this approach converges to the target distribution and use a simulation study to demonstrate its finite-sample performance. Although computationally intensive, this approach has several advantages over previously proposed methods, including the use of statistical criteria to select parameter values, simultaneous calibration of multiple parameters to multiple data sources, incorporation of information via prior distributions, description of parameter identifiability, and the ability to obtain interval estimates of model parameters. We develop a microsimulation model for colorectal cancer and use our proposed method to calibrate model parameters. The microsimulation model provides a good fit to the calibration data. We find evidence that some parameters are identified primarily through prior distributions. Our results underscore the need to incorporate multiple sources of variability (i.e., due to calibration data, unknown parameters, and estimated parameters and predicted values) when calibrating and applying microsimulation models.
Bayesian model selection and isocurvature perturbations
NASA Astrophysics Data System (ADS)
Beltrán, María; García-Bellido, Juan; Lesgourgues, Julien; Liddle, Andrew R.; Slosar, Anže
2005-03-01
Present cosmological data are well explained assuming purely adiabatic perturbations, but an admixture of isocurvature perturbations is also permitted. We use a Bayesian framework to compare the performance of cosmological models including isocurvature modes with the purely adiabatic case; this framework automatically and consistently penalizes models which use more parameters to fit the data. We compute the Bayesian evidence for fits to a data set comprised of WMAP and other microwave anisotropy data, the galaxy power spectrum from 2dFGRS and SDSS, and Type Ia supernovae luminosity distances. We find that Bayesian model selection favors the purely adiabatic models, but so far only at low significance.
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.
Walter, W. David; Smith, Rick; Vanderklok, Mike; VerCauteren, Kurt C.
2014-01-01
Bovine tuberculosis is a bacterial disease caused by Mycobacterium bovis in livestock and wildlife with hosts that include Eurasian badgers (Meles meles), brushtail possum (Trichosurus vulpecula), and white-tailed deer (Odocoileus virginianus). Risk-assessment efforts in Michigan have been initiated on farms to minimize interactions of cattle with wildlife hosts but research on M. bovis on cattle farms has not investigated the spatial context of disease epidemiology. To incorporate spatially explicit data, initial likelihood of infection probabilities for cattle farms tested for M. bovis, prevalence of M. bovis in white-tailed deer, deer density, and environmental variables for each farm were modeled in a Bayesian hierarchical framework. We used geo-referenced locations of 762 cattle farms that have been tested for M. bovis, white-tailed deer prevalence, and several environmental variables that may lead to long-term survival and viability of M. bovis on farms and surrounding habitats (i.e., soil type, habitat type). Bayesian hierarchical analyses identified deer prevalence and proportion of sandy soil within our sampling grid as the most supported model. Analysis of cattle farms tested for M. bovis identified that for every 1% increase in sandy soil resulted in an increase in odds of infection by 4%. Our analysis revealed that the influence of prevalence of M. bovis in white-tailed deer was still a concern even after considerable efforts to prevent cattle interactions with white-tailed deer through on-farm mitigation and reduction in the deer population. Cattle farms test positive for M. bovis annually in our study area suggesting that the potential for an environmental source either on farms or in the surrounding landscape may contributing to new or re-infections with M. bovis. Our research provides an initial assessment of potential environmental factors that could be incorporated into additional modeling efforts as more knowledge of deer herd factors and cattle
Walter, W David; Smith, Rick; Vanderklok, Mike; VerCauteren, Kurt C
2014-01-01
Bovine tuberculosis is a bacterial disease caused by Mycobacterium bovis in livestock and wildlife with hosts that include Eurasian badgers (Meles meles), brushtail possum (Trichosurus vulpecula), and white-tailed deer (Odocoileus virginianus). Risk-assessment efforts in Michigan have been initiated on farms to minimize interactions of cattle with wildlife hosts but research on M. bovis on cattle farms has not investigated the spatial context of disease epidemiology. To incorporate spatially explicit data, initial likelihood of infection probabilities for cattle farms tested for M. bovis, prevalence of M. bovis in white-tailed deer, deer density, and environmental variables for each farm were modeled in a Bayesian hierarchical framework. We used geo-referenced locations of 762 cattle farms that have been tested for M. bovis, white-tailed deer prevalence, and several environmental variables that may lead to long-term survival and viability of M. bovis on farms and surrounding habitats (i.e., soil type, habitat type). Bayesian hierarchical analyses identified deer prevalence and proportion of sandy soil within our sampling grid as the most supported model. Analysis of cattle farms tested for M. bovis identified that for every 1% increase in sandy soil resulted in an increase in odds of infection by 4%. Our analysis revealed that the influence of prevalence of M. bovis in white-tailed deer was still a concern even after considerable efforts to prevent cattle interactions with white-tailed deer through on-farm mitigation and reduction in the deer population. Cattle farms test positive for M. bovis annually in our study area suggesting that the potential for an environmental source either on farms or in the surrounding landscape may contributing to new or re-infections with M. bovis. Our research provides an initial assessment of potential environmental factors that could be incorporated into additional modeling efforts as more knowledge of deer herd factors and cattle
A Bayesian model of context-sensitive value attribution.
Rigoli, Francesco; Friston, Karl J; Martinelli, Cristina; Selaković, Mirjana; Shergill, Sukhwinder S; Dolan, Raymond J
2016-06-22
Substantial evidence indicates that incentive value depends on an anticipation of rewards within a given context. However, the computations underlying this context sensitivity remain unknown. To address this question, we introduce a normative (Bayesian) account of how rewards map to incentive values. This assumes that the brain inverts a model of how rewards are generated. Key features of our account include (i) an influence of prior beliefs about the context in which rewards are delivered (weighted by their reliability in a Bayes-optimal fashion), (ii) the notion that incentive values correspond to precision-weighted prediction errors, (iii) and contextual information unfolding at different hierarchical levels. This formulation implies that incentive value is intrinsically context-dependent. We provide empirical support for this model by showing that incentive value is influenced by context variability and by hierarchically nested contexts. The perspective we introduce generates new empirical predictions that might help explaining psychopathologies, such as addiction.
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.
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
Predicting brain activity using a Bayesian spatial model.
Derado, Gordana; Bowman, F Dubois; Zhang, Lijun
2013-08-01
Increasing the clinical applicability of functional neuroimaging technology is an emerging objective, e.g. for diagnostic and treatment purposes. We propose a novel Bayesian spatial hierarchical framework for predicting follow-up neural activity based on an individual's baseline functional neuroimaging data. Our approach attempts to overcome some shortcomings of the modeling methods used in other neuroimaging settings, by borrowing strength from the spatial correlations present in the data. Our proposed methodology is applicable to data from various imaging modalities including functional magnetic resonance imaging and positron emission tomography, and we provide an illustration here using positron emission tomography data from a study of Alzheimer's disease to predict disease progression.
NASA Astrophysics Data System (ADS)
Burky, A.; Mustac, M.; Tkalcic, H.; Dreger, D. S.
2015-12-01
The Geysers geothermal region in northern California is a valuable resource for the production of geothermal electric power. Injection of water into the reservoir is necessary to maintain pressure and causes an increase in the number of earthquakes per day, but their source mechanisms are not well understood (Johnson, 2015). Previous studies of source mechanisms for events in the Geysers have identified a large number of events with significant isotropic and compensated linear vector dipole components. These source complexities most likely arise from the presence of pressurized liquids and gases, as well as temperature changes, at depth. The existence of non-double couple components in volcanic and geothermal environments has been extensively documented by previous studies, but it has also been shown that spurious components might occur due to a range of factors such as an inadequate knowledge of Earth structure and earthquake location, or noisy waveform data. Therefore, it is not entirely surprising that non-double-couple components from different source studies, each following a different experimental method and using different data types, do not agree well (e.g. Guilhem et al., 2014). The assessment of the solution robustness is critical for the physical interpretation of source mechanisms.Here, we apply a hierarchical Bayesian approach (Mustac and Tkalcic, 2015) to waveform data from M>4.5 events in the Geysers in order to produce moment tensor "solutions" and simultaneously estimate their robustness. By using a Bayesian inversion, we quantify the uncertainties from an ensemble of probable solutions instead of a single optimized solution and sample solutions at a range of centroid locations. Moreover, the hierarchical approach allows noise in the data to be sampled as a free parameter in the inversion. A rigorous approach in accounting for the data correlated noise covariance matrix prevents "over-interpretation" of noise, thus avoiding erroneous solutions. We
What’s in a Name: A Bayesian Hierarchical Analysis of the Name-Letter Effect
Dyjas, Oliver; Grasman, Raoul P. P. P.; Wetzels, Ruud; van der Maas, Han L. J.; Wagenmakers, Eric-Jan
2012-01-01
People generally prefer their initials to the other letters of the alphabet, a phenomenon known as the name-letter effect. This effect, researchers have argued, makes people move to certain cities, buy particular brands of consumer products, and choose particular professions (e.g., Angela moves to Los Angeles, Phil buys a Philips TV, and Dennis becomes a dentist). In order to establish such associations between people’s initials and their behavior, researchers typically carry out statistical analyses of large databases. Current methods of analysis ignore the hierarchical structure of the data, do not naturally handle order-restrictions, and are fundamentally incapable of confirming the null hypothesis. Here we outline a Bayesian hierarchical analysis that avoids these limitations and allows coherent inference both on the level of the individual and on the level of the group. To illustrate our method, we re-analyze two data sets that address the question of whether people are disproportionately likely to live in cities that resemble their name. PMID:23055989
ERIC Educational Resources Information Center
Tchumtchoua, Sylvie; Dey, Dipak K.
2012-01-01
This paper proposes a semiparametric Bayesian framework for the analysis of associations among multivariate longitudinal categorical variables in high-dimensional data settings. This type of data is frequent, especially in the social and behavioral sciences. A semiparametric hierarchical factor analysis model is developed in which the…
ERIC Educational Resources Information Center
Wang, Qiu; Diemer, Matthew A.; Maier, Kimberly S.
2013-01-01
This study integrated Bayesian hierarchical modeling and receiver operating characteristic analysis (BROCA) to evaluate how interest strength (IS) and interest differentiation (ID) predicted low–socioeconomic status (SES) youth's interest-major congruence (IMC). Using large-scale Kuder Career Search online-assessment data, this study fit three…
Hierarchical Models of the Nearshore Complex System
2004-01-01
unclassified unclassified /,andard Form 7 7Qien. -pii Prescrbed by ANS Sid 239-18 zgB -10z Hierarchical Models of the Nearshore Complex System: Final...TITLE AND SUBTITLE S. FUNDING NUMBERS Hierarchical Models of the Nearshore Complex System N00014-02-1-0358 6. AUTHOR(S) Brad Werner 7. PERFORMING...8217 ........... The long-term goal of this reasearch was to develop and test predictive models for nearshore processes. This grant was terminaton funding for the
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…
Weakly Informative Prior for Point Estimation of Covariance Matrices in Hierarchical Models
ERIC Educational Resources Information Center
Chung, Yeojin; Gelman, Andrew; Rabe-Hesketh, Sophia; Liu, Jingchen; Dorie, Vincent
2015-01-01
When fitting hierarchical regression models, maximum likelihood (ML) estimation has computational (and, for some users, philosophical) advantages compared to full Bayesian inference, but when the number of groups is small, estimates of the covariance matrix (S) of group-level varying coefficients are often degenerate. One can do better, even from…
Bayesian modeling of unknown diseases for biosurveillance.
Shen, Yanna; Cooper, Gregory F
2009-11-14
This paper investigates Bayesian modeling of unknown causes of events in the context of disease-outbreak detection. We introduce a Bayesian approach that models and detects both (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 key contribution of this paper is that it introduces a Bayesian approach for jointly modeling both known and unknown causes of events. Such modeling has broad applicability in medical informatics, where the space of known causes of outcomes of interest is seldom complete.
Current Challenges in Bayesian Model Choice
NASA Astrophysics Data System (ADS)
Clyde, M. A.; Berger, J. O.; Bullard, F.; Ford, E. B.; Jefferys, W. H.; Luo, R.; Paulo, R.; Loredo, T.
2007-11-01
Model selection (and the related issue of model uncertainty) arises in many astronomical problems, and, in particular, has been one of the focal areas of the Exoplanet working group under the SAMSI (Statistics and Applied Mathematical Sciences Institute) Astrostatistcs Exoplanet program. We provide an overview of the Bayesian approach to model selection and highlight the challenges involved in implementing Bayesian model choice in four stylized problems. We review some of the current methods used by statisticians and astronomers and present recent developments in the area. We discuss the applicability, computational challenges, and performance of suggested methods and conclude with recommendations and open questions.
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…
An Integrated Bayesian Model for DIF Analysis
ERIC Educational Resources Information Center
Soares, Tufi M.; Goncalves, Flavio B.; Gamerman, Dani
2009-01-01
In this article, an integrated Bayesian model for differential item functioning (DIF) analysis is proposed. The model is integrated in the sense of modeling the responses along with the DIF analysis. This approach allows DIF detection and explanation in a simultaneous setup. Previous empirical studies and/or subjective beliefs about the item…
Bayesian modeling of flexible cognitive control
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
Hierarchical animal movement models for population-level inference
Hooten, Mevin B.; Buderman, Frances E.; Brost, Brian M.; Hanks, Ephraim M.; Ivans, Jacob S.
2016-01-01
New methods for modeling animal movement based on telemetry data are developed regularly. With advances in telemetry capabilities, animal movement models are becoming increasingly sophisticated. Despite a need for population-level inference, animal movement models are still predominantly developed for individual-level inference. Most efforts to upscale the inference to the population level are either post hoc or complicated enough that only the developer can implement the model. Hierarchical Bayesian models provide an ideal platform for the development of population-level animal movement models but can be challenging to fit due to computational limitations or extensive tuning required. We propose a two-stage procedure for fitting hierarchical animal movement models to telemetry data. The two-stage approach is statistically rigorous and allows one to fit individual-level movement models separately, then resample them using a secondary MCMC algorithm. The primary advantages of the two-stage approach are that the first stage is easily parallelizable and the second stage is completely unsupervised, allowing for an automated fitting procedure in many cases. We demonstrate the two-stage procedure with two applications of animal movement models. The first application involves a spatial point process approach to modeling telemetry data, and the second involves a more complicated continuous-time discrete-space animal movement model. We fit these models to simulated data and real telemetry data arising from a population of monitored Canada lynx in Colorado, USA.
Analysis hierarchical model for discrete event systems
NASA Astrophysics Data System (ADS)
Ciortea, E. M.
2015-11-01
The This paper presents the hierarchical model based on discrete event network for robotic systems. Based on the hierarchical approach, Petri network is analysed as a network of the highest conceptual level and the lowest level of local control. For modelling and control of complex robotic systems using extended Petri nets. Such a system is structured, controlled and analysed in this paper by using Visual Object Net ++ package that is relatively simple and easy to use, and the results are shown as representations easy to interpret. The hierarchical structure of the robotic system is implemented on computers analysed using specialized programs. Implementation of hierarchical model discrete event systems, as a real-time operating system on a computer network connected via a serial bus is possible, where each computer is dedicated to local and Petri model of a subsystem global robotic system. Since Petri models are simplified to apply general computers, analysis, modelling, complex manufacturing systems control can be achieved using Petri nets. Discrete event systems is a pragmatic tool for modelling industrial systems. For system modelling using Petri nets because we have our system where discrete event. To highlight the auxiliary time Petri model using transport stream divided into hierarchical levels and sections are analysed successively. Proposed robotic system simulation using timed Petri, offers the opportunity to view the robotic time. Application of goods or robotic and transmission times obtained by measuring spot is obtained graphics showing the average time for transport activity, using the parameters sets of finished products. individually.
Survey of Bayesian Models for Modelling of Stochastic Temporal Processes
Ng, B
2006-10-12
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.
Walter, William D.; Smith, Rick; Vanderklok, Mike; VerCauterren, Kurt C.
2014-01-01
Bovine tuberculosis is a bacterial disease caused by Mycobacterium bovis in livestock and wildlife with hosts that include Eurasian badgers (Meles meles), brushtail possum (Trichosurus vulpecula), and white-tailed deer (Odocoileus virginianus). Risk-assessment efforts in Michigan have been initiated on farms to minimize interactions of cattle with wildlife hosts but research onM. bovis on cattle farms has not investigated the spatial context of disease epidemiology. To incorporate spatially explicit data, initial likelihood of infection probabilities for cattle farms tested for M. bovis, prevalence of M. bovis in white-tailed deer, deer density, and environmental variables for each farm were modeled in a Bayesian hierarchical framework. We used geo-referenced locations of 762 cattle farms that have been tested for M. bovis, white-tailed deer prevalence, and several environmental variables that may lead to long-term survival and viability of M. bovis on farms and surrounding habitats (i.e., soil type, habitat type). Bayesian hierarchical analyses identified deer prevalence and proportion of sandy soil within our sampling grid as the most supported model. Analysis of cattle farms tested for M. bovisidentified that for every 1% increase in sandy soil resulted in an increase in odds of infection by 4%. Our analysis revealed that the influence of prevalence of M. bovis in white-tailed deer was still a concern even after considerable efforts to prevent cattle interactions with white-tailed deer through on-farm mitigation and reduction in the deer population. Cattle farms test positive for M. bovis annually in our study area suggesting that the potential for an environmental source either on farms or in the surrounding landscape may contributing to new or re-infections with M. bovis. Our research provides an initial assessment of potential environmental factors that could be incorporated into additional modeling efforts as more knowledge of deer herd
Kelly, Brandon C.; Goodman, Alyssa A.; Shetty, Rahul; Stutz, Amelia M.; Launhardt, Ralf; Kauffmann, Jens
2012-06-10
We present a hierarchical Bayesian method for fitting infrared spectral energy distributions (SEDs) of dust emission to observed fluxes. Under the standard assumption of optically thin single temperature (T) sources, the dust SED as represented by a power-law-modified blackbody is subject to a strong degeneracy between T and the spectral index {beta}. The traditional non-hierarchical approaches, typically based on {chi}{sup 2} minimization, are severely limited by this degeneracy, as it produces an artificial anti-correlation between T and {beta} even with modest levels of observational noise. The hierarchical Bayesian method rigorously and self-consistently treats measurement uncertainties, including calibration and noise, resulting in more precise SED fits. As a result, the Bayesian fits do not produce any spurious anti-correlations between the SED parameters due to measurement uncertainty. We demonstrate that the Bayesian method is substantially more accurate than the {chi}{sup 2} fit in recovering the SED parameters, as well as the correlations between them. As an illustration, we apply our method to Herschel and submillimeter ground-based observations of the star-forming Bok globule CB244. This source is a small, nearby molecular cloud containing a single low-mass protostar and a starless core. We find that T and {beta} are weakly positively correlated-in contradiction with the {chi}{sup 2} fits, which indicate a T-{beta} anti-correlation from the same data set. Additionally, in comparison to the {chi}{sup 2} fits the Bayesian SED parameter estimates exhibit a reduced range in values.
Bayesian state space models for dynamic genetic network construction across multiple tissues.
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 Hierarchical Process-Dissociation Model
ERIC Educational Resources Information Center
Rouder, Jeffrey N.; Lu, Jun; Morey, Richard D.; Sun, Dongchu; Speckman, Paul L.
2008-01-01
In fitting the process-dissociation model (L. L. Jacoby, 1991) to observed data, researchers aggregate outcomes across participant, items, or both. T. Curran and D. L. Hintzman (1995) demonstrated how biases from aggregation may lead to artifactual support for the model. The authors develop a hierarchical process-dissociation model that does not…
Bayesian joint modeling of longitudinal and spatial survival AIDS data.
Martins, Rui; Silva, Giovani L; Andreozzi, Valeska
2016-08-30
Joint analysis of longitudinal and survival data has received increasing attention in the recent years, especially for analyzing cancer and AIDS data. As both repeated measurements (longitudinal) and time-to-event (survival) outcomes are observed in an individual, a joint modeling is more appropriate because it takes into account the dependence between the two types of responses, which are often analyzed separately. We propose a Bayesian hierarchical model for jointly modeling longitudinal and survival data considering functional time and spatial frailty effects, respectively. That is, the proposed model deals with non-linear longitudinal effects and spatial survival effects accounting for the unobserved heterogeneity among individuals living in the same region. This joint approach is applied to a cohort study of patients with HIV/AIDS in Brazil during the years 2002-2006. Our Bayesian joint model presents considerable improvements in the estimation of survival times of the Brazilian HIV/AIDS patients when compared with those obtained through a separate survival model and shows that the spatial risk of death is the same across the different Brazilian states. Copyright © 2016 John Wiley & Sons, Ltd.
Statistical label fusion with hierarchical performance models
NASA Astrophysics Data System (ADS)
Asman, Andrew J.; Dagley, Alexander S.; Landman, Bennett A.
2014-03-01
Label fusion is a critical step in many image segmentation frameworks (e.g., multi-atlas segmentation) as it provides a mechanism for generalizing a collection of labeled examples into a single estimate of the underlying segmentation. In the multi-label case, typical label fusion algorithms treat all labels equally - fully neglecting the known, yet complex, anatomical relationships exhibited in the data. To address this problem, we propose a generalized statistical fusion framework using hierarchical models of rater performance. Building on the seminal work in statistical fusion, we reformulate the traditional rater performance model from a multi-tiered hierarchical perspective. This new approach provides a natural framework for leveraging known anatomical relationships and accurately modeling the types of errors that raters (or atlases) make within a hierarchically consistent formulation. Herein, we describe several contributions. First, we derive a theoretical advancement to the statistical fusion framework that enables the simultaneous estimation of multiple (hierarchical) performance models within the statistical fusion context. Second, we demonstrate that the proposed hierarchical formulation is highly amenable to the state-of-the-art advancements that have been made to the statistical fusion framework. Lastly, in an empirical whole-brain segmentation task we demonstrate substantial qualitative and significant quantitative improvement in overall segmentation accuracy.
A hierarchical community occurrence model for North Carolina stream fish
Midway, S.R.; Wagner, Tyler; Tracy, B.H.
2016-01-01
The southeastern USA is home to one of the richest—and most imperiled and threatened—freshwater fish assemblages in North America. For many of these rare and threatened species, conservation efforts are often limited by a lack of data. Drawing on a unique and extensive data set spanning over 20 years, we modeled occurrence probabilities of 126 stream fish species sampled throughout North Carolina, many of which occur more broadly in the southeastern USA. Specifically, we developed species-specific occurrence probabilities from hierarchical Bayesian multispecies models that were based on common land use and land cover covariates. We also used index of biotic integrity tolerance classifications as a second level in the model hierarchy; we identify this level as informative for our work, but it is flexible for future model applications. Based on the partial-pooling property of the models, we were able to generate occurrence probabilities for many imperiled and data-poor species in addition to highlighting a considerable amount of occurrence heterogeneity that supports species-specific investigations whenever possible. Our results provide critical species-level information on many threatened and imperiled species as well as information that may assist with re-evaluation of existing management strategies, such as the use of surrogate species. Finally, we highlight the use of a relatively simple hierarchical model that can easily be generalized for similar situations in which conventional models fail to provide reliable estimates for data-poor groups.
Bayesian Multiscale Modeling of Closed Curves in Point Clouds.
Gu, Kelvin; Pati, Debdeep; Dunson, David B
2014-10-01
Modeling object boundaries based on image or point cloud data is frequently necessary in medical and scientific applications ranging from detecting tumor contours for targeted radiation therapy, to the classification of organisms based on their structural information. In low-contrast images or sparse and noisy point clouds, there is often insufficient data to recover local segments of the boundary in isolation. Thus, it becomes critical to model the entire boundary in the form of a closed curve. To achieve this, we develop a Bayesian hierarchical model that expresses highly diverse 2D objects in the form of closed curves. The model is based on a novel multiscale deformation process. By relating multiple objects through a hierarchical formulation, we can successfully recover missing boundaries by borrowing structural information from similar objects at the appropriate scale. Furthermore, the model's latent parameters help interpret the population, indicating dimensions of significant structural variability and also specifying a 'central curve' that summarizes the collection. Theoretical properties of our prior are studied in specific cases and efficient Markov chain Monte Carlo methods are developed, evaluated through simulation examples and applied to panorex teeth images for modeling teeth contours and also to a brain tumor contour detection problem.
Objective Bayesian model selection for Cox regression.
Held, Leonhard; Gravestock, Isaac; Sabanés Bové, Daniel
2016-12-20
There is now a large literature on objective Bayesian model selection in the linear model based on the g-prior. The methodology has been recently extended to generalized linear models using test-based Bayes factors. In this paper, we show that test-based Bayes factors can also be applied to the Cox proportional hazards model. If the goal is to select a single model, then both the maximum a posteriori and the median probability model can be calculated. For clinical prediction of survival, we shrink the model-specific log hazard ratio estimates with subsequent calculation of the Breslow estimate of the cumulative baseline hazard function. A Bayesian model average can also be employed. We illustrate the proposed methodology with the analysis of survival data on primary biliary cirrhosis patients and the development of a clinical prediction model for future cardiovascular events based on data from the Second Manifestations of ARTerial disease (SMART) cohort study. Cross-validation is applied to compare the predictive performance with alternative model selection approaches based on Harrell's c-Index, the calibration slope and the integrated Brier score. Finally, a novel application of Bayesian variable selection to optimal conditional prediction via landmarking is described. Copyright © 2016 John Wiley & Sons, Ltd.
Parameter Expanded Algorithms for Bayesian Latent Variable Modeling of Genetic Pleiotropy Data.
Xu, Lizhen; Craiu, Radu V; Sun, Lei; Paterson, Andrew D
2016-01-01
Motivated by genetic association studies of pleiotropy, we propose a Bayesian latent variable approach to jointly study multiple outcomes. The models studied here can incorporate both continuous and binary responses, and can account for serial and cluster correlations. We consider Bayesian estimation for the model parameters, and we develop a novel MCMC algorithm that builds upon hierarchical centering and parameter expansion techniques to efficiently sample from the posterior distribution. We evaluate the proposed method via extensive simulations and demonstrate its utility with an application to aa association study of various complication outcomes related to type 1 diabetes. This article has supplementary material online.
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.
Link, William A; Sauer, John R
2016-07-01
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.
Normativity, interpretation, and Bayesian models
Oaksford, Mike
2014-01-01
It has been suggested that evaluative normativity should be expunged from the psychology of reasoning. A broadly Davidsonian response to these arguments is presented. It is suggested that two distinctions, between different types of rationality, are more permeable than this argument requires and that the fundamental objection is to selecting theories that make the most rational sense of the data. It is argued that this is inevitable consequence of radical interpretation where understanding others requires assuming they share our own norms of reasoning. This requires evaluative normativity and it is shown that when asked to evaluate others’ arguments participants conform to rational Bayesian norms. It is suggested that logic and probability are not in competition and that the variety of norms is more limited than the arguments against evaluative normativity suppose. Moreover, the universality of belief ascription suggests that many of our norms are universal and hence evaluative. It is concluded that the union of evaluative normativity and descriptive psychology implicit in Davidson and apparent in the psychology of reasoning is a good thing. PMID:24860519
Bayesian Multiscale Modeling of Closed Curves in Point Clouds
Gu, Kelvin; Pati, Debdeep; Dunson, David B.
2014-01-01
Modeling object boundaries based on image or point cloud data is frequently necessary in medical and scientific applications ranging from detecting tumor contours for targeted radiation therapy, to the classification of organisms based on their structural information. In low-contrast images or sparse and noisy point clouds, there is often insufficient data to recover local segments of the boundary in isolation. Thus, it becomes critical to model the entire boundary in the form of a closed curve. To achieve this, we develop a Bayesian hierarchical model that expresses highly diverse 2D objects in the form of closed curves. The model is based on a novel multiscale deformation process. By relating multiple objects through a hierarchical formulation, we can successfully recover missing boundaries by borrowing structural information from similar objects at the appropriate scale. Furthermore, the model’s latent parameters help interpret the population, indicating dimensions of significant structural variability and also specifying a ‘central curve’ that summarizes the collection. Theoretical properties of our prior are studied in specific cases and efficient Markov chain Monte Carlo methods are developed, evaluated through simulation examples and applied to panorex teeth images for modeling teeth contours and also to a brain tumor contour detection problem. PMID:25544786
Hierarchical Context Modeling for Video Event Recognition.
Wang, Xiaoyang; Ji, Qiang
2016-10-11
Current video event recognition research remains largely target-centered. For real-world surveillance videos, targetcentered event recognition faces great challenges due to large intra-class target variation, limited image resolution, and poor detection and tracking results. To mitigate these challenges, we introduced a context-augmented video event recognition approach. Specifically, we explicitly capture different types of contexts from three levels including image level, semantic level, and prior level. At the image level, we introduce two types of contextual features including the appearance context features and interaction context features to capture the appearance of context objects and their interactions with the target objects. At the semantic level, we propose a deep model based on deep Boltzmann machine to learn event object representations and their interactions. At the prior level, we utilize two types of prior-level contexts including scene priming and dynamic cueing. Finally, we introduce a hierarchical context model that systematically integrates the contextual information at different levels. Through the hierarchical context model, contexts at different levels jointly contribute to the event recognition. We evaluate the hierarchical context model for event recognition on benchmark surveillance video datasets. Results show that incorporating contexts in each level can improve event recognition performance, and jointly integrating three levels of contexts through our hierarchical model achieves the best performance.
Bayesian network modelling of upper gastrointestinal bleeding
NASA Astrophysics Data System (ADS)
Aisha, Nazziwa; Shohaimi, Shamarina; Adam, Mohd Bakri
2013-09-01
Bayesian networks are graphical probabilistic models that represent causal and other relationships between domain variables. In the context of medical decision making, these models have been explored to help in medical diagnosis and prognosis. In this paper, we discuss the Bayesian network formalism in building medical support systems and we learn a tree augmented naive Bayes Network (TAN) from gastrointestinal bleeding data. The accuracy of the TAN in classifying the source of gastrointestinal bleeding into upper or lower source is obtained. The TAN achieves a high classification accuracy of 86% and an area under curve of 92%. A sensitivity analysis of the model shows relatively high levels of entropy reduction for color of the stool, history of gastrointestinal bleeding, consistency and the ratio of blood urea nitrogen to creatinine. The TAN facilitates the identification of the source of GIB and requires further validation.
Modeling the Climatology of Tornado Occurrence with Bayesian Inference
NASA Astrophysics Data System (ADS)
Cheng, Vincent Y. S.
-related variables are more uniform across seasons. The residual variability of the same modeling framework (a reflection of the fidelity of the statistical formulation considered) is subsequently used to delineate distinct geographical patterns of tornado activity. This piece of information provides the foundation for the Bayesian hierarchical prognostic model presented in the third chapter of my dissertation. The results of the latter approach reinforce my earlier finding that the spatial variability of the annual and warm seasonal tornado occurrence is well explained by convective available potential energy and storm relative helicity alone, while vertical wind shear is better at reproducing the cool season tornado activity. The Bayesian hierarchical modeling framework offers a promising methodological tool for understanding regional tornado environments and obtaining reliable predictions in North America.
Designing and testing inflationary models with Bayesian networks
Price, Layne C.; Peiris, Hiranya V.; Frazer, Jonathan; Easther, Richard E-mail: h.peiris@ucl.ac.uk E-mail: r.easther@auckland.ac.nz
2016-02-01
Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters. We use N{sub f}-quadratic inflation as an illustrative example, finding that the number of e-folds N{sub *} between horizon exit for the pivot scale and the end of inflation is typically the most important parameter, even when the number of fields, their masses and initial conditions are unknown, along with possible conditional dependencies between these parameters.
Reginal Frequency Analysis Based on Scaling Properties and Bayesian Models
NASA Astrophysics Data System (ADS)
Kwon, Hyun-Han; Lee, Jeong-Ju; Moon, Young-Il
2010-05-01
A regional frequency analysis based on Hierarchical Bayesian Network (HBN) and scaling theory was developmed. Many recording rain gauges over South Korea were used for the analysis. First, a scaling approach combined with extreme distribution was employed to derive regional formula for frequency analysis. Second, HBN model was used to represent additional information about the regional structure of the scaling parameters, especially the location parameter and shape parameter. The location and shape parameters of the extreme distribution were estimated by utilizing scaling properties in a regression framework, and the scaling parameters linking the parameters (location and shape) to various duration times were simultaneously estimated. It was found that the regional frequency analysis combined with HBN and scaling properties show promising results in terms of establishing regional IDF curves.
Chan, Yvonne L; Schanzenbach, David; Hickerson, Michael J
2014-09-01
Methods that integrate population-level sampling from multiple taxa into a single community-level analysis are an essential addition to the comparative phylogeographic toolkit. Detecting how species within communities have demographically tracked each other in space and time is important for understanding the effects of future climate and landscape changes and the resulting acceleration of extinctions, biological invasions, and potential surges in adaptive evolution. Here, we present a statistical framework for such an analysis based on hierarchical approximate Bayesian computation (hABC) with the goal of detecting concerted demographic histories across an ecological assemblage. Our method combines population genetic data sets from multiple taxa into a single analysis to estimate: 1) the proportion of a community sample that demographically expanded in a temporally clustered pulse and 2) when the pulse occurred. To validate the accuracy and utility of this new approach, we use simulation cross-validation experiments and subsequently analyze an empirical data set of 32 avian populations from Australia that are hypothesized to have expanded from smaller refugia populations in the late Pleistocene. The method can accommodate data set heterogeneity such as variability in effective population size, mutation rates, and sample sizes across species and exploits the statistical strength from the simultaneous analysis of multiple species. This hABC framework used in a multitaxa demographic context can increase our understanding of the impact of historical climate change by determining what proportion of the community responded in concert or independently and can be used with a wide variety of comparative phylogeographic data sets as biota-wide DNA barcoding data sets accumulate.
Chan, Yvonne L.; Schanzenbach, David; Hickerson, Michael J.
2014-01-01
Methods that integrate population-level sampling from multiple taxa into a single community-level analysis are an essential addition to the comparative phylogeographic toolkit. Detecting how species within communities have demographically tracked each other in space and time is important for understanding the effects of future climate and landscape changes and the resulting acceleration of extinctions, biological invasions, and potential surges in adaptive evolution. Here, we present a statistical framework for such an analysis based on hierarchical approximate Bayesian computation (hABC) with the goal of detecting concerted demographic histories across an ecological assemblage. Our method combines population genetic data sets from multiple taxa into a single analysis to estimate: 1) the proportion of a community sample that demographically expanded in a temporally clustered pulse and 2) when the pulse occurred. To validate the accuracy and utility of this new approach, we use simulation cross-validation experiments and subsequently analyze an empirical data set of 32 avian populations from Australia that are hypothesized to have expanded from smaller refugia populations in the late Pleistocene. The method can accommodate data set heterogeneity such as variability in effective population size, mutation rates, and sample sizes across species and exploits the statistical strength from the simultaneous analysis of multiple species. This hABC framework used in a multitaxa demographic context can increase our understanding of the impact of historical climate change by determining what proportion of the community responded in concert or independently and can be used with a wide variety of comparative phylogeographic data sets as biota-wide DNA barcoding data sets accumulate. PMID:24925925
Managing Clustered Data Using Hierarchical Linear Modeling
ERIC Educational Resources Information Center
Warne, Russell T.; Li, Yan; McKyer, E. Lisako J.; Condie, Rachel; Diep, Cassandra S.; Murano, Peter S.
2012-01-01
Researchers in nutrition research often use cluster or multistage sampling to gather participants for their studies. These sampling methods often produce violations of the assumption of data independence that most traditional statistics share. Hierarchical linear modeling is a statistical method that can overcome violations of the independence…
A Bayesian Model of Biases in Artificial Language Learning: The Case of a Word-Order Universal
ERIC Educational Resources Information Center
Culbertson, Jennifer; Smolensky, Paul
2012-01-01
In this article, we develop a hierarchical Bayesian model of learning in a general type of artificial language-learning experiment in which learners are exposed to a mixture of grammars representing the variation present in real learners' input, particularly at times of language change. The modeling goal is to formalize and quantify hypothesized…
Bayesian model selection analysis of WMAP3
Parkinson, David; Mukherjee, Pia; Liddle, Andrew R.
2006-06-15
We present a Bayesian model selection analysis of WMAP3 data using our code CosmoNest. We focus on the density perturbation spectral index n{sub S} and the tensor-to-scalar ratio r, which define the plane of slow-roll inflationary models. We find that while the Bayesian evidence supports the conclusion that n{sub S}{ne}1, the data are not yet powerful enough to do so at a strong or decisive level. If tensors are assumed absent, the current odds are approximately 8 to 1 in favor of n{sub S}{ne}1 under our assumptions, when WMAP3 data is used together with external data sets. WMAP3 data on its own is unable to distinguish between the two models. Further, inclusion of r as a parameter weakens the conclusion against the Harrison-Zel'dovich case (n{sub S}=1, r=0), albeit in a prior-dependent way. In appendices we describe the CosmoNest code in detail, noting its ability to supply posterior samples as well as to accurately compute the Bayesian evidence. We make a first public release of CosmoNest, now available at www.cosmonest.org.
Hierarchical Models in the Brain
Friston, Karl
2008-01-01
This paper describes a general model that subsumes many parametric models for continuous data. The model comprises hidden layers of state-space or dynamic causal models, arranged so that the output of one provides input to another. The ensuing hierarchy furnishes a model for many types of data, of arbitrary complexity. Special cases range from the general linear model for static data to generalised convolution models, with system noise, for nonlinear time-series analysis. Crucially, all of these models can be inverted using exactly the same scheme, namely, dynamic expectation maximization. This means that a single model and optimisation scheme can be used to invert a wide range of models. We present the model and a brief review of its inversion to disclose the relationships among, apparently, diverse generative models of empirical data. We then show that this inversion can be formulated as a simple neural network and may provide a useful metaphor for inference and learning in the brain. PMID:18989391
A Bayesian model of context-sensitive value attribution
Rigoli, Francesco; Friston, Karl J; Martinelli, Cristina; Selaković, Mirjana; Shergill, Sukhwinder S; Dolan, Raymond J
2016-01-01
Substantial evidence indicates that incentive value depends on an anticipation of rewards within a given context. However, the computations underlying this context sensitivity remain unknown. To address this question, we introduce a normative (Bayesian) account of how rewards map to incentive values. This assumes that the brain inverts a model of how rewards are generated. Key features of our account include (i) an influence of prior beliefs about the context in which rewards are delivered (weighted by their reliability in a Bayes-optimal fashion), (ii) the notion that incentive values correspond to precision-weighted prediction errors, (iii) and contextual information unfolding at different hierarchical levels. This formulation implies that incentive value is intrinsically context-dependent. We provide empirical support for this model by showing that incentive value is influenced by context variability and by hierarchically nested contexts. The perspective we introduce generates new empirical predictions that might help explaining psychopathologies, such as addiction. DOI: http://dx.doi.org/10.7554/eLife.16127.001 PMID:27328323
Bayesian structural equation modeling in sport and exercise psychology.
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.
Hierarchical model of vulnerabilities for emotional disorders.
Norton, Peter J; Mehta, Paras D
2007-01-01
Clark and Watson's (1991) tripartite model of anxiety and depression has had a dramatic impact on our understanding of the dispositional variables underlying emotional disorders. More recently, calls have been made to examine not simply the influence of negative affectivity (NA) but also mediating factors that might better explain how NA influences anxious and depressive syndromes (e.g. Taylor, 1998; Watson, 2005). Extending preliminary projects, this study evaluated two hierarchical models of NA, mediating factors of anxiety sensitivity and intolerance of uncertainty, and specific emotional manifestations. Data provided a very good fit to a model elaborated from preliminary studies, lending further support to hierarchical models of emotional vulnerabilities. Implications for classification and diagnosis are discussed.
Bayesian Nonparametric Models for Multiway Data Analysis.
Xu, Zenglin; Yan, Feng; Qi, Yuan
2015-02-01
Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches-such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)-amount to multi-linear factorization. They are insufficient to model (i) complex interactions between data entities, (ii) various data types (e.g., missing data and binary data), and (iii) noisy observations and outliers. To address these issues, we propose tensor-variate latent nonparametric Bayesian models for multiway data analysis. We name these models InfTucker. These new models essentially conduct Tucker decomposition in an infinite feature space. Unlike classical tensor decomposition models, our new approaches handle both continuous and binary data in a probabilistic framework. Unlike previous Bayesian models on matrices and tensors, our models are based on latent Gaussian or t processes with nonlinear covariance functions. Moreover, on network data, our models reduce to nonparametric stochastic blockmodels and can be used to discover latent groups and predict missing interactions. To learn the models efficiently from data, we develop a variational inference technique and explore properties of the Kronecker product for computational efficiency. Compared with a classical variational implementation, this technique reduces both time and space complexities by several orders of magnitude. On real multiway and network data, our new models achieved significantly higher prediction accuracy than state-of-art tensor decomposition methods and blockmodels.
Neural decoding with hierarchical generative models.
van Gerven, Marcel A J; de Lange, Floris P; Heskes, Tom
2010-12-01
Recent research has shown that reconstruction of perceived images based on hemodynamic response as measured with functional magnetic resonance imaging (fMRI) is starting to become feasible. In this letter, we explore reconstruction based on a learned hierarchy of features by employing a hierarchical generative model that consists of conditional restricted Boltzmann machines. In an unsupervised phase, we learn a hierarchy of features from data, and in a supervised phase, we learn how brain activity predicts the states of those features. Reconstruction is achieved by sampling from the model, conditioned on brain activity. We show that by using the hierarchical generative model, we can obtain good-quality reconstructions of visual images of handwritten digits presented during an fMRI scanning session.
Inference and Hierarchical Modeling in the Social Sciences.
ERIC Educational Resources Information Center
Draper, David
1995-01-01
The use of hierarchical models in social science research is discussed, with emphasis on causal inference and consideration of the limitations of hierarchical models. The increased use of Gibbs sampling and other Markov-chain Monte Carlo methods in the application of hierarchical models is recommended. (SLD)
Pardo, Mario A; Gerrodette, Tim; Beier, Emilio; Gendron, Diane; Forney, Karin A; Chivers, Susan J; Barlow, Jay; Palacios, Daniel M
2015-01-01
We inferred the population densities of blue whales (Balaenoptera musculus) and short-beaked common dolphins (Delphinus delphis) in the Northeast Pacific Ocean as functions of the water-column's physical structure by implementing hierarchical models in a Bayesian framework. This approach allowed us to propagate the uncertainty of the field observations into the inference of species-habitat relationships and to generate spatially explicit population density predictions with reduced effects of sampling heterogeneity. Our hypothesis was that the large-scale spatial distributions of these two cetacean species respond primarily to ecological processes resulting from shoaling and outcropping of the pycnocline in regions of wind-forced upwelling and eddy-like circulation. Physically, these processes affect the thermodynamic balance of the water column, decreasing its volume and thus the height of the absolute dynamic topography (ADT). Biologically, they lead to elevated primary productivity and persistent aggregation of low-trophic-level prey. Unlike other remotely sensed variables, ADT provides information about the structure of the entire water column and it is also routinely measured at high spatial-temporal resolution by satellite altimeters with uniform global coverage. Our models provide spatially explicit population density predictions for both species, even in areas where the pycnocline shoals but does not outcrop (e.g. the Costa Rica Dome and the North Equatorial Countercurrent thermocline ridge). Interannual variations in distribution during El Niño anomalies suggest that the population density of both species decreases dramatically in the Equatorial Cold Tongue and the Costa Rica Dome, and that their distributions retract to particular areas that remain productive, such as the more oceanic waters in the central California Current System, the northern Gulf of California, the North Equatorial Countercurrent thermocline ridge, and the more southern portion of the
Pardo, Mario A.; Gerrodette, Tim; Beier, Emilio; Gendron, Diane; Forney, Karin A.; Chivers, Susan J.; Barlow, Jay; Palacios, Daniel M.
2015-01-01
We inferred the population densities of blue whales (Balaenoptera musculus) and short-beaked common dolphins (Delphinus delphis) in the Northeast Pacific Ocean as functions of the water-column’s physical structure by implementing hierarchical models in a Bayesian framework. This approach allowed us to propagate the uncertainty of the field observations into the inference of species-habitat relationships and to generate spatially explicit population density predictions with reduced effects of sampling heterogeneity. Our hypothesis was that the large-scale spatial distributions of these two cetacean species respond primarily to ecological processes resulting from shoaling and outcropping of the pycnocline in regions of wind-forced upwelling and eddy-like circulation. Physically, these processes affect the thermodynamic balance of the water column, decreasing its volume and thus the height of the absolute dynamic topography (ADT). Biologically, they lead to elevated primary productivity and persistent aggregation of low-trophic-level prey. Unlike other remotely sensed variables, ADT provides information about the structure of the entire water column and it is also routinely measured at high spatial-temporal resolution by satellite altimeters with uniform global coverage. Our models provide spatially explicit population density predictions for both species, even in areas where the pycnocline shoals but does not outcrop (e.g. the Costa Rica Dome and the North Equatorial Countercurrent thermocline ridge). Interannual variations in distribution during El Niño anomalies suggest that the population density of both species decreases dramatically in the Equatorial Cold Tongue and the Costa Rica Dome, and that their distributions retract to particular areas that remain productive, such as the more oceanic waters in the central California Current System, the northern Gulf of California, the North Equatorial Countercurrent thermocline ridge, and the more southern portion of
Barboza, Gia Elise
2016-04-01
This study quantifies the spatiotemporal risk of child abuse and neglect in Los Angeles at the census tract level over a recent 4-year period, identifies areas of increased risk, and evaluates the role of structural disadvantage in substantiated child maltreatment referrals. Child maltreatment data on 83,379 child maltreatment cases in 1,678 census tracts spanning 2006-2009 were obtained from the Los Angeles County Department of Children and Family Services. Substantiated referral counts were analyzed across census tracts with Bayesian hierarchical spatial models using integrated nested Laplace approximations. Results showed that the unadjusted yearly rate of child abuse and neglect held fairly steady over the study period decreasing by only 2.57%. However, the temporal term in the spatiotemporal model reflected a downward trend beginning in 2007. High rates of abuse and neglect were predicted by several neighborhood-level measures of structural burden. Every 1-unit decrease in the social vulnerability index reduced the risk of child abuse and neglect by 98.3% (95% CrI = 1.869-2.1042) while every 1-unit increase in the Black-White dissimilarity index decreased child abuse and neglect risk by 70.6%. The interaction of these variables demonstrated the protective effect of racial heterogeneity in socially vulnerable neighborhoods. No such effect was found in neighborhoods characterized by low levels of vulnerability. Population-based child abuse and neglect prevention and intervention efforts should be aided by the characteristics of neighborhoods that demonstrate strong spatial patterns even after accounting for the role of race and place.
Assessing global vegetation activity using spatio-temporal Bayesian modelling
NASA Astrophysics Data System (ADS)
Mulder, Vera L.; van Eck, Christel M.; Friedlingstein, Pierre; Regnier, Pierre A. G.
2016-04-01
This work demonstrates the potential of modelling vegetation activity using a hierarchical Bayesian spatio-temporal model. This approach allows modelling changes in vegetation and climate simultaneous in space and time. Changes of vegetation activity such as phenology are modelled as a dynamic process depending on climate variability in both space and time. Additionally, differences in observed vegetation status can be contributed to other abiotic ecosystem properties, e.g. soil and terrain properties. Although these properties do not change in time, they do change in space and may provide valuable information in addition to the climate dynamics. The spatio-temporal Bayesian models were calibrated at a regional scale because the local trends in space and time can be better captured by the model. The regional subsets were defined according to the SREX segmentation, as defined by the IPCC. Each region is considered being relatively homogeneous in terms of large-scale climate and biomes, still capturing small-scale (grid-cell level) variability. Modelling within these regions is hence expected to be less uncertain due to the absence of these large-scale patterns, compared to a global approach. This overall modelling approach allows the comparison of model behavior for the different regions and may provide insights on the main dynamic processes driving the interaction between vegetation and climate within different regions. The data employed in this study encompasses the global datasets for soil properties (SoilGrids), terrain properties (Global Relief Model based on SRTM DEM and ETOPO), monthly time series of satellite-derived vegetation indices (GIMMS NDVI3g) and climate variables (Princeton Meteorological Forcing Dataset). The findings proved the potential of a spatio-temporal Bayesian modelling approach for assessing vegetation dynamics, at a regional scale. The observed interrelationships of the employed data and the different spatial and temporal trends support
Hierarchical Bayesian approaches for detecting inconsistency in network meta-analysis.
Zhao, Hong; Hodges, James S; Ma, Haijun; Jiang, Qi; Carlin, Bradley P
2016-09-10
Network meta-analysis (NMA), also known as multiple treatment comparisons, is commonly used to incorporate direct and indirect evidence comparing treatments. With recent advances in methods and software, Bayesian approaches to NMA have become quite popular and allow models of previously unanticipated complexity. However, when direct and indirect evidence differ in an NMA, the model is said to suffer from inconsistency. Current inconsistency detection in NMA is usually based on contrast-based (CB) models; however, this approach has certain limitations. In this work, we propose an arm-based random effects model, where we detect discrepancy of direct and indirect evidence for comparing two treatments using the fixed effects in the model while flagging extreme trials using the random effects. We define discrepancy factors to characterize evidence of inconsistency for particular treatment comparisons, which is novel in NMA research. Our approaches permit users to address issues previously tackled via CB models. We compare sources of inconsistency identified by our approach and existing loop-based CB methods using real and simulated datasets and demonstrate that our methods can offer powerful inconsistency detection. Copyright © 2016 John Wiley & Sons, Ltd.
Bayesian variable selection for latent class models.
Ghosh, Joyee; Herring, Amy H; Siega-Riz, Anna Maria
2011-09-01
In this article, we develop a latent class model with class probabilities that depend on subject-specific covariates. One of our major goals is to identify important predictors of latent classes. We consider methodology that allows estimation of latent classes while allowing for variable selection uncertainty. We propose a Bayesian variable selection approach and implement a stochastic search Gibbs sampler for posterior computation to obtain model-averaged estimates of quantities of interest such as marginal inclusion probabilities of predictors. Our methods are illustrated through simulation studies and application to data on weight gain during pregnancy, where it is of interest to identify important predictors of latent weight gain classes.
A hierarchical nest survival model integrating incomplete temporally varying covariates
Converse, Sarah J; Royle, J Andrew; Adler, Peter H; Urbanek, Richard P; Barzen, Jeb A
2013-01-01
Nest success is a critical determinant of the dynamics of avian populations, and nest survival modeling has played a key role in advancing avian ecology and management. Beginning with the development of daily nest survival models, and proceeding through subsequent extensions, the capacity for modeling the effects of hypothesized factors on nest survival has expanded greatly. We extend nest survival models further by introducing an approach to deal with incompletely observed, temporally varying covariates using a hierarchical model. Hierarchical modeling offers a way to separate process and observational components of demographic models to obtain estimates of the parameters of primary interest, and to evaluate structural effects of ecological and management interest. We built a hierarchical model for daily nest survival to analyze nest data from reintroduced whooping cranes (Grus americana) in the Eastern Migratory Population. This reintroduction effort has been beset by poor reproduction, apparently due primarily to nest abandonment by breeding birds. We used the model to assess support for the hypothesis that nest abandonment is caused by harassment from biting insects. We obtained indices of blood-feeding insect populations based on the spatially interpolated counts of insects captured in carbon dioxide traps. However, insect trapping was not conducted daily, and so we had incomplete information on a temporally variable covariate of interest. We therefore supplemented our nest survival model with a parallel model for estimating the values of the missing insect covariates. We used Bayesian model selection to identify the best predictors of daily nest survival. Our results suggest that the black fly Simulium annulus may be negatively affecting nest survival of reintroduced whooping cranes, with decreasing nest survival as abundance of S. annulus increases. The modeling framework we have developed will be applied in the future to a larger data set to evaluate the
A hierarchical nest survival model integrating incomplete temporally varying covariates.
Converse, Sarah J; Royle, J Andrew; Adler, Peter H; Urbanek, Richard P; Barzen, Jeb A
2013-11-01
Nest success is a critical determinant of the dynamics of avian populations, and nest survival modeling has played a key role in advancing avian ecology and management. Beginning with the development of daily nest survival models, and proceeding through subsequent extensions, the capacity for modeling the effects of hypothesized factors on nest survival has expanded greatly. We extend nest survival models further by introducing an approach to deal with incompletely observed, temporally varying covariates using a hierarchical model. Hierarchical modeling offers a way to separate process and observational components of demographic models to obtain estimates of the parameters of primary interest, and to evaluate structural effects of ecological and management interest. We built a hierarchical model for daily nest survival to analyze nest data from reintroduced whooping cranes (Grus americana) in the Eastern Migratory Population. This reintroduction effort has been beset by poor reproduction, apparently due primarily to nest abandonment by breeding birds. We used the model to assess support for the hypothesis that nest abandonment is caused by harassment from biting insects. We obtained indices of blood-feeding insect populations based on the spatially interpolated counts of insects captured in carbon dioxide traps. However, insect trapping was not conducted daily, and so we had incomplete information on a temporally variable covariate of interest. We therefore supplemented our nest survival model with a parallel model for estimating the values of the missing insect covariates. We used Bayesian model selection to identify the best predictors of daily nest survival. Our results suggest that the black fly Simulium annulus may be negatively affecting nest survival of reintroduced whooping cranes, with decreasing nest survival as abundance of S. annulus increases. The modeling framework we have developed will be applied in the future to a larger data set to evaluate the
A hierarchical nest survival model integrating incomplete temporally varying covariates
Converse, Sarah J.; Royle, J. Andrew; Adler, Peter H.; Urbanek, Richard P.; Barzan, Jeb A.
2013-01-01
Nest success is a critical determinant of the dynamics of avian populations, and nest survival modeling has played a key role in advancing avian ecology and management. Beginning with the development of daily nest survival models, and proceeding through subsequent extensions, the capacity for modeling the effects of hypothesized factors on nest survival has expanded greatly. We extend nest survival models further by introducing an approach to deal with incompletely observed, temporally varying covariates using a hierarchical model. Hierarchical modeling offers a way to separate process and observational components of demographic models to obtain estimates of the parameters of primary interest, and to evaluate structural effects of ecological and management interest. We built a hierarchical model for daily nest survival to analyze nest data from reintroduced whooping cranes (Grus americana) in the Eastern Migratory Population. This reintroduction effort has been beset by poor reproduction, apparently due primarily to nest abandonment by breeding birds. We used the model to assess support for the hypothesis that nest abandonment is caused by harassment from biting insects. We obtained indices of blood-feeding insect populations based on the spatially interpolated counts of insects captured in carbon dioxide traps. However, insect trapping was not conducted daily, and so we had incomplete information on a temporally variable covariate of interest. We therefore supplemented our nest survival model with a parallel model for estimating the values of the missing insect covariates. We used Bayesian model selection to identify the best predictors of daily nest survival. Our results suggest that the black fly Simulium annulus may be negatively affecting nest survival of reintroduced whooping cranes, with decreasing nest survival as abundance of S. annulus increases. The modeling framework we have developed will be applied in the future to a larger data set to evaluate the
ERIC Educational Resources Information Center
Zhang, Zhidong
2016-01-01
This study explored an alternative assessment procedure to examine learning trajectories of matrix multiplication. It took rule-based analytical and cognitive task analysis methods specifically to break down operation rules for a given matrix multiplication. Based on the analysis results, a hierarchical Bayesian network, an assessment model,…
A Bayesian Shrinkage Approach for AMMI Models
de Oliveira, Luciano Antonio; Nuvunga, Joel Jorge; Pamplona, Andrezza Kéllen Alves
2015-01-01
Linear-bilinear models, especially the additive main effects and multiplicative interaction (AMMI) model, are widely applicable to genotype-by-environment interaction (GEI) studies in plant breeding programs. These models allow a parsimonious modeling of GE interactions, retaining a small number of principal components in the analysis. However, one aspect of the AMMI model that is still debated is the selection criteria for determining the number of multiplicative terms required to describe the GE interaction pattern. Shrinkage estimators have been proposed as selection criteria for the GE interaction components. In this study, a Bayesian approach was combined with the AMMI model with shrinkage estimators for the principal components. A total of 55 maize genotypes were evaluated in nine different environments using a complete blocks design with three replicates. The results show that the traditional Bayesian AMMI model produces low shrinkage of singular values but avoids the usual pitfalls in determining the credible intervals in the biplot. On the other hand, Bayesian shrinkage AMMI models have difficulty with the credible interval for model parameters, but produce stronger shrinkage of the principal components, converging to GE matrices that have more shrinkage than those obtained using mixed models. This characteristic allowed more parsimonious models to be chosen, and resulted in models being selected that were similar to those obtained by the Cornelius F-test (α = 0.05) in traditional AMMI models and cross validation based on leave-one-out. This characteristic allowed more parsimonious models to be chosen and more GEI pattern retained on the first two components. The resulting model chosen by posterior distribution of singular value was also similar to those produced by the cross-validation approach in traditional AMMI models. Our method enables the estimation of credible interval for AMMI biplot plus the choice of AMMI model based on direct posterior
A Bayesian Shrinkage Approach for AMMI Models.
da Silva, Carlos Pereira; de Oliveira, Luciano Antonio; Nuvunga, Joel Jorge; Pamplona, Andrezza Kéllen Alves; Balestre, Marcio
2015-01-01
Linear-bilinear models, especially the additive main effects and multiplicative interaction (AMMI) model, are widely applicable to genotype-by-environment interaction (GEI) studies in plant breeding programs. These models allow a parsimonious modeling of GE interactions, retaining a small number of principal components in the analysis. However, one aspect of the AMMI model that is still debated is the selection criteria for determining the number of multiplicative terms required to describe the GE interaction pattern. Shrinkage estimators have been proposed as selection criteria for the GE interaction components. In this study, a Bayesian approach was combined with the AMMI model with shrinkage estimators for the principal components. A total of 55 maize genotypes were evaluated in nine different environments using a complete blocks design with three replicates. The results show that the traditional Bayesian AMMI model produces low shrinkage of singular values but avoids the usual pitfalls in determining the credible intervals in the biplot. On the other hand, Bayesian shrinkage AMMI models have difficulty with the credible interval for model parameters, but produce stronger shrinkage of the principal components, converging to GE matrices that have more shrinkage than those obtained using mixed models. This characteristic allowed more parsimonious models to be chosen, and resulted in models being selected that were similar to those obtained by the Cornelius F-test (α = 0.05) in traditional AMMI models and cross validation based on leave-one-out. This characteristic allowed more parsimonious models to be chosen and more GEI pattern retained on the first two components. The resulting model chosen by posterior distribution of singular value was also similar to those produced by the cross-validation approach in traditional AMMI models. Our method enables the estimation of credible interval for AMMI biplot plus the choice of AMMI model based on direct posterior
Bayesian analysis of a reduced-form air quality model.
Foley, Kristen M; Reich, Brian J; Napelenok, Sergey L
2012-07-17
Numerical air quality models are being used for assessing emission control strategies for improving ambient pollution levels across the globe. This paper applies probabilistic modeling to evaluate the effectiveness of emission reduction scenarios aimed at lowering ground-level ozone concentrations. A Bayesian hierarchical model is used to combine air quality model output and monitoring data in order to characterize the impact of emissions reductions while accounting for different degrees of uncertainty in the modeled emissions inputs. The probabilistic model predictions are weighted based on population density in order to better quantify the societal benefits/disbenefits of four hypothetical emission reduction scenarios in which domain-wide NO(x) emissions from various sectors are reduced individually and then simultaneously. Cross validation analysis shows the statistical model performs well compared to observed ozone levels. Accounting for the variability and uncertainty in the emissions and atmospheric systems being modeled is shown to impact how emission reduction scenarios would be ranked, compared to standard methodology.
An Accessible Method for Implementing Hierarchical Models with Spatio-Temporal Abundance Data
Ross, Beth E.; Hooten, Mevin B.; Koons, David N.
2012-01-01
A common goal in ecology and wildlife management is to determine the causes of variation in population dynamics over long periods of time and across large spatial scales. Many assumptions must nevertheless be overcome to make appropriate inference about spatio-temporal variation in population dynamics, such as autocorrelation among data points, excess zeros, and observation error in count data. To address these issues, many scientists and statisticians have recommended the use of Bayesian hierarchical models. Unfortunately, hierarchical statistical models remain somewhat difficult to use because of the necessary quantitative background needed to implement them, or because of the computational demands of using Markov Chain Monte Carlo algorithms to estimate parameters. Fortunately, new tools have recently been developed that make it more feasible for wildlife biologists to fit sophisticated hierarchical Bayesian models (i.e., Integrated Nested Laplace Approximation, ‘INLA’). We present a case study using two important game species in North America, the lesser and greater scaup, to demonstrate how INLA can be used to estimate the parameters in a hierarchical model that decouples observation error from process variation, and accounts for unknown sources of excess zeros as well as spatial and temporal dependence in the data. Ultimately, our goal was to make unbiased inference about spatial variation in population trends over time. PMID:23166658
An accessible method for implementing hierarchical models with spatio-temporal abundance data
Ross, Beth E.; Hooten, Melvin B.; Koons, David N.
2012-01-01
A common goal in ecology and wildlife management is to determine the causes of variation in population dynamics over long periods of time and across large spatial scales. Many assumptions must nevertheless be overcome to make appropriate inference about spatio-temporal variation in population dynamics, such as autocorrelation among data points, excess zeros, and observation error in count data. To address these issues, many scientists and statisticians have recommended the use of Bayesian hierarchical models. Unfortunately, hierarchical statistical models remain somewhat difficult to use because of the necessary quantitative background needed to implement them, or because of the computational demands of using Markov Chain Monte Carlo algorithms to estimate parameters. Fortunately, new tools have recently been developed that make it more feasible for wildlife biologists to fit sophisticated hierarchical Bayesian models (i.e., Integrated Nested Laplace Approximation, ‘INLA’). We present a case study using two important game species in North America, the lesser and greater scaup, to demonstrate how INLA can be used to estimate the parameters in a hierarchical model that decouples observation error from process variation, and accounts for unknown sources of excess zeros as well as spatial and temporal dependence in the data. Ultimately, our goal was to make unbiased inference about spatial variation in population trends over time.
Burn, Robert W; Underwood, Fiona M; Blanc, Julian
2011-01-01
Elephant poaching and the ivory trade remain high on the agenda at meetings of the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES). Well-informed debates require robust estimates of trends, the spatial distribution of poaching, and drivers of poaching. We present an analysis of trends and drivers of an indicator of elephant poaching of all elephant species. The site-based monitoring system known as Monitoring the Illegal Killing of Elephants (MIKE), set up by the 10(th) Conference of the Parties of CITES in 1997, produces carcass encounter data reported mainly by anti-poaching patrols. Data analyzed were site by year totals of 6,337 carcasses from 66 sites in Africa and Asia from 2002-2009. Analysis of these observational data is a serious challenge to traditional statistical methods because of the opportunistic and non-random nature of patrols, and the heterogeneity across sites. Adopting a bayesian hierarchical modeling approach, we used the proportion of carcasses that were illegally killed (PIKE) as a poaching index, to estimate the trend and the effects of site- and country-level factors associated with poaching. Important drivers of illegal killing that emerged at country level were poor governance and low levels of human development, and at site level, forest cover and area of the site in regions where human population density is low. After a drop from 2002, PIKE remained fairly constant from 2003 until 2006, after which it increased until 2008. The results for 2009 indicate a decline. Sites with PIKE ranging from the lowest to the highest were identified. The results of the analysis provide a sound information base for scientific evidence-based decision making in the CITES process.
Sinclair, Alison; Xie, Xuanqian; Saab, Lama; Dendukuri, Nandini
2016-01-01
Background: Recent meta-analyses of the efficacy of probiotics for preventing diarrhea associated with Clostridium difficile have concluded there is a large effect favouring probiotics. We reexamined this evidence, which contradicts the results of a more recent large randomized controlled trial that found no benefit of Lactobacillus probiotics for preventing C. difficile-associated diarrhea. Methods: We performed a systematic review of the efficacy of treatment with Lactobacillus probiotics for preventing nosocomial C. difficile-associated diarrhea in adults and carried out a meta-analysis using a Bayesian hierarchical model. We used credibility analysis and meta-regression to characterize the heterogeneity between studies. Results: Ten studies met our inclusion criteria. The pooled risk ratio was highly statistically significant, at 0.25 (95% credible interval 0.08-0.47). However, the 95% prediction interval for the risk ratio in a future study, 0.02-1.34, was wider than the credible interval, owing to heterogeneity between studies. Furthermore, a credibility analysis showed that the strength of the evidence was weaker than the observed number of cases of C. difficile-associated diarrhea across studies would suggest. Meta-regression suggested that the beneficial effect of probiotics was more likely to be reported in studies with an increased risk of C. difficile-associated diarrhea in the control group, although this association was not statistically significant. Interpretation: Accounting for between-study heterogeneity showed that there is considerable uncertainty regarding the apparently large efficacy estimate associated with Lactobacillus probiotic treatment in preventing C. difficile-associated diarrhea. Most studies to date have been carried out in populations with a low risk of C. difficile-associated diarrhea, such that the evidence is inconclusive and inadequate to support a policy concerning routine use of probiotics in to prevent this condition. PMID
Burn, Robert W.; Underwood, Fiona M.; Blanc, Julian
2011-01-01
Elephant poaching and the ivory trade remain high on the agenda at meetings of the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES). Well-informed debates require robust estimates of trends, the spatial distribution of poaching, and drivers of poaching. We present an analysis of trends and drivers of an indicator of elephant poaching of all elephant species. The site-based monitoring system known as Monitoring the Illegal Killing of Elephants (MIKE), set up by the 10th Conference of the Parties of CITES in 1997, produces carcass encounter data reported mainly by anti-poaching patrols. Data analyzed were site by year totals of 6,337 carcasses from 66 sites in Africa and Asia from 2002–2009. Analysis of these observational data is a serious challenge to traditional statistical methods because of the opportunistic and non-random nature of patrols, and the heterogeneity across sites. Adopting a Bayesian hierarchical modeling approach, we used the proportion of carcasses that were illegally killed (PIKE) as a poaching index, to estimate the trend and the effects of site- and country-level factors associated with poaching. Important drivers of illegal killing that emerged at country level were poor governance and low levels of human development, and at site level, forest cover and area of the site in regions where human population density is low. After a drop from 2002, PIKE remained fairly constant from 2003 until 2006, after which it increased until 2008. The results for 2009 indicate a decline. Sites with PIKE ranging from the lowest to the highest were identified. The results of the analysis provide a sound information base for scientific evidence-based decision making in the CITES process. PMID:21912670
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…
Nonparametric Bayesian inference of the microcanonical stochastic block model
NASA Astrophysics Data System (ADS)
Peixoto, Tiago P.
2017-01-01
A principled approach to characterize the hidden modular structure of networks is to formulate generative models and then infer their parameters from data. When the desired structure is composed of modules or "communities," a suitable choice for this task is the stochastic block model (SBM), where nodes are divided into groups, and the placement of edges is conditioned on the group memberships. Here, we present a nonparametric Bayesian method to infer the modular structure of empirical networks, including the number of modules and their hierarchical organization. We focus on a microcanonical variant of the SBM, where the structure is imposed via hard constraints, i.e., the generated networks are not allowed to violate the patterns imposed by the model. We show how this simple model variation allows simultaneously for two important improvements over more traditional inference approaches: (1) deeper Bayesian hierarchies, with noninformative priors replaced by sequences of priors and hyperpriors, which not only remove limitations that seriously degrade the inference on large networks but also reveal structures at multiple scales; (2) a very efficient inference algorithm that scales well not only for networks with a large number of nodes and edges but also with an unlimited number of modules. We show also how this approach can be used to sample modular hierarchies from the posterior distribution, as well as to perform model selection. We discuss and analyze the differences between sampling from the posterior and simply finding the single parameter estimate that maximizes it. Furthermore, we expose a direct equivalence between our microcanonical approach and alternative derivations based on the canonical SBM.
Model feedback in Bayesian propensity score estimation.
Zigler, Corwin M; Watts, Krista; Yeh, Robert W; Wang, Yun; Coull, Brent A; Dominici, Francesca
2013-03-01
Methods based on the propensity score comprise one set of valuable tools for comparative effectiveness research and for estimating causal effects more generally. These methods typically consist of two distinct stages: (1) a propensity score stage where a model is fit to predict the propensity to receive treatment (the propensity score), and (2) an outcome stage where responses are compared in treated and untreated units having similar values of the estimated propensity score. Traditional techniques conduct estimation in these two stages separately; estimates from the first stage are treated as fixed and known for use in the second stage. Bayesian methods have natural appeal in these settings because separate likelihoods for the two stages can be combined into a single joint likelihood, with estimation of the two stages carried out simultaneously. One key feature of joint estimation in this context is "feedback" between the outcome stage and the propensity score stage, meaning that quantities in a model for the outcome contribute information to posterior distributions of quantities in the model for the propensity score. We provide a rigorous assessment of Bayesian propensity score estimation to show that model feedback can produce poor estimates of causal effects absent strategies that augment propensity score adjustment with adjustment for individual covariates. We illustrate this phenomenon with a simulation study and with a comparative effectiveness investigation of carotid artery stenting versus carotid endarterectomy among 123,286 Medicare beneficiaries hospitlized for stroke in 2006 and 2007.
Experience With Bayesian Image Based Surface Modeling
NASA Technical Reports Server (NTRS)
Stutz, John C.
2005-01-01
Bayesian surface modeling from images requires modeling both the surface and the image generation process, in order to optimize the models by comparing actual and generated images. Thus it differs greatly, both conceptually and in computational difficulty, from conventional stereo surface recovery techniques. But it offers the possibility of using any number of images, taken under quite different conditions, and by different instruments that provide independent and often complementary information, to generate a single surface model that fuses all available information. I describe an implemented system, with a brief introduction to the underlying mathematical models and the compromises made for computational efficiency. I describe successes and failures achieved on actual imagery, where we went wrong and what we did right, and how our approach could be improved. Lastly I discuss how the same approach can be extended to distinct types of instruments, to achieve true sensor fusion.
NASA Astrophysics Data System (ADS)
Ogle, Kiona; Ryan, Edmund; Dijkstra, Feike A.; Pendall, Elise
2016-12-01
Nonsteady state chambers are often employed to measure soil CO2 fluxes. CO2 concentrations (C) in the headspace are sampled at different times (t), and fluxes (f) are calculated from regressions of C versus t based on a limited number of observations. Variability in the data can lead to poor fits and unreliable f estimates; groups with too few observations or poor fits are often discarded, resulting in "missing" f values. We solve these problems by fitting linear (steady state) and nonlinear (nonsteady state, diffusion based) models of C versus t, within a hierarchical Bayesian framework. Data are from the Prairie Heating and CO2 Enrichment study that manipulated atmospheric CO2, temperature, soil moisture, and vegetation. CO2 was collected from static chambers biweekly during five growing seasons, resulting in >12,000 samples and >3100 groups and associated fluxes. We compare f estimates based on nonhierarchical and hierarchical Bayesian (B versus HB) versions of the linear and diffusion-based (L versus D) models, resulting in four different models (BL, BD, HBL, and HBD). Three models fit the data exceptionally well (R2 ≥ 0.98), but the BD model was inferior (R2 = 0.87). The nonhierarchical models (BL and BD) produced highly uncertain f estimates (wide 95% credible intervals), whereas the hierarchical models (HBL and HBD) produced very precise estimates. Of the hierarchical versions, the linear model (HBL) underestimated f by 33% relative to the nonsteady state model (HBD). The hierarchical models offer improvements upon traditional nonhierarchical approaches to estimating f, and we provide example code for the models.
Royle, J. Andrew; Dorazio, Robert M.
2008-01-01
A guide to data collection, modeling and inference strategies for biological survey data using Bayesian and classical statistical methods. This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical models, with a strict focus on the use of probability models and parametric inference. Hierarchical models represent a paradigm shift in the application of statistics to ecological inference problems because they combine explicit models of ecological system structure or dynamics with models of how ecological systems are observed. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community, and metacommunity systems. The book provides the first synthetic treatment of many recent methodological advances in ecological modeling and unifies disparate methods and procedures. The authors apply principles of hierarchical modeling to ecological problems, including * occurrence or occupancy models for estimating species distribution * abundance models based on many sampling protocols, including distance sampling * capture-recapture models with individual effects * spatial capture-recapture models based on camera trapping and related methods * population and metapopulation dynamic models * models of biodiversity, community structure and dynamics.
NASA Astrophysics Data System (ADS)
Wang, Li; Gac, Nicolas; Mohammad-Djafari, Ali
2015-01-01
In order to improve quality of 3D X-ray tomography reconstruction for Non Destructive Testing (NDT), we investigate in this paper hierarchical Bayesian methods. In NDT, useful prior information on the volume like the limited number of materials or the presence of homogeneous area can be included in the iterative reconstruction algorithms. In hierarchical Bayesian methods, not only the volume is estimated thanks to the prior model of the volume but also the hyper parameters of this prior. This additional complexity in the reconstruction methods when applied to large volumes (from 5123 to 81923 voxels) results in an increasing computational cost. To reduce it, the hierarchical Bayesian methods investigated in this paper lead to an algorithm acceleration by Variational Bayesian Approximation (VBA) [1] and hardware acceleration thanks to projection and back-projection operators paralleled on many core processors like GPU [2]. In this paper, we will consider a Student-t prior on the gradient of the image implemented in a hierarchical way [3, 4, 1]. Operators H (forward or projection) and Ht (adjoint or back-projection) implanted in multi-GPU [2] have been used in this study. Different methods will be evalued on synthetic volume "Shepp and Logan" in terms of quality and time of reconstruction. We used several simple regularizations of order 1 and order 2. Other prior models also exists [5]. Sometimes for a discrete image, we can do the segmentation and reconstruction at the same time, then the reconstruction can be done with less projections.
Genome Scans for Detecting Footprints of Local Adaptation Using a Bayesian Factor Model
Duforet-Frebourg, Nicolas; Bazin, Eric; Blum, Michael G.B.
2014-01-01
There is a considerable impetus in population genomics to pinpoint loci involved in local adaptation. A powerful approach to find genomic regions subject to local adaptation is to genotype numerous molecular markers and look for outlier loci. One of the most common approaches for selection scans is based on statistics that measure population differentiation such as FST. However, there are important caveats with approaches related to FST because they require grouping individuals into populations and they additionally assume a particular model of population structure. Here, we implement a more flexible individual-based approach based on Bayesian factor models. Factor models capture population structure with latent variables called factors, which can describe clustering of individuals into populations or isolation-by-distance patterns. Using hierarchical Bayesian modeling, we both infer population structure and identify outlier loci that are candidates for local adaptation. In order to identify outlier loci, the hierarchical factor model searches for loci that are atypically related to population structure as measured by the latent factors. In a model of population divergence, we show that it can achieve a 2-fold or more reduction of false discovery rate compared with the software BayeScan or with an FST approach. We show that our software can handle large data sets by analyzing the single nucleotide polymorphisms of the Human Genome Diversity Project. The Bayesian factor model is implemented in the open-source PCAdapt software. PMID:24899666
Hopes and Cautions in Implementing Bayesian Structural Equation Modeling
ERIC Educational Resources Information Center
MacCallum, Robert C.; Edwards, Michael C.; Cai, Li
2012-01-01
Muthen and Asparouhov (2012) have proposed and demonstrated an approach to model specification and estimation in structural equation modeling (SEM) using Bayesian methods. Their contribution builds on previous work in this area by (a) focusing on the translation of conventional SEM models into a Bayesian framework wherein parameters fixed at zero…
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
A Bayesian Model of Category-Specific Emotional Brain Responses
Wager, Tor D.; Kang, Jian; Johnson, Timothy D.; Nichols, Thomas E.; Satpute, Ajay B.; Barrett, Lisa Feldman
2015-01-01
Understanding emotion is critical for a science of healthy and disordered brain function, but the neurophysiological basis of emotional experience is still poorly understood. We analyzed human brain activity patterns from 148 studies of emotion categories (2159 total participants) using a novel hierarchical Bayesian model. The model allowed us to classify which of five categories—fear, anger, disgust, sadness, or happiness—is engaged by a study with 66% accuracy (43-86% across categories). Analyses of the activity patterns encoded in the model revealed that each emotion category is associated with unique, prototypical patterns of activity across multiple brain systems including the cortex, thalamus, amygdala, and other structures. The results indicate that emotion categories are not contained within any one region or system, but are represented as configurations across multiple brain networks. The model provides a precise summary of the prototypical patterns for each emotion category, and demonstrates that a sufficient characterization of emotion categories relies on (a) differential patterns of involvement in neocortical systems that differ between humans and other species, and (b) distinctive patterns of cortical-subcortical interactions. Thus, these findings are incompatible with several contemporary theories of emotion, including those that emphasize emotion-dedicated brain systems and those that propose emotion is localized primarily in subcortical activity. They are consistent with componential and constructionist views, which propose that emotions are differentiated by a combination of perceptual, mnemonic, prospective, and motivational elements. Such brain-based models of emotion provide a foundation for new translational and clinical approaches. PMID:25853490
Bayesian spatio-temporal modeling of particulate matter concentrations in Peninsular Malaysia
NASA Astrophysics Data System (ADS)
Manga, Edna; Awang, Norhashidah
2016-06-01
This article presents an application of a Bayesian spatio-temporal Gaussian process (GP) model on particulate matter concentrations from Peninsular Malaysia. We analyze daily PM10 concentration levels from 35 monitoring sites in June and July 2011. The spatiotemporal model set in a Bayesian hierarchical framework allows for inclusion of informative covariates, meteorological variables and spatiotemporal interactions. Posterior density estimates of the model parameters are obtained by Markov chain Monte Carlo methods. Preliminary data analysis indicate information on PM10 levels at sites classified as industrial locations could explain part of the space time variations. We include the site-type indicator in our modeling efforts. Results of the parameter estimates for the fitted GP model show significant spatio-temporal structure and positive effect of the location-type explanatory variable. We also compute some validation criteria for the out of sample sites that show the adequacy of the model for predicting PM10 at unmonitored sites.
Effect on Prediction when Modeling Covariates in Bayesian Nonparametric Models.
Cruz-Marcelo, Alejandro; Rosner, Gary L; Müller, Peter; Stewart, Clinton F
2013-04-01
In biomedical research, it is often of interest to characterize biologic processes giving rise to observations and to make predictions of future observations. Bayesian nonparametric methods provide a means for carrying out Bayesian inference making as few assumptions about restrictive parametric models as possible. There are several proposals in the literature for extending Bayesian nonparametric models to include dependence on covariates. Limited attention, however, has been directed to the following two aspects. In this article, we examine the effect on fitting and predictive performance of incorporating covariates in a class of Bayesian nonparametric models by one of two primary ways: either in the weights or in the locations of a discrete random probability measure. We show that different strategies for incorporating continuous covariates in Bayesian nonparametric models can result in big differences when used for prediction, even though they lead to otherwise similar posterior inferences. When one needs the predictive density, as in optimal design, and this density is a mixture, it is better to make the weights depend on the covariates. We demonstrate these points via a simulated data example and in an application in which one wants to determine the optimal dose of an anticancer drug used in pediatric oncology.
Bayesian spatially dependent variable selection for small area health modeling.
Choi, Jungsoon; Lawson, Andrew B
2016-06-16
Statistical methods for spatial health data to identify the significant covariates associated with the health outcomes are of critical importance. Most studies have developed variable selection approaches in which the covariates included appear within the spatial domain and their effects are fixed across space. However, the impact of covariates on health outcomes may change across space and ignoring this behavior in spatial epidemiology may cause the wrong interpretation of the relations. Thus, the development of a statistical framework for spatial variable selection is important to allow for the estimation of the space-varying patterns of covariate effects as well as the early detection of disease over space. In this paper, we develop flexible spatial variable selection approaches to find the spatially-varying subsets of covariates with significant effects. A Bayesian hierarchical latent model framework is applied to account for spatially-varying covariate effects. We present a simulation example to examine the performance of the proposed models with the competing models. We apply our models to a county-level low birth weight incidence dataset in Georgia.
Merging Digital Surface Models Implementing Bayesian Approaches
NASA Astrophysics Data System (ADS)
Sadeq, H.; Drummond, J.; Li, Z.
2016-06-01
In this research different DSMs from different sources have been merged. The merging is based on a probabilistic model using a Bayesian Approach. The implemented data have been sourced from very high resolution satellite imagery sensors (e.g. WorldView-1 and Pleiades). It is deemed preferable to use a Bayesian Approach when the data obtained from the sensors are limited and it is difficult to obtain many measurements or it would be very costly, thus the problem of the lack of data can be solved by introducing a priori estimations of data. To infer the prior data, it is assumed that the roofs of the buildings are specified as smooth, and for that purpose local entropy has been implemented. In addition to the a priori estimations, GNSS RTK measurements have been collected in the field which are used as check points to assess the quality of the DSMs and to validate the merging result. The model has been applied in the West-End of Glasgow containing different kinds of buildings, such as flat roofed and hipped roofed buildings. Both quantitative and qualitative methods have been employed to validate the merged DSM. The validation results have shown that the model was successfully able to improve the quality of the DSMs and improving some characteristics such as the roof surfaces, which consequently led to better representations. In addition to that, the developed model has been compared with the well established Maximum Likelihood model and showed similar quantitative statistical results and better qualitative results. Although the proposed model has been applied on DSMs that were derived from satellite imagery, it can be applied to any other sourced DSMs.
Cressie, Noel; Calder, Catherine A; Clark, James S; Ver Hoef, Jay M; Wikle, Christopher K
2009-04-01
Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises.
A Bayesian Analysis of Finite Mixtures in the LISREL Model.
ERIC Educational Resources Information Center
Zhu, Hong-Tu; Lee, Sik-Yum
2001-01-01
Proposes a Bayesian framework for estimating finite mixtures of the LISREL model. The model augments the observed data of the manifest variables with the latent variables and allocation variables and uses the Gibbs sampler to obtain the Bayesian solution. Discusses other associated statistical inferences. (SLD)
Bayesian model of Snellen visual acuity.
Nestares, Oscar; Navarro, Rafael; Antona, Beatriz
2003-07-01
A Bayesian model of Snellen visual acuity (VA) has been developed that, as far as we know, is the first one that includes the three main stages of VA: (1) optical degradations, (2) neural image representation and contrast thresholding, and (3) character recognition. The retinal image of a Snellen test chart is obtained from experimental wave-aberration data. Then a subband image decomposition with a set of visual channels tuned to different spatial frequencies and orientations is applied to the retinal image, as in standard computational models of early cortical image representation. A neural threshold is applied to the contrast responses to include the effect of the neural contrast sensitivity. The resulting image representation is the base of a Bayesian pattern-recognition method robust to the presence of optical aberrations. The model is applied to images containing sets of letter optotypes at different scales, and the number of correct answers is obtained at each scale; the final output is the decimal Snellen VA. The model has no free parameters to adjust. The main input data are the eye's optical aberrations, and standard values are used for all other parameters, including the Stiles-Crawford effect, visual channels, and neural contrast threshold, when no subject specific values are available. When aberrations are large, Snellen VA involving pattern recognition differs from grating acuity, which is based on a simpler detection (or orientation-discrimination) task and hence is basically unaffected by phase distortions introduced by the optical transfer function. A preliminary test of the model in one subject produced close agreement between actual measurements and predicted VA values. Two examples are also included: (1) application of the method to the prediction of the VAin refractive-surgery patients and (2) simulation of the VA attainable by correcting ocular aberrations.
NASA Astrophysics Data System (ADS)
Urban, Michael A.; Nelson, David M.; Kelly, Ryan; Ibrahim, Tahir; Dietze, Michael; Pearson, Ann; Hu, Feng Sheng
2013-11-01
Differentiating C3 and C4 grass pollen in the paleorecord is difficult because of their morphological similarity. Using a spooling wire microcombustion device interfaced with an isotope ratio mass spectrometer, Single Pollen Isotope Ratio AnaLysis (SPIRAL) enables classification of grass pollen as C3 or C4 based upon δ13C values. To address several limitations of this novel technique, we expanded an existing SPIRAL training dataset of pollen δ13C data from 8 to 31 grass species. For field validation, we analyzed δ13C of individual grains of grass pollen from the surface sediments of 15 lakes in Africa and Australia, added these results to a prior dataset of 10 lakes from North America, and compared C4-pollen abundance in surface sediments with C4-grass abundance on the surrounding landscape. We also developed and tested a hierarchical Bayesian model to estimate the relative abundance of C3- and C4-grass pollen in unknown samples, including an estimation of the likelihood that either pollen type is present in a sample. The mean (±SD) δ13C values for the C3 and C4 grasses in the training dataset were -29.6 ± 9.5‰ and -13.8 ± 9.5‰, respectively. Across a range of % C4 in samples of known composition, the average bias of the Bayesian model was <3% for C4 in samples of at least 50 grains, indicating that the model accurately predicted the relative abundance of C4 grass pollen. The hierarchical framework of the model resulted in less bias than a previous threshold-based C3/C4 classification method, especially near the high or low extremes of C4 abundance. In addition, the percent of C4 grass pollen in surface-sediment samples estimated using the model was strongly related to the abundance of C4 grasses on the landscape (n = 24, p < 0.001, r2 = 0.65). These results improve δ13C-based quantitative reconstructions of grass community composition in the paleorecord and demonstrate the utility of the Bayesian framework to aid the interpretation of stable isotope
NASA Technical Reports Server (NTRS)
He, Yuning
2015-01-01
The behavior of complex aerospace systems is governed by numerous parameters. For safety analysis it is important to understand how the system behaves with respect to these parameter values. In particular, understanding the boundaries between safe and unsafe regions is of major importance. In this paper, we describe a hierarchical Bayesian statistical modeling approach for the online detection and characterization of such boundaries. Our method for classification with active learning uses a particle filter-based model and a boundary-aware metric for best performance. From a library of candidate shapes incorporated with domain expert knowledge, the location and parameters of the boundaries are estimated using advanced Bayesian modeling techniques. The results of our boundary analysis are then provided in a form understandable by the domain expert. We illustrate our approach using a simulation model of a NASA neuro-adaptive flight control system, as well as a system for the detection of separation violations in the terminal airspace.
Partially linear models with autoregressive scale-mixtures of normal errors: A Bayesian approach
NASA Astrophysics Data System (ADS)
Ferreira, Guillermo; Castro, Mauricio; Lachos, Victor H.
2012-10-01
Normality and independence of error terms is a typical assumption for partial linear models. However, such an assumption may be unrealistic on many fields such as economics, finance and biostatistics. In this paper, we develop a Bayesian analysis for partial linear model with first-order autoregressive errors belonging to the class of scale mixtures of normal (SMN) distributions. The proposed model provides a useful generalization of the symmetrical linear regression models with independent error, since the error distribution cover both correlated and thick-tailed distribution, and has a convenient hierarchical representation allowing to us an easily implementation of a Markov chain Monte Carlo (MCMC) scheme. In order to examine the robustness of this distribution against outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler (K-L) divergence. The proposed methodology is applied to the Cuprum Company monthly returns.
Bayesian Modeling of Haplotype Effects in Multiparent Populations
Zhang, Zhaojun; Wang, Wei; Valdar, William
2014-01-01
A general Bayesian model, Diploffect, is described for estimating the effects of founder haplotypes at quantitative trait loci (QTL) detected in multiparental genetic populations; such populations include the Collaborative Cross (CC), Heterogeneous Socks (HS), and many others for which local genetic variation is well described by an underlying, usually probabilistically inferred, haplotype mosaic. Our aim is to provide a framework for coherent estimation of haplotype and diplotype (haplotype pair) effects that takes into account the following: uncertainty in haplotype composition for each individual; uncertainty arising from small sample sizes and infrequently observed haplotype combinations; possible effects of dominance (for noninbred subjects); genetic background; and that provides a means to incorporate data that may be incomplete or has a hierarchical structure. Using the results of a probabilistic haplotype reconstruction as prior information, we obtain posterior distributions at the QTL for both haplotype effects and haplotype composition. Two alternative computational approaches are supplied: a Markov chain Monte Carlo sampler and a procedure based on importance sampling of integrated nested Laplace approximations. Using simulations of QTL in the incipient CC (pre-CC) and Northport HS populations, we compare the accuracy of Diploffect, approximations to it, and more commonly used approaches based on Haley–Knott regression, describing trade-offs between these methods. We also estimate effects for three QTL previously identified in those populations, obtaining posterior intervals that describe how the phenotype might be affected by diplotype substitutions at the modeled locus. PMID:25236455
Bayesian model selection for LISA pathfinder
NASA Astrophysics Data System (ADS)
Karnesis, Nikolaos; Nofrarias, Miquel; Sopuerta, Carlos F.; Gibert, Ferran; Armano, Michele; Audley, Heather; Congedo, Giuseppe; Diepholz, Ingo; Ferraioli, Luigi; Hewitson, Martin; Hueller, Mauro; Korsakova, Natalia; McNamara, Paul W.; Plagnol, Eric; Vitale, Stefano
2014-03-01
The main goal of the LISA Pathfinder (LPF) mission is to fully characterize the acceleration noise models and to test key technologies for future space-based gravitational-wave observatories similar to the eLISA concept. The data analysis team has developed complex three-dimensional models of the LISA Technology Package (LTP) experiment onboard the LPF. These models are used for simulations, but, more importantly, they will be used for parameter estimation purposes during flight operations. One of the tasks of the data analysis team is to identify the physical effects that contribute significantly to the properties of the instrument noise. A way of approaching this problem is to recover the essential parameters of a LTP model fitting the data. Thus, we want to define the simplest model that efficiently explains the observations. To do so, adopting a Bayesian framework, one has to estimate the so-called Bayes factor between two competing models. In our analysis, we use three main different methods to estimate it: the reversible jump Markov chain Monte Carlo method, the Schwarz criterion, and the Laplace approximation. They are applied to simulated LPF experiments in which the most probable LTP model that explains the observations is recovered. The same type of analysis presented in this paper is expected to be followed during flight operations. Moreover, the correlation of the output of the aforementioned methods with the design of the experiment is explored.
A multivariate Bayesian model for embryonic growth.
Willemsen, Sten P; Eilers, Paul H C; Steegers-Theunissen, Régine P M; Lesaffre, Emmanuel
2015-04-15
Most longitudinal growth curve models evaluate the evolution of each of the anthropometric measurements separately. When applied to a 'reference population', this exercise leads to univariate reference curves against which new individuals can be evaluated. However, growth should be evaluated in totality, that is, by evaluating all body characteristics jointly. Recently, Cole et al. suggested the Superimposition by Translation and Rotation (SITAR) model, which expresses individual growth curves by three subject-specific parameters indicating their deviation from a flexible overall growth curve. This model allows the characterization of normal growth in a flexible though compact manner. In this paper, we generalize the SITAR model in a Bayesian way to multiple dimensions. The multivariate SITAR model allows us to create multivariate reference regions, which is advantageous for prediction. The usefulness of the model is illustrated on longitudinal measurements of embryonic growth obtained in the first semester of pregnancy, collected in the ongoing Rotterdam Predict study. Further, we demonstrate how the model can be used to find determinants of embryonic growth.
Bayesian Modeling of Population Variability -- Practical Guidance and Pitfalls
Dana L. Kelly; Corwin L. Atwood
2008-05-01
With the advent of easy-to-use open-source software for Markov chain Monte Carlo (MCMC) simulation, hierarchical Bayesian analysis is gaining in popularity. This paper presents practical guidance for hierarchical Bayes analysis of typical problems in probabilistic safety assessment (PSA). The guidance is related to choosing parameterizations that accelerate convergence of the MCMC sampling and to illustrating the potential sensitivity of the results to the functional form chosen for the first-stage prior. This latter issue has significant ramifications because the mean of the average population variability curve (PVC) from hierarchical Bayes (or the mean of the point estimate distribution from empirical Bayes) can be very sensitive to this choice in cases where variability is large. Numerical examples are provided to illustrate the issues discussed.
A SEMIPARAMETRIC BAYESIAN MODEL FOR CIRCULAR-LINEAR REGRESSION
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 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…
Implementing Relevance Feedback in the Bayesian Network Retrieval Model.
ERIC Educational Resources Information Center
de Campos, Luis M.; Fernandez-Luna, Juan M.; Huete, Juan F.
2003-01-01
Discussion of relevance feedback in information retrieval focuses on a proposal for the Bayesian Network Retrieval Model. Bases the proposal on the propagation of partial evidences in the Bayesian network, representing new information obtained from the user's relevance judgments to compute the posterior relevance probabilities of the documents…
Bayesian Student Modeling and the Problem of Parameter Specification.
ERIC Educational Resources Information Center
Millan, Eva; Agosta, John Mark; Perez de la Cruz, Jose Luis
2001-01-01
Discusses intelligent tutoring systems and the application of Bayesian networks to student modeling. Considers reasons for not using Bayesian networks, including the computational complexity of the algorithms and the difficulty of knowledge acquisition, and proposes an approach to simplify knowledge acquisition that applies causal independence to…
Bayesian analysis. II. Signal detection and model selection
NASA Astrophysics Data System (ADS)
Bretthorst, G. Larry
In the preceding. paper, Bayesian analysis was applied to the parameter estimation problem, given quadrature NMR data. Here Bayesian analysis is extended to the problem of selecting the model which is most probable in view of the data and all the prior information. In addition to the analytic calculation, two examples are given. The first example demonstrates how to use Bayesian probability theory to detect small signals in noise. The second example uses Bayesian probability theory to compute the probability of the number of decaying exponentials in simulated T1 data. The Bayesian answer to this question is essentially a microcosm of the scientific method and a quantitative statement of Ockham's razor: theorize about possible models, compare these to experiment, and select the simplest model that "best" fits the data.
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…
Royle, J. Andrew; Converse, Sarah J.
2014-01-01
Capture–recapture studies are often conducted on populations that are stratified by space, time or other factors. In this paper, we develop a Bayesian spatial capture–recapture (SCR) modelling framework for stratified populations – when sampling occurs within multiple distinct spatial and temporal strata.We describe a hierarchical model that integrates distinct models for both the spatial encounter history data from capture–recapture sampling, and also for modelling variation in density among strata. We use an implementation of data augmentation to parameterize the model in terms of a latent categorical stratum or group membership variable, which provides a convenient implementation in popular BUGS software packages.We provide an example application to an experimental study involving small-mammal sampling on multiple trapping grids over multiple years, where the main interest is in modelling a treatment effect on population density among the trapping grids.Many capture–recapture studies involve some aspect of spatial or temporal replication that requires some attention to modelling variation among groups or strata. We propose a hierarchical model that allows explicit modelling of group or strata effects. Because the model is formulated for individual encounter histories and is easily implemented in the BUGS language and other free software, it also provides a general framework for modelling individual effects, such as are present in SCR models.
Medical Inpatient Journey Modeling and Clustering: A Bayesian Hidden Markov Model Based Approach
Huang, Zhengxing; Dong, Wei; Wang, Fei; Duan, Huilong
2015-01-01
Modeling and clustering medical inpatient journeys is useful to healthcare organizations for a number of reasons including inpatient journey reorganization in a more convenient way for understanding and browsing, etc. In this study, we present a probabilistic model-based approach to model and cluster medical inpatient journeys. Specifically, we exploit a Bayesian Hidden Markov Model based approach to transform medical inpatient journeys into a probabilistic space, which can be seen as a richer representation of inpatient journeys to be clustered. Then, using hierarchical clustering on the matrix of similarities, inpatient journeys can be clustered into different categories w.r.t their clinical and temporal characteristics. We evaluated the proposed approach on a real clinical data set pertaining to the unstable angina treatment process. The experimental results reveal that our method can identify and model latent treatment topics underlying in personalized inpatient journeys, and yield impressive clustering quality. PMID:26958200
Bayesian analysis of the backreaction models
Kurek, Aleksandra; Bolejko, Krzysztof; Szydlowski, Marek
2010-03-15
We present a Bayesian analysis of four different types of backreaction models, which are based on the Buchert equations. In this approach, one considers a solution to the Einstein equations for a general matter distribution and then an average of various observable quantities is taken. Such an approach became of considerable interest when it was shown that it could lead to agreement with observations without resorting to dark energy. In this paper we compare the {Lambda}CDM model and the backreaction models with type Ia supernovae, baryon acoustic oscillations, and cosmic microwave background data, and find that the former is favored. However, the tested models were based on some particular assumptions about the relation between the average spatial curvature and the backreaction, as well as the relation between the curvature and curvature index. In this paper we modified the latter assumption, leaving the former unchanged. We find that, by varying the relation between the curvature and curvature index, we can obtain a better fit. Therefore, some further work is still needed--in particular, the relation between the backreaction and the curvature should be revisited in order to fully determine the feasibility of the backreaction models to mimic dark energy.
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.
Hierarchical Multinomial Processing Tree Models: A Latent-Trait Approach
ERIC Educational Resources Information Center
Klauer, Karl Christoph
2010-01-01
Multinomial processing tree models are widely used in many areas of psychology. A hierarchical extension of the model class is proposed, using a multivariate normal distribution of person-level parameters with the mean and covariance matrix to be estimated from the data. The hierarchical model allows one to take variability between persons into…
Stochastic model updating utilizing Bayesian approach and Gaussian process model
NASA Astrophysics Data System (ADS)
Wan, Hua-Ping; Ren, Wei-Xin
2016-03-01
Stochastic model updating (SMU) has been increasingly applied in quantifying structural parameter uncertainty from responses variability. SMU for parameter uncertainty quantification refers to the problem of inverse uncertainty quantification (IUQ), which is a nontrivial task. Inverse problem solved with optimization usually brings about the issues of gradient computation, ill-conditionedness, and non-uniqueness. Moreover, the uncertainty present in response makes the inverse problem more complicated. In this study, Bayesian approach is adopted in SMU for parameter uncertainty quantification. The prominent strength of Bayesian approach for IUQ problem is that it solves IUQ problem in a straightforward manner, which enables it to avoid the previous issues. However, when applied to engineering structures that are modeled with a high-resolution finite element model (FEM), Bayesian approach is still computationally expensive since the commonly used Markov chain Monte Carlo (MCMC) method for Bayesian inference requires a large number of model runs to guarantee the convergence. Herein we reduce computational cost in two aspects. On the one hand, the fast-running Gaussian process model (GPM) is utilized to approximate the time-consuming high-resolution FEM. On the other hand, the advanced MCMC method using delayed rejection adaptive Metropolis (DRAM) algorithm that incorporates local adaptive strategy with global adaptive strategy is employed for Bayesian inference. In addition, we propose the use of the powerful variance-based global sensitivity analysis (GSA) in parameter selection to exclude non-influential parameters from calibration parameters, which yields a reduced-order model and thus further alleviates the computational burden. A simulated aluminum plate and a real-world complex cable-stayed pedestrian bridge are presented to illustrate the proposed framework and verify its feasibility.
A guide to Bayesian model selection for ecologists
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.
Bayesian Case-deletion Model Complexity and Information Criterion
Zhu, Hongtu; Ibrahim, Joseph G.; Chen, Qingxia
2015-01-01
We establish a connection between Bayesian case influence measures for assessing the influence of individual observations and Bayesian predictive methods for evaluating the predictive performance of a model and comparing different models fitted to the same dataset. Based on such a connection, we formally propose a new set of Bayesian case-deletion model complexity (BCMC) measures for quantifying the effective number of parameters in a given statistical model. Its properties in linear models are explored. Adding some functions of BCMC to a conditional deviance function leads to a Bayesian case-deletion information criterion (BCIC) for comparing models. We systematically investigate some properties of BCIC and its connection with other information criteria, such as the Deviance Information Criterion (DIC). We illustrate the proposed methodology on linear mixed models with simulations and a real data example. PMID:26180578
Sheng, Yanyan
2017-01-01
The half-t family has been suggested for the scale hyperparameter in Bayesian hierarchical modeling. Two parameters define a half-t distribution: the scale s and the degree-of-freedom ν. When s is set at a finite value that is slightly larger than the actual standard deviation of the parameters, the half-t prior density can be vaguely informative. This paper focused on such densities, and applied them to the hierarchical three-parameter item response theory (IRT) model. Monte Carlo simulations were carried out to investigate the performance of such specifications in parameter recovery and model comparisons under situations where the actual variability of item parameters varied, and results suggest that the half-t family does offer advantages over the commonly adopted uniform or inverse-gamma prior density by allowing the variability for item parameters to be either very small or large. A real data example is also provided to further illustrate this.
Sheng, Yanyan
2017-01-01
The half-t family has been suggested for the scale hyperparameter in Bayesian hierarchical modeling. Two parameters define a half-t distribution: the scale s and the degree-of-freedom ν. When s is set at a finite value that is slightly larger than the actual standard deviation of the parameters, the half-t prior density can be vaguely informative. This paper focused on such densities, and applied them to the hierarchical three-parameter item response theory (IRT) model. Monte Carlo simulations were carried out to investigate the performance of such specifications in parameter recovery and model comparisons under situations where the actual variability of item parameters varied, and results suggest that the half-t family does offer advantages over the commonly adopted uniform or inverse-gamma prior density by allowing the variability for item parameters to be either very small or large. A real data example is also provided to further illustrate this. PMID:28220096
Bayesian analysis of a disability model for lung cancer survival.
Armero, C; Cabras, S; Castellanos, M E; Perra, S; Quirós, A; Oruezábal, M J; Sánchez-Rubio, J
2016-02-01
Bayesian reasoning, survival analysis and multi-state models are used to assess survival times for Stage IV non-small-cell lung cancer patients and the evolution of the disease over time. Bayesian estimation is done using minimum informative priors for the Weibull regression survival model, leading to an automatic inferential procedure. Markov chain Monte Carlo methods have been used for approximating posterior distributions and the Bayesian information criterion has been considered for covariate selection. In particular, the posterior distribution of the transition probabilities, resulting from the multi-state model, constitutes a very interesting tool which could be useful to help oncologists and patients make efficient and effective decisions.
From least squares to multilevel modeling: A graphical introduction to Bayesian inference
NASA Astrophysics Data System (ADS)
Loredo, Thomas J.
2016-01-01
This tutorial presentation will introduce some of the key ideas and techniques involved in applying Bayesian methods to problems in astrostatistics. The focus will be on the big picture: understanding the foundations (interpreting probability, Bayes's theorem, the law of total probability and marginalization), making connections to traditional methods (propagation of errors, least squares, chi-squared, maximum likelihood, Monte Carlo simulation), and highlighting problems where a Bayesian approach can be particularly powerful (Poisson processes, density estimation and curve fitting with measurement error). The "graphical" component of the title reflects an emphasis on pictorial representations of some of the math, but also on the use of graphical models (multilevel or hierarchical models) for analyzing complex data. Code for some examples from the talk will be available to participants, in Python and in the Stan probabilistic programming language.
Modelling the presence of disease under spatial misalignment using Bayesian latent Gaussian models.
Barber, Xavier; Conesa, David; Lladosa, Silvia; López-Quílez, Antonio
2016-04-18
Modelling patterns of the spatial incidence of diseases using local environmental factors has been a growing problem in the last few years. Geostatistical models have become popular lately because they allow estimating and predicting the underlying disease risk and relating it with possible risk factors. Our approach to these models is based on the fact that the presence/absence of a disease can be expressed with a hierarchical Bayesian spatial model that incorporates the information provided by the geographical and environmental characteristics of the region of interest. Nevertheless, our main interest here is to tackle the misalignment problem arising when information about possible covariates are partially (or totally) different than those of the observed locations and those in which we want to predict. As a result, we present two different models depending on the fact that there is uncertainty on the covariates or not. In both cases, Bayesian inference on the parameters and prediction of presence/absence in new locations are made by considering the model as a latent Gaussian model, which allows the use of the integrated nested Laplace approximation. In particular, the spatial effect is implemented with the stochastic partial differential equation approach. The methodology is evaluated on the presence of the Fasciola hepatica in Galicia, a North-West region of Spain.
Vercelloni, Julie; Caley, M Julian; Kayal, Mohsen; Low-Choy, Samantha; Mengersen, Kerrie
2014-01-01
Recently, attempts to improve decision making in species management have focussed on uncertainties associated with modelling temporal fluctuations in populations. Reducing model uncertainty is challenging; while larger samples improve estimation of species trajectories and reduce statistical errors, they typically amplify variability in observed trajectories. In particular, traditional modelling approaches aimed at estimating population trajectories usually do not account well for nonlinearities and uncertainties associated with multi-scale observations characteristic of large spatio-temporal surveys. We present a Bayesian semi-parametric hierarchical model for simultaneously quantifying uncertainties associated with model structure and parameters, and scale-specific variability over time. We estimate uncertainty across a four-tiered spatial hierarchy of coral cover from the Great Barrier Reef. Coral variability is well described; however, our results show that, in the absence of additional model specifications, conclusions regarding coral trajectories become highly uncertain when considering multiple reefs, suggesting that management should focus more at the scale of individual reefs. The approach presented facilitates the description and estimation of population trajectories and associated uncertainties when variability cannot be attributed to specific causes and origins. We argue that our model can unlock value contained in large-scale datasets, provide guidance for understanding sources of uncertainty, and support better informed decision making.
Vercelloni, Julie; Caley, M. Julian; Kayal, Mohsen; Low-Choy, Samantha; Mengersen, Kerrie
2014-01-01
Recently, attempts to improve decision making in species management have focussed on uncertainties associated with modelling temporal fluctuations in populations. Reducing model uncertainty is challenging; while larger samples improve estimation of species trajectories and reduce statistical errors, they typically amplify variability in observed trajectories. In particular, traditional modelling approaches aimed at estimating population trajectories usually do not account well for nonlinearities and uncertainties associated with multi-scale observations characteristic of large spatio-temporal surveys. We present a Bayesian semi-parametric hierarchical model for simultaneously quantifying uncertainties associated with model structure and parameters, and scale-specific variability over time. We estimate uncertainty across a four-tiered spatial hierarchy of coral cover from the Great Barrier Reef. Coral variability is well described; however, our results show that, in the absence of additional model specifications, conclusions regarding coral trajectories become highly uncertain when considering multiple reefs, suggesting that management should focus more at the scale of individual reefs. The approach presented facilitates the description and estimation of population trajectories and associated uncertainties when variability cannot be attributed to specific causes and origins. We argue that our model can unlock value contained in large-scale datasets, provide guidance for understanding sources of uncertainty, and support better informed decision making. PMID:25364915
Nonparametric Bayesian Modeling for Automated Database Schema Matching
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.
ERIC Educational Resources Information Center
Hao, Haijing
2013-01-01
Information technology adoption and diffusion is currently a significant challenge in the healthcare delivery setting. This thesis includes three papers that explore social influence on information technology adoption and sustained use in the healthcare delivery environment using conventional regression models and novel hierarchical Bayesian…
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 the 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
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
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
Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.
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.
Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models
NASA Astrophysics Data System (ADS)
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.
Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models
Daunizeau, J.; Friston, K.J.; Kiebel, S.J.
2009-01-01
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. PMID:19862351
A Bayesian approach for inducing sparsity in generalized linear models with multi-category response
2015-01-01
Background The dimension and complexity of high-throughput gene expression data create many challenges for downstream analysis. Several approaches exist to reduce the number of variables with respect to small sample sizes. In this study, we utilized the Generalized Double Pareto (GDP) prior to induce sparsity in a Bayesian Generalized Linear Model (GLM) setting. The approach was evaluated using a publicly available microarray dataset containing 99 samples corresponding to four different prostate cancer subtypes. Results A hierarchical Sparse Bayesian GLM using GDP prior (SBGG) was developed to take into account the progressive nature of the response variable. We obtained an average overall classification accuracy between 82.5% and 94%, which was higher than Support Vector Machine, Random Forest or a Sparse Bayesian GLM using double exponential priors. Additionally, SBGG outperforms the other 3 methods in correctly identifying pre-metastatic stages of cancer progression, which can prove extremely valuable for therapeutic and diagnostic purposes. Importantly, using Geneset Cohesion Analysis Tool, we found that the top 100 genes produced by SBGG had an average functional cohesion p-value of 2.0E-4 compared to 0.007 to 0.131 produced by the other methods. Conclusions Using GDP in a Bayesian GLM model applied to cancer progression data results in better subclass prediction. In particular, the method identifies pre-metastatic stages of prostate cancer with substantially better accuracy and produces more functionally relevant gene sets. PMID:26423345
Calibrating Bayesian Network Representations of Social-Behavioral Models
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 empirical comparison with data taken from the Minorities at Risk Organizational Behaviors database.
Bayesian Hierarchical Models to Augment the Mediterranean Forecast System
2012-02-17
collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT...Oceanography Group (GNOO; Grupo Nazionale di Oceanografia Operativa) and access to computing resources of the National Climate Center (CMCC: Centro euro...the interannual variability is controlled by the influence North Atlantic Oscillation, some of the long- term large-scale changes in the Mediterranean
Bayesian Hierarchical Models to Augment the Mediterranean Ocean Forecast System
2006-06-15
vector. Conversely, in low wind speed events (e.g. see the Tyrrhenian Sea ), the wind direction is arbitrary as reflected in the distributions that span a...every other BHM prediction grid location (prediction grid resolution is 0.25◦) in the western basin of the Mediterranean Sea . A green vector within...winds do not influence the ECMWF analyses at the resolution of the oceanic mesoscale in the Mediterranean Sea (Milliff and Morzel, 2003). Conversely
Bayesian Hierarchical Models to Augment the Mediterranean Forecast System
2006-09-30
case for SSH uncertainty. Relative minima in SST initial condition uncertainty occur east of Majorca, in the northern Tyrrhenian Sea , and in the...demonstrate forecast uncertainties during difficult to predict regime transitions in the Mediterranean Sea (e.g. the Fall transition, deep water formation...variance, or “spread” at each MFS-Wind-BHM output grid location in a blow-up of the western Mediterranean Sea , centered on the Gulf of Lions (Fig 1
Testing Adaptive Toolbox Models: A Bayesian Hierarchical Approach
ERIC Educational Resources Information Center
Scheibehenne, Benjamin; Rieskamp, Jorg; Wagenmakers, Eric-Jan
2013-01-01
Many theories of human cognition postulate that people are equipped with a repertoire of strategies to solve the tasks they face. This theoretical framework of a cognitive toolbox provides a plausible account of intra- and interindividual differences in human behavior. Unfortunately, it is often unclear how to rigorously test the toolbox…
Bayesian Hierarchical Modeling of Cardiac Response to Particulate Matter Exposure
Studies have linked increased levels of particulate air pollution to decreased autonomic control, as measured by heart rate variability (HRV), particularly in populations such as the elderly. In this study, we use data obtained from the 1998 USEPA epidemiology-exposure longitudin...
INACTIVATION OF BACILLUS GLOBIGII BY CHLORINATION: A HIERARCHICAL BAYESIAN MODEL
Recent events where spores of Bacillus anthracis have been used as a bioterrorist weapon have prompted interest in determining the resistance of this organism to commonly used disinfectants, such as chlorine, chlorine dioxide and ozone. This work was undertaken to study ...
BAYESIAN HIERARCHICAL MODELING OF PERSONAL EXPOSURE TO PARTICULATE MATTER
In the US EPA's 1998 Baltimore Epidemiology-Exposure Panel Study, a group of 21 residents of a single building retirement community wore personal monitors recording personal fine particulate air pollution concentrations (PM_{2.5}) for 27 days, while other monitors recorde...
Bayesian Hierarchical Models to Augment the Mediterranean Forecast System
2016-06-07
demonstrate forecast uncertainties during difficult to predict regime transitions in the Mediterranean Sea (e.g. the Fall transition, deep water ...corresponds to a strong Mistral event, and deep- water formation (DWF) response, in the Gulf of Lions. The blue SVW clusters provide a pictorial... water formation experiments were presented in a seminar at ONR headquarters in May 2006. Prof. Pinardi (U. Bologna/INGV) traveled to Washington to
Bayesian Hierarchical Models to Augment the Mediterranean Forecast System
2016-06-07
demonstrate forecast uncertainties during difficult to predict regime transitions in the Mediterranean Sea (e.g. the Fall transition, deep water formation...event, and deep- water formation (DWF) response, in the Gulf of Lions. The blue SVW clusters provide a pictorial representation of SVW ensemble...Preliminary results of the MFS-Wind-BHM deep water formation experiments were presented in a seminar at ONR headquarters in May 2006. Prof. Pinardi
Bayesian approach to decompression sickness model parameter estimation.
Howle, L E; Weber, P W; Nichols, J M
2017-03-01
We examine both maximum likelihood and Bayesian approaches for estimating probabilistic decompression sickness model parameters. Maximum likelihood estimation treats parameters as fixed values and determines the best estimate through repeated trials, whereas the Bayesian approach treats parameters as random variables and determines the parameter probability distributions. We would ultimately like to know the probability that a parameter lies in a certain range rather than simply make statements about the repeatability of our estimator. Although both represent powerful methods of inference, for models with complex or multi-peaked likelihoods, maximum likelihood parameter estimates can prove more difficult to interpret than the estimates of the parameter distributions provided by the Bayesian approach. For models of decompression sickness, we show that while these two estimation methods are complementary, the credible intervals generated by the Bayesian approach are more naturally suited to quantifying uncertainty in the model parameters.
BAYESIAN METHODS FOR REGIONAL-SCALE EUTROPHICATION MODELS. (R830887)
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...
Hierarchical inverse Gaussian models and multiple testing: application to gene expression data.
Labbe, Aurelie; Thompson, Mary
2005-01-01
Detecting differentially expressed genes in microarray experiments is a topic that has been well studied in the literature. Many hypothesis testing methods have been proposed that rely on strong distributional assumptions for the gene intensities. However, the shape of microarray data may vary substantially from one experiment to another, and model assumptions may be seriously violated in many cases. The literature on microarray data is mainly based on two distributions: the log-normal and the gamma distributions, that often appear to be effective when used in a Bayesian hierarchical framework. However, if a model that fits the data well in a global manner seems attractive, two points should be regarded with attention: the ability of the model to fit the tail of the observed distribution, and its robustness to a wrong specification of the model, in terms of error rates for the hypothesis tests. In order to focus on these aspects, we propose to use Bayesian models involving the inverse Gaussian distribution to describe gene expression data. We show that these models can be good competitors to the traditional Bayesian or random effect gamma or log-normal models in some situations. A multiple testing procedure is then proposed, based on an asymptotic property of the posterior probability of the one-sided alternative hypothesis. We show that the asymptotic property is well approximated for inverse Gaussian models, even when the number of observations available for each test is very small.
Higher-Order Item Response Models for Hierarchical Latent Traits
ERIC Educational Resources Information Center
Huang, Hung-Yu; Wang, Wen-Chung; Chen, Po-Hsi; Su, Chi-Ming
2013-01-01
Many latent traits in the human sciences have a hierarchical structure. This study aimed to develop a new class of higher order item response theory models for hierarchical latent traits that are flexible in accommodating both dichotomous and polytomous items, to estimate both item and person parameters jointly, to allow users to specify…
Modelling modal gating of ion channels with hierarchical Markov models
Fackrell, Mark; Crampin, Edmund J.; Taylor, Peter
2016-01-01
Many ion channels spontaneously switch between different levels of activity. Although this behaviour known as modal gating has been observed for a long time it is currently not well understood. Despite the fact that appropriately representing activity changes is essential for accurately capturing time course data from ion channels, systematic approaches for modelling modal gating are currently not available. In this paper, we develop a modular approach for building such a model in an iterative process. First, stochastic switching between modes and stochastic opening and closing within modes are represented in separate aggregated Markov models. Second, the continuous-time hierarchical Markov model, a new modelling framework proposed here, then enables us to combine these components so that in the integrated model both mode switching as well as the kinetics within modes are appropriately represented. A mathematical analysis reveals that the behaviour of the hierarchical Markov model naturally depends on the properties of its components. We also demonstrate how a hierarchical Markov model can be parametrized using experimental data and show that it provides a better representation than a previous model of the same dataset. Because evidence is increasing that modal gating reflects underlying molecular properties of the channel protein, it is likely that biophysical processes are better captured by our new approach than in earlier models. PMID:27616917
Modeling Non-Gaussian Time Series with Nonparametric Bayesian Model.
Xu, Zhiguang; MacEachern, Steven; Xu, Xinyi
2015-02-01
We present a class of Bayesian copula models whose major components are the marginal (limiting) distribution of a stationary time series and the internal dynamics of the series. We argue that these are the two features with which an analyst is typically most familiar, and hence that these are natural components with which to work. For the marginal distribution, we use a nonparametric Bayesian prior distribution along with a cdf-inverse cdf transformation to obtain large support. For the internal dynamics, we rely on the traditionally successful techniques of normal-theory time series. Coupling the two components gives us a family of (Gaussian) copula transformed autoregressive models. The models provide coherent adjustments of time scales and are compatible with many extensions, including changes in volatility of the series. We describe basic properties of the models, show their ability to recover non-Gaussian marginal distributions, and use a GARCH modification of the basic model to analyze stock index return series. The models are found to provide better fit and improved short-range and long-range predictions than Gaussian competitors. The models are extensible to a large variety of fields, including continuous time models, spatial models, models for multiple series, models driven by external covariate streams, and non-stationary models.
Qian, Song S; Schulman, Andrew; Koplos, Jonathan; Kotros, Alison; Kellar, Penny
2004-02-15
Water quality studies often include the analytical challenge of incorporating censored data and quantifying error of estimation. Many analytical methods exist for estimating distribution parameters when censored data are present. This paper presents a Bayesian-based hierarchical model for estimating the national distribution of the mean concentrations of chemicals occurring in U.S. public drinking water systems using fluoride and thallium as examples. The data used are Safe Drinking Water Act compliance monitoring data (with a significant proportion of left-censored data). The model, which assumes log-normality, was evaluated using simulated data sets generated from a series of Weibull distributions to illustrate the robustness of the model. The hierarchical model is easily implemented using the Markov chain Monte Carlo simulation method. In addition, the Bayesian method is able to quantify the uncertainty in the estimated cumulative density function. The estimated fluoride and thallium national distributions are presented. Results from this study can be used to develop prior distributions for future U.S. drinking water regulatory studies of contaminant occurrence.
Bayesian graphical models for genomewide association studies.
Verzilli, Claudio J; Stallard, Nigel; Whittaker, John C
2006-07-01
As the extent of human genetic variation becomes more fully characterized, the research community is faced with the challenging task of using this information to dissect the heritable components of complex traits. Genomewide association studies offer great promise in this respect, but their analysis poses formidable difficulties. In this article, we describe a computationally efficient approach to mining genotype-phenotype associations that scales to the size of the data sets currently being collected in such studies. We use discrete graphical models as a data-mining tool, searching for single- or multilocus patterns of association around a causative site. The approach is fully Bayesian, allowing us to incorporate prior knowledge on the spatial dependencies around each marker due to linkage disequilibrium, which reduces considerably the number of possible graphical structures. A Markov chain-Monte Carlo scheme is developed that yields samples from the posterior distribution of graphs conditional on the data from which probabilistic statements about the strength of any genotype-phenotype association can be made. Using data simulated under scenarios that vary in marker density, genotype relative risk of a causative allele, and mode of inheritance, we show that the proposed approach has better localization properties and leads to lower false-positive rates than do single-locus analyses. Finally, we present an application of our method to a quasi-synthetic data set in which data from the CYP2D6 region are embedded within simulated data on 100K single-nucleotide polymorphisms. Analysis is quick (<5 min), and we are able to localize the causative site to a very short interval.
Assessing Fit of Unidimensional Graded Response Models Using Bayesian Methods
ERIC Educational Resources Information Center
Zhu, Xiaowen; Stone, Clement A.
2011-01-01
The posterior predictive model checking method is a flexible Bayesian model-checking tool and has recently been used to assess fit of dichotomous IRT models. This paper extended previous research to polytomous IRT models. A simulation study was conducted to explore the performance of posterior predictive model checking in evaluating different…
Maximizing the Divergence from a Hierarchical Model of Quantum States
NASA Astrophysics Data System (ADS)
Weis, Stephan; Knauf, Andreas; Ay, Nihat; Zhao, Ming-Jing
2015-03-01
We study many-party correlations quantified in terms of the Umegaki relative entropy (divergence) from a Gibbs family known as a hierarchical model. We derive these quantities from the maximum-entropy principle which was used earlier to define the closely related irreducible correlation. We point out the differences between quantum states and probability vectors which exist in hierarchical models, in the divergence from a hierarchical model and in local maximizers of this divergence. The differences are, respectively, missing factorization, discontinuity and reduction of uncertainty. We discuss global maximizers of the mutual information of separable qubit states.
Choi, Kyuwan
2014-06-01
In this study, a real-time cortical activity monitoring system was constructed, which could estimate cortical activities every 125 milliseconds over 2,240 vertexes from 64 channel electroencephalography signals through the Hierarchical Bayesian estimation that uses functional magnetic resonance imaging data as its prior information. Recently, functional magnetic resonance imaging has mostly been used in the neurofeedback field because it allows for high spatial resolution. However, in functional magnetic resonance imaging, the time for the neurofeedback information to reach the patient is delayed several seconds because of its poor temporal resolution. Therefore, a number of problems need to be solved to effectively implement feedback training paradigms in patients. To address this issue, this study used a new cortical activity monitoring system that improved both spatial and temporal resolution by using both functional magnetic resonance imaging data and electroencephalography signals in conjunction with one another. This system is advantageous as it can improve applications in the fields of real-time diagnosis, neurofeedback, and the brain-machine interface.
Hwang, Kyu-Baek; Zhang, Byoung-Tak
2005-12-01
Bayesian model averaging (BMA) can resolve the overfitting problem by explicitly incorporating the model uncertainty into the analysis procedure. Hence, it can be used to improve the generalization performance of Bayesian network classifiers. Until now, BMA of Bayesian network classifiers has only been performed in some restricted forms, e.g., the model is averaged given a single node-order, because of its heavy computational burden. However, it can be hard to obtain a good node-order when the available training dataset is sparse. To alleviate this problem, we propose BMA of Bayesian network classifiers over several distinct node-orders obtained using the Markov chain Monte Carlo sampling technique. The proposed method was examined using two synthetic problems and four real-life datasets. First, we show that the proposed method is especially effective when the given dataset is very sparse. The classification accuracy of averaging over multiple node-orders was higher in most cases than that achieved using a single node-order in our experiments. We also present experimental results for test datasets with unobserved variables, where the quality of the averaged node-order is more important. Through these experiments, we show that the difference in classification performance between the cases of multiple node-orders and single node-order is related to the level of noise, confirming the relative benefit of averaging over multiple node-orders for incomplete data. We conclude that BMA of Bayesian network classifiers over multiple node-orders has an apparent advantage when the given dataset is sparse and noisy, despite the method's heavy computational cost.
Technical note: Bayesian calibration of dynamic ruminant nutrition models.
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.
Ismaila, Afisi S; Canty, Angelo; Thabane, Lehana
2007-01-01
Background This study compares the Bayesian and frequentist (non-Bayesian) approaches in the modelling of the association between the risk of preterm birth and maternal proximity to hazardous waste and pollution from the Sydney Tar Pond site in Nova Scotia, Canada. Methods The data includes 1604 observed cases of preterm birth out of a total population of 17559 at risk of preterm birth from 144 enumeration districts in the Cape Breton Regional Municipality. Other covariates include the distance from the Tar Pond; the rate of unemployment to population; the proportion of persons who are separated, divorced or widowed; the proportion of persons who have no high school diploma; the proportion of persons living alone; the proportion of single parent families and average income. Bayesian hierarchical Poisson regression, quasi-likelihood Poisson regression and weighted linear regression models were fitted to the data. Results The results of the analyses were compared together with their limitations. Conclusion The results of the weighted linear regression and the quasi-likelihood Poisson regression agrees with the result from the Bayesian hierarchical modelling which incorporates the spatial effects. PMID:17845717
NASA Astrophysics Data System (ADS)
Pham, Hai V.; Tsai, Frank T.-C.
2015-09-01
The lack of hydrogeological data and knowledge often results in different propositions (or alternatives) to represent uncertain model components and creates many candidate groundwater models using the same data. Uncertainty of groundwater head prediction may become unnecessarily high. This study introduces an experimental design to identify propositions in each uncertain model component and decrease the prediction uncertainty by reducing conceptual model uncertainty. A discrimination criterion is developed based on posterior model probability that directly uses data to evaluate model importance. Bayesian model averaging (BMA) is used to predict future observation data. The experimental design aims to find the optimal number and location of future observations and the number of sampling rounds such that the desired discrimination criterion is met. Hierarchical Bayesian model averaging (HBMA) is adopted to assess if highly probable propositions can be identified and the conceptual model uncertainty can be reduced by the experimental design. The experimental design is implemented to a groundwater study in the Baton Rouge area, Louisiana. We design a new groundwater head observation network based on existing USGS observation wells. The sources of uncertainty that create multiple groundwater models are geological architecture, boundary condition, and fault permeability architecture. All possible design solutions are enumerated using a multi-core supercomputer. Several design solutions are found to achieve an 80%-identifiable groundwater model in 5 years by using six or more existing USGS wells. The HBMA result shows that each highly probable proposition can be identified for each uncertain model component once the discrimination criterion is achieved. The variances of groundwater head predictions are significantly decreased by reducing posterior model probabilities of unimportant propositions.
Using consensus bayesian network to model the reactive oxygen species regulatory pathway.
Hu, Liangdong; Wang, Limin
2013-01-01
Bayesian network is one of the most successful graph models for representing the reactive oxygen species regulatory pathway. With the increasing number of microarray measurements, it is possible to construct the bayesian network from microarray data directly. Although large numbers of bayesian network learning algorithms have been developed, when applying them to learn bayesian networks from microarray data, the accuracies are low due to that the databases they used to learn bayesian networks contain too few microarray data. In this paper, we propose a consensus bayesian network which is constructed by combining bayesian networks from relevant literatures and bayesian networks learned from microarray data. It would have a higher accuracy than the bayesian networks learned from one database. In the experiment, we validated the bayesian network combination algorithm on several classic machine learning databases and used the consensus bayesian network to model the Escherichia coli's ROS pathway.
Zero-inflated hierarchical models for faecal egg counts to assess anthelmintic efficacy.
Wang, Craig; Torgerson, Paul R; Höglund, Johan; Furrer, Reinhard
2017-02-15
The prevalence of anthelmintic resistance has increased in recent years, as a result of the extensive use of anthelmintic drugs to reduce the infection of parasitic worms in livestock. In order to detect the resistance, the number of parasite eggs in animal faeces is counted. Typically a subsample of the diluted faeces is examined, and the mean egg counts from both untreated and treated animals are compared. However, the conventional method ignores the variabilities introduced by the counting process and by different infection levels across animals. In addition, there can be extra zero counts, which arise as a result of the unexposed animals in an infected population or animals. In this paper, we propose the zero-inflated Bayesian hierarchical models to estimate the reduction in faecal egg counts. The simulation study compares the Bayesian models with the conventional faecal egg count reduction test and other methods such as bootstrap and quasi-Poisson regression. The results show the Bayesian models are more robust and they perform well in terms of both the bias and the coverage. We further illustrate the advantages of our proposed model using a case study about the anthelmintic resistance in Swedish sheep flocks.
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…
Non-parametric Bayesian graph models reveal community structure in resting state fMRI.
Andersen, Kasper Winther; Madsen, Kristoffer H; Siebner, Hartwig Roman; Schmidt, Mikkel N; Mørup, Morten; Hansen, Lars Kai
2014-10-15
Modeling of resting state functional magnetic resonance imaging (rs-fMRI) data using network models is of increasing interest. It is often desirable to group nodes into clusters to interpret the communication patterns between nodes. In this study we consider three different nonparametric Bayesian models for node clustering in complex networks. In particular, we test their ability to predict unseen data and their ability to reproduce clustering across datasets. The three generative models considered are the Infinite Relational Model (IRM), Bayesian Community Detection (BCD), and the Infinite Diagonal Model (IDM). The models define probabilities of generating links within and between clusters and the difference between the models lies in the restrictions they impose upon the between-cluster link probabilities. IRM is the most flexible model with no restrictions on the probabilities of links between clusters. BCD restricts the between-cluster link probabilities to be strictly lower than within-cluster link probabilities to conform to the community structure typically seen in social networks. IDM only models a single between-cluster link probability, which can be interpreted as a background noise probability. These probabilistic models are compared against three other approaches for node clustering, namely Infomap, Louvain modularity, and hierarchical clustering. Using 3 different datasets comprising healthy volunteers' rs-fMRI we found that the BCD model was in general the most predictive and reproducible model. This suggests that rs-fMRI data exhibits community structure and furthermore points to the significance of modeling heterogeneous between-cluster link probabilities.
Hierarchical Linear Modeling in Salary-Equity Studies.
ERIC Educational Resources Information Center
Loeb, Jane W.
2003-01-01
Provides information on how hierarchical linear modeling can be used as an alternative to multiple regression analysis for conducting salary-equity studies. Salary data are used to compare and contrast the two approaches. (EV)
Constitutive modelling of a reinforced soil using hierarchical model
NASA Astrophysics Data System (ADS)
Varadarajan, A.; Sharma, K. G.; Soni, K. M.
1999-03-01
Drained triaxial tests are conducted on natural and reinforced sand under various stress paths. Direct shear tests and pull-out tests are conducted on soil-reinforcement interface and on reinforcement, respectively. The effects of two types of reinforcement, viz, woven and non-woven geotextile and number of layers of reinforcement are investigated. Hierarchical single surface model is used to depict the behaviour of natural and reinforced soil by treating the soil as a single composite material and by considering soil, reinforcement and interface as independent elements. It is shown that the material parameters are very much affected by the type and the number of layers of reinforcement. The hierarchical model provides satisfactory prediction for both natural and reinforced soil.
A hierarchical model for estimating change in American Woodcock populations
Sauer, J.R.; Link, W.A.; Kendall, W.L.; Kelley, J.R.; Niven, D.K.
2008-01-01
The Singing-Ground Survey (SGS) is a primary source of information on population change for American woodcock (Scolopax minor). We analyzed the SGS using a hierarchical log-linear model and compared the estimates of change and annual indices of abundance to a route regression analysis of SGS data. We also grouped SGS routes into Bird Conservation Regions (BCRs) and estimated population change and annual indices using BCRs within states and provinces as strata. Based on the hierarchical model?based estimates, we concluded that woodcock populations were declining in North America between 1968 and 2006 (trend = -0.9%/yr, 95% credible interval: -1.2, -0.5). Singing-Ground Survey results are generally similar between analytical approaches, but the hierarchical model has several important advantages over the route regression. Hierarchical models better accommodate changes in survey efficiency over time and space by treating strata, years, and observers as random effects in the context of a log-linear model, providing trend estimates that are derived directly from the annual indices. We also conducted a hierarchical model analysis of woodcock data from the Christmas Bird Count and the North American Breeding Bird Survey. All surveys showed general consistency in patterns of population change, but the SGS had the shortest credible intervals. We suggest that population management and conservation planning for woodcock involving interpretation of the SGS use estimates provided by the hierarchical model.
Bayesian Networks for Modeling Dredging Decisions
2011-10-01
position unless so designated by other authorized documents. DESTROY THIS REPORT WHEN NO LONGER NEEDED. DO NOT RETURN IT TO THE ORIGINATOR. ERDC/EL TR...links within a network often do indicate causality and it is usually best to work from information about... work in this area. ERDC/EL TR-11-14 16 Table 1. Bayesian network applications reviewed in the literature. Author(s) Year Substantive issue
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…
Bayesian failure probability model sensitivity study. Final report
Not Available
1986-05-30
The Office of the Manager, National Communications System (OMNCS) has developed a system-level approach for estimating the effects of High-Altitude Electromagnetic Pulse (HEMP) on the connectivity of telecommunications networks. This approach incorporates a Bayesian statistical model which estimates the HEMP-induced failure probabilities of telecommunications switches and transmission facilities. The purpose of this analysis is to address the sensitivity of the Bayesian model. This is done by systematically varying two model input parameters--the number of observations, and the equipment failure rates. Throughout the study, a non-informative prior distribution is used. The sensitivity of the Bayesian model to the noninformative prior distribution is investigated from a theoretical mathematical perspective.
Bayesian Case Influence Measures for Statistical Models with Missing Data
Zhu, Hongtu; Ibrahim, Joseph G.; Cho, Hyunsoon; Tang, Niansheng
2011-01-01
We examine three Bayesian case influence measures including the φ-divergence, Cook's posterior mode distance and Cook's posterior mean distance for identifying a set of influential observations for a variety of statistical models with missing data including models for longitudinal data and latent variable models in the absence/presence of missing data. Since it can be computationally prohibitive to compute these Bayesian case influence measures in models with missing data, we derive simple first-order approximations to the three Bayesian case influence measures by using the Laplace approximation formula and examine the applications of these approximations to the identification of influential sets. All of the computations for the first-order approximations can be easily done using Markov chain Monte Carlo samples from the posterior distribution based on the full data. Simulated data and an AIDS dataset are analyzed to illustrate the methodology. PMID:23399928
BAYESIAN SPATIAL-TEMPORAL MODELING OF ECOLOGICAL ZERO-INFLATED COUNT DATA
Wang, Xia; Chen, Ming-Hui; Kuo, Rita C.; Dey, Dipak K.
2015-01-01
A Bayesian hierarchical model is developed for count data with spatial and temporal correlations as well as excessive zeros, uneven sampling intensities, and inference on missing spots. Our contribution is to develop a model on zero-inflated count data that provides flexibility in modeling spatial patterns in a dynamic manner and also improves the computational efficiency via dimension reduction. The proposed methodology is of particular importance for studying species presence and abundance in the field of ecological sciences. The proposed model is employed in the analysis of the survey data by the Northeast Fisheries Sciences Center (NEFSC) for estimation and prediction of the Atlantic cod in the Gulf of Maine - Georges Bank region. Model comparisons based on the deviance information criterion and the log predictive score show the improvement by the proposed spatial-temporal model. PMID:26997848
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…
Bayesian non-parametrics and the probabilistic approach to modelling
Ghahramani, Zoubin
2013-01-01
Modelling is fundamental to many fields of science and engineering. A model can be thought of as a representation of possible data one could predict from a system. The probabilistic approach to modelling uses probability theory to express all aspects of uncertainty in the model. The probabilistic approach is synonymous with Bayesian modelling, which simply uses the rules of probability theory in order to make predictions, compare alternative models, and learn model parameters and structure from data. This simple and elegant framework is most powerful when coupled with flexible probabilistic models. Flexibility is achieved through the use of Bayesian non-parametrics. This article provides an overview of probabilistic modelling and an accessible survey of some of the main tools in Bayesian non-parametrics. The survey covers the use of Bayesian non-parametrics for modelling unknown functions, density estimation, clustering, time-series modelling, and representing sparsity, hierarchies, and covariance structure. More specifically, it gives brief non-technical overviews of Gaussian processes, Dirichlet processes, infinite hidden Markov models, Indian buffet processes, Kingman’s coalescent, Dirichlet diffusion trees and Wishart processes. PMID:23277609
A General Bayesian Model for Testlets: Theory and Applications.
ERIC Educational Resources Information Center
Wang, Xiaohui; Bradlow, Eric T.; Wainer, Howard
2002-01-01
Proposes a modified version of commonly employed item response models in a fully Bayesian framework and obtains inferences under the model using Markov chain Monte Carlo techniques. Demonstrates use of the model in a series of simulations and with operational data from the North Carolina Test of Computer Skills and the Test of Spoken English…
Bayesian Network Models for Local Dependence among Observable Outcome Variables
ERIC Educational Resources Information Center
Almond, Russell G.; Mulder, Joris; Hemat, Lisa A.; Yan, Duanli
2009-01-01
Bayesian network models offer a large degree of flexibility for modeling dependence among observables (item outcome variables) from the same task, which may be dependent. This article explores four design patterns for modeling locally dependent observations: (a) no context--ignores dependence among observables; (b) compensatory context--introduces…
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…
NASA Astrophysics Data System (ADS)
Piecuch, C. G.; Huybers, P. J.; Tingley, M.
2015-12-01
Tide gauge records of mean sea level are some of the most valuable instrumental time series of oceanic variability and change. Yet these time series sometimes have short record lengths and intermittently missing values. Such issues can limit the utility of the data, for example, precluding rigorous analyses of return periods of extreme mean sea level events and whether they are unprecedented. With a view to filling gaps in the tide gauge mean sea level time series, we describe a hierarchical Bayesian modeling approach. The model, which is predicated on the notion of conditional probabilities, comprises three levels: a process level, which casts mean sea level as a field with spatiotemporal covariance; a data level, which represents tide gauge observations as noisy, biased versions of the true process; and a prior level, which gives prior functional forms to model parameters. Using Bayes' rule, this technique gives estimates of the posterior probability of the process and the parameters given the observations. To demonstrate the approach, we apply it to 2,967 station-years of annual mean sea level observations over 1856-2013 from 70 tide gauges along the United States East Coast from Florida to Maine (i.e., 26.8% record completeness). The model overcomes the data paucity by sharing information across space and time. The result is an ensemble of realizations, each member of which is a possible history of sea level changes at these locations over this period, which is consistent with and equally likely given the tide gauge data and underlying model assumptions. Using the ensemble of histories furnished by the Bayesian model, we identify extreme events of mean sea level change in the tide gauge time series. Specifically, we use the model to address the particular hypothesis (with rigorous uncertainty quantification) that a recently reported interannual sea level rise during 2008-2010 was unprecedented in the instrumental record along the northeast coast of North
Modeling the deformation behavior of nanocrystalline alloy with hierarchical microstructures
NASA Astrophysics Data System (ADS)
Liu, Hongxi; Zhou, Jianqiu; Zhao, Yonghao
2016-02-01
A mechanism-based plasticity model based on dislocation theory is developed to describe the mechanical behavior of the hierarchical nanocrystalline alloys. The stress-strain relationship is derived by invoking the impeding effect of the intra-granular solute clusters and the inter-granular nanostructures on the dislocation movements along the sliding path. We found that the interaction between dislocations and the hierarchical microstructures contributes to the strain hardening property and greatly influence the ductility of nanocrystalline metals. The analysis indicates that the proposed model can successfully describe the enhanced strength of the nanocrystalline hierarchical alloy. Moreover, the strain hardening rate is sensitive to the volume fraction of the hierarchical microstructures. The present model provides a new perspective to design the microstructures for optimizing the mechanical properties in nanostructural metals.
Bayesian Inference: with ecological applications
Link, William A.; Barker, Richard J.
2010-01-01
This text provides a mathematically rigorous yet accessible and engaging introduction to Bayesian inference with relevant examples that will be of interest to biologists working in the fields of ecology, wildlife management and environmental studies as well as students in advanced undergraduate statistics.. This text opens the door to Bayesian inference, taking advantage of modern computational efficiencies and easily accessible software to evaluate complex hierarchical models.
Bayesian generalized linear mixed modeling of Tuberculosis using informative priors
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
Bayesian generalized linear mixed modeling of Tuberculosis using informative priors.
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.
Hierarchical Model Validation of Symbolic Performance Models of Scientific Kernels
Alam, Sadaf R; Vetter, Jeffrey S
2006-08-01
Multi-resolution validation of hierarchical performance models of scientific applications is critical primarily for two reasons. First, the step-by-step validation determines the correctness of all essential components or phases in a science simulation. Second, a model that is validated at multiple resolution levels is the very first step to generate predictive performance models, for not only existing systems but also for emerging systems and future problem sizes. We present the design and validation of hierarchical performance models of two scientific benchmarks using a new technique called the modeling assertions (MA). Our MA prototype framework generates symbolic performance models that can be evaluated efficiently by generating the equivalent model representations in Octave and MATLAB. The multi-resolution modeling and validation is conducted on two contemporary, massively-parallel systems, XT3 and Blue Gene/L system. The workload distribution and the growth rates predictions generated by the MA models are confirmed by the experimental data collected on the MPP platforms. In addition, the physical memory requirements that are generated by the MA models are verified by the runtime values on the Blue Gene/L system, which has 512 MBytes and 256 MBytes physical memory capacity in its two unique execution modes.
Lifting a veil on diversity: a Bayesian approach to fitting relative-abundance models.
Golicher, Duncan J; O'Hara, Robert B; Ruíz-Montoya, Lorena; Cayuela, Luis
2006-02-01
Bayesian methods incorporate prior knowledge into a statistical analysis. This prior knowledge is usually restricted to assumptions regarding the form of probability distributions of the parameters of interest, leaving their values to be determined mainly through the data. Here we show how a Bayesian approach can be applied to the problem of drawing inference regarding species abundance distributions and comparing diversity indices between sites. The classic log series and the lognormal models of relative- abundance distribution are apparently quite different in form. The first is a sampling distribution while the other is a model of abundance of the underlying population. Bayesian methods help unite these two models in a common framework. Markov chain Monte Carlo simulation can be used to fit both distributions as small hierarchical models with shared common assumptions. Sampling error can be assumed to follow a Poisson distribution. Species not found in a sample, but suspected to be present in the region or community of interest, can be given zero abundance. This not only simplifies the process of model fitting, but also provides a convenient way of calculating confidence intervals for diversity indices. The method is especially useful when a comparison of species diversity between sites with different sample sizes is the key motivation behind the research. We illustrate the potential of the approach using data on fruit-feeding butterflies in southern Mexico. We conclude that, once all assumptions have been made transparent, a single data set may provide support for the belief that diversity is negatively affected by anthropogenic forest disturbance. Bayesian methods help to apply theory regarding the distribution of abundance in ecological communities to applied conservation.
Hierarchical abstract semantic model for image classification
NASA Astrophysics Data System (ADS)
Ye, Zhipeng; Liu, Peng; Zhao, Wei; Tang, Xianglong
2015-09-01
Semantic gap limits the performance of bag-of-visual-words. To deal with this problem, a hierarchical abstract semantics method that builds abstract semantic layers, generates semantic visual vocabularies, measures semantic gap, and constructs classifiers using the Adaboost strategy is proposed. First, abstract semantic layers are proposed to narrow the semantic gap between visual features and their interpretation. Then semantic visual words are extracted as features to train semantic classifiers. One popular form of measurement is used to quantify the semantic gap. The Adaboost training strategy is used to combine weak classifiers into strong ones to further improve performance. For a testing image, the category is estimated layer-by-layer. Corresponding abstract hierarchical structures for popular datasets, including Caltech-101 and MSRC, are proposed for evaluation. The experimental results show that the proposed method is capable of narrowing semantic gaps effectively and performs better than other categorization methods.
Hierarchical model analysis of the Atlantic Flyway Breeding Waterfowl Survey
Sauer, John R.; Zimmerman, Guthrie S.; Klimstra, Jon D.; Link, William A.
2014-01-01
We used log-linear hierarchical models to analyze data from the Atlantic Flyway Breeding Waterfowl Survey. The survey has been conducted by state biologists each year since 1989 in the northeastern United States from Virginia north to New Hampshire and Vermont. Although yearly population estimates from the survey are used by the United States Fish and Wildlife Service for estimating regional waterfowl population status for mallards (Anas platyrhynchos), black ducks (Anas rubripes), wood ducks (Aix sponsa), and Canada geese (Branta canadensis), they are not routinely adjusted to control for time of day effects and other survey design issues. The hierarchical model analysis permits estimation of year effects and population change while accommodating the repeated sampling of plots and controlling for time of day effects in counting. We compared population estimates from the current stratified random sample analysis to population estimates from hierarchical models with alternative model structures that describe year to year changes as random year effects, a trend with random year effects, or year effects modeled as 1-year differences. Patterns of population change from the hierarchical model results generally were similar to the patterns described by stratified random sample estimates, but significant visibility differences occurred between twilight to midday counts in all species. Controlling for the effects of time of day resulted in larger population estimates for all species in the hierarchical model analysis relative to the stratified random sample analysis. The hierarchical models also provided a convenient means of estimating population trend as derived statistics from the analysis. We detected significant declines in mallard and American black ducks and significant increases in wood ducks and Canada geese, a trend that had not been significant for 3 of these 4 species in the prior analysis. We recommend using hierarchical models for analysis of the Atlantic
Bayesian Estimation in the One-Parameter Latent Trait Model.
1980-03-01
3 MASSACHUSETTS LNIV AMHERST LAB OF PSYCHOMETRIC AND -- ETC F/G 12/1 BAYESIAN ESTIMATION IN THE ONE-PARA1ETER LATENT TRAIT MODEL. (U) MAR 80 H...TEST CHART VVNN lfl’ ,. [’ COD BAYESIAN ESTIMATION IN THE ONE-PARAMETER LATENT TRAIT MODEL 0 wtHAR IHARAN SWA I NATHAN AND JANICE A. GIFFORD Research...block numbef) latent trait theory Bayesain estimation 20. ABSTRACT (Continue on reveso aide If neceaar and identlfy by Nock mambe) ,-When several
Bayesian Analysis of Order-Statistics Models for Ranking Data.
ERIC Educational Resources Information Center
Yu, Philip L. H.
2000-01-01
Studied the order-statistics models, extending the usual normal order-statistics model into one in which the underlying random variables followed a multivariate normal distribution. Used a Bayesian approach and the Gibbs sampling technique. Applied the proposed method to analyze presidential election data from the American Psychological…
Bayesian Finite Mixtures for Nonlinear Modeling of Educational Data.
ERIC Educational Resources Information Center
Tirri, Henry; And Others
A Bayesian approach for finding latent classes in data is discussed. The approach uses finite mixture models to describe the underlying structure in the data and demonstrate that the possibility of using full joint probability models raises interesting new prospects for exploratory data analysis. The concepts and methods discussed are illustrated…
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…
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…
Small Sample Properties of Bayesian Multivariate Autoregressive Time Series Models
ERIC Educational Resources Information Center
Price, Larry R.
2012-01-01
The aim of this study was to compare the small sample (N = 1, 3, 5, 10, 15) performance of a Bayesian multivariate vector autoregressive (BVAR-SEM) time series model relative to frequentist power and parameter estimation bias. A multivariate autoregressive model was developed based on correlated autoregressive time series vectors of varying…
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,…
Bayesian methods for characterizing unknown parameters of material models
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
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 to characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.
Bayesian log-periodic model for financial crashes
NASA Astrophysics Data System (ADS)
Rodríguez-Caballero, Carlos Vladimir; Knapik, Oskar
2014-10-01
This paper introduces a Bayesian approach in econophysics literature about financial bubbles in order to estimate the most probable time for a financial crash to occur. To this end, we propose using noninformative prior distributions to obtain posterior distributions. Since these distributions cannot be performed analytically, we develop a Markov Chain Monte Carlo algorithm to draw from posterior distributions. We consider three Bayesian models that involve normal and Student's t-distributions in the disturbances and an AR(1)-GARCH(1,1) structure only within the first case. In the empirical part of the study, we analyze a well-known example of financial bubble - the S&P 500 1987 crash - to show the usefulness of the three methods under consideration and crashes of Merval-94, Bovespa-97, IPCMX-94, Hang Seng-97 using the simplest method. The novelty of this research is that the Bayesian models provide 95% credible intervals for the estimated crash time.
The Role of Prototype Learning in Hierarchical Models of Vision
ERIC Educational Resources Information Center
Thomure, Michael David
2014-01-01
I conduct a study of learning in HMAX-like models, which are hierarchical models of visual processing in biological vision systems. Such models compute a new representation for an image based on the similarity of image sub-parts to a number of specific patterns, called prototypes. Despite being a central piece of the overall model, the issue of…
Eacker, Daniel R; Lukacs, Paul M; Proffitt, Kelly M; Hebblewhite, Mark
2017-02-11
To successfully respond to changing habitat, climate or harvest, managers need to identify the most effective strategies to reverse population trends of declining species and/or manage harvest of game species. A classic approach in conservation biology for the last two decades has been the use of matrix population models to determine the most important vital rates affecting population growth rate (λ), that is, sensitivity. Ecologists quickly realized the critical role of environmental variability in vital rates affecting population growth rate by developing approaches such as life-stage simulation analysis (LSA) that account for both sensitivity and variability of a vital rate. These LSA methods used matrix-population modeling and Monte Carlo simulation methods, but faced challenges in integrating data from different sources, disentangling process and sampling variation, and in their flexibility. Here, we developed a Bayesian integrated population model (IPM) for two populations of a large herbivore, elk (Cervus canadensis) in Montana, USA. We then extended the IPM to evaluate sensitivity in a Bayesian framework. We integrated known-fate survival data from radio-marked adults and juveniles, fecundity data, and population counts in a hierarchical population model that explicitly accounted for process and sampling variance. Next, we tested the prevailing paradigm in large herbivore population ecology that juvenile survival of neonates <90 days old drives λ using our Bayesian LSA approach. In contrast to the prevailing paradigm in large herbivore ecology, we found that adult female survival explained more of the variation in λ than elk calf survival, and that summer and winter elk calf survival periods were nearly equivalent in importance for λ. Our Bayesian IPM improved precision of our vital rate estimates and highlighted discrepancies between count and vital rate data that could refine population monitoring, demonstrating that combining sensitivity analysis
NASA Technical Reports Server (NTRS)
Shih, Ann T.; Ancel, Ersin; Jones, Sharon M.
2012-01-01
The concern for reducing aviation safety risk is rising as the National Airspace System in the United States transforms to the Next Generation Air Transportation System (NextGen). The NASA Aviation Safety Program is committed to developing an effective aviation safety technology portfolio to meet the challenges of this transformation and to mitigate relevant safety risks. The paper focuses on the reasoning of selecting Object-Oriented Bayesian Networks (OOBN) as the technique and commercial software for the accident modeling and portfolio assessment. To illustrate the benefits of OOBN in a large and complex aviation accident model, the in-flight Loss-of-Control Accident Framework (LOCAF) constructed as an influence diagram is presented. An OOBN approach not only simplifies construction and maintenance of complex causal networks for the modelers, but also offers a well-organized hierarchical network that is easier for decision makers to exploit the model examining the effectiveness of risk mitigation strategies through technology insertions.
Chen, Jinsong
2013-05-01
Development of a hierarchical Bayesian model to estimate the spatiotemporal distribution of aqueous geochemical parameters associated with in-situ bioremediation using surface spectral induced polarization (SIP) data and borehole geochemical measurements collected during a bioremediation experiment at a uranium-contaminated site near Rifle, Colorado. The SIP data are first inverted for Cole-Cole parameters including chargeability, time constant, resistivity at the DC frequency and dependence factor, at each pixel of two-dimensional grids using a previously developed stochastic method. Correlations between the inverted Cole-Cole parameters and the wellbore-based groundwater chemistry measurements indicative of key metabolic processes within the aquifer (e.g. ferrous iron, sulfate, uranium) were established and used as a basis for petrophysical model development. The developed Bayesian model consists of three levels of statistical sub-models: 1) data model, providing links between geochemical and geophysical attributes, 2) process model, describing the spatial and temporal variability of geochemical properties in the subsurface system, and 3) parameter model, describing prior distributions of various parameters and initial conditions. The unknown parameters are estimated using Markov chain Monte Carlo methods. By combining the temporally distributed geochemical data with the spatially distributed geophysical data, we obtain the spatio-temporal distribution of ferrous iron, sulfate and sulfide, and their associated uncertainity information. The obtained results can be used to assess the efficacy of the bioremediation treatment over space and time and to constrain reactive transport models.
Hierarchical modeling of bycatch rates of sea turtles in the western North Atlantic
Gardner, B.; Sullivan, P.J.; Epperly, S.; Morreale, S.J.
2008-01-01
Previous studies indicate that the locations of the endangered loggerhead Caretta caretta and critically endangered leatherback Dermochelys coriacea sea turtles are influenced by water temperatures, and that incidental catch rates in the pelagic longline fishery vary by region. We present a Bayesian hierarchical model to examine the effects of environmental variables, including water temperature, on the number of sea turtles captured in the US pelagic longline fishery in the western North Atlantic. The modeling structure is highly flexible, utilizes a Bayesian model selection technique, and is fully implemented in the software program WinBUGS. The number of sea turtles captured is modeled as a zero-inflated Poisson distribution and the model incorporates fixed effects to examine region-specific differences in the parameter estimates. Results indicate that water temperature, region, bottom depth, and target species are all significant predictors of the number of loggerhead sea turtles captured. For leatherback sea turtles, the model with only target species had the most posterior model weight, though a re-parameterization of the model indicates that temperature influences the zero-inflation parameter. The relationship between the number of sea turtles captured and the variables of interest all varied by region. This suggests that management decisions aimed at reducing sea turtle bycatch may be more effective if they are spatially explicit. ?? Inter-Research 2008.
Free-Energy Bounds for Hierarchical Spin Models
NASA Astrophysics Data System (ADS)
Castellana, Michele; Barra, Adriano; Guerra, Francesco
2014-04-01
In this paper we study two non-mean-field (NMF) spin models built on a hierarchical lattice: the hierarchical Edward-Anderson model (HEA) of a spin glass, and Dyson's hierarchical model (DHM) of a ferromagnet. For the HEA, we prove the existence of the thermodynamic limit of the free energy and the replica-symmetry-breaking (RSB) free-energy bounds previously derived for the Sherrington-Kirkpatrick model of a spin glass. These RSB mean-field bounds are exact only if the order-parameter fluctuations (OPF) vanish: given that such fluctuations are not negligible in NMF models, we develop a novel strategy to tackle part of OPF in hierarchical models. The method is based on absorbing part of OPF of a block of spins into an effective Hamiltonian of the underlying spin blocks. We illustrate this method for DHM and show that, compared to the mean-field bound for the free energy, it provides a tighter NMF bound, with a critical temperature closer to the exact one. To extend this method to the HEA model, a suitable generalization of Griffith's correlation inequalities for Ising ferromagnets is needed: since correlation inequalities for spin glasses are still an open topic, we leave the extension of this method to hierarchical spin glasses as a future perspective.
Lele, Subhash R; Dennis, Brian; Lutscher, Frithjof
2007-07-01
We introduce a new statistical computing method, called data cloning, to calculate maximum likelihood estimates and their standard errors for complex ecological models. Although the method uses the Bayesian framework and exploits the computational simplicity of the Markov chain Monte Carlo (MCMC) algorithms, it provides valid frequentist inferences such as the maximum likelihood estimates and their standard errors. The inferences are completely invariant to the choice of the prior distributions and therefore avoid the inherent subjectivity of the Bayesian approach. The data cloning method is easily implemented using standard MCMC software. Data cloning is particularly useful for analysing ecological situations in which hierarchical statistical models, such as state-space models and mixed effects models, are appropriate. We illustrate the method by fitting two nonlinear population dynamics models to data in the presence of process and observation noise.
Reduction and Retrospection Approach to Modeling of Hierarchical Biological Rhythms
NASA Astrophysics Data System (ADS)
Nakao, Mitsuyuki; Okayama, Hiroshi; Katayama, Norihiro; Karashima, Akihiro
Physiome inherently investigates hierarchical layers of biological system. In the post genome era, the number of layers should increase because possible mechanisms at molecular level are always referred to. However, biological modeling in the post genome era has to face unavoidable uncertainties in biological measurements and explosion of degree of freedom. An exhaustive modeling seems to be necessary to understand possible mechanisms underlying biological phenomena at every hierarchical level. However, simultaneously it looks like an impossible or reckless trial. In order to get rid of them, we propose a novel modeling strategy that integrates the top-down retrospection and bottom-up reduction modeling. Here, our strategy is applied to modeling of biological rhythms which is an appropriate system to study because of the penetration of rhythmic dynamics through all of the hierarchical layers.
Hierarchic plate and shell models based on p-extension
NASA Technical Reports Server (NTRS)
Szabo, Barna A.; Sahrmann, Glenn J.
1988-01-01
Formulations of finite element models for beams, arches, plates and shells based on the principle of virtual work was studied. The focus is on computer implementation of hierarchic sequences of finite element models suitable for numerical solution of a large variety of practical problems which may concurrently contain thin and thick plates and shells, stiffeners, and regions where three dimensional representation is required. The approximate solutions corresponding to the hierarchic sequence of models converge to the exact solution of the fully three dimensional model. The stopping criterion is based on: (1) estimation of the relative error in energy norm; (2) equilibrium tests, and (3) observation of the convergence of quantities of interest.
ERIC Educational Resources Information Center
Park, Joonwook; Desarbo, Wayne S.; Liechty, John
2008-01-01
Multidimensional scaling (MDS) models for the analysis of dominance data have been developed in the psychometric and classification literature to simultaneously capture subjects' "preference heterogeneity" and the underlying dimentional structure for a set of designated stimuli in a parsimonious manner. There are two major types of latent utility…
Determining Predictor Importance in Hierarchical Linear Models Using Dominance Analysis
ERIC Educational Resources Information Center
Luo, Wen; Azen, Razia
2013-01-01
Dominance analysis (DA) is a method used to evaluate the relative importance of predictors that was originally proposed for linear regression models. This article proposes an extension of DA that allows researchers to determine the relative importance of predictors in hierarchical linear models (HLM). Commonly used measures of model adequacy in…
Measuring Learning Progressions Using Bayesian Modeling in Complex Assessments
ERIC Educational Resources Information Center
Rutstein, Daisy Wise
2012-01-01
This research examines issues regarding model estimation and robustness in the use of Bayesian Inference Networks (BINs) for measuring Learning Progressions (LPs). It provides background information on LPs and how they might be used in practice. Two simulation studies are performed, along with real data examples. The first study examines the case…
Shortlist B: A Bayesian Model of Continuous Speech Recognition
ERIC Educational Resources Information Center
Norris, Dennis; McQueen, James M.
2008-01-01
A Bayesian model of continuous speech recognition is presented. It is based on Shortlist (D. Norris, 1994; D. Norris, J. M. McQueen, A. Cutler, & S. Butterfield, 1997) and shares many of its key assumptions: parallel competitive evaluation of multiple lexical hypotheses, phonologically abstract prelexical and lexical representations, a feedforward…
Abdelnour, Farras; Genovese, Christopher; Huppert, Theodore
2010-01-01
Diffuse optical tomography (DOT) is a non-invasive brain imaging technique that uses low-levels of near-infrared light to measure optical absorption changes due to regional blood flow and blood oxygen saturation in the brain. By arranging light sources and detectors in a grid over the surface of the scalp, DOT studies attempt to spatially localize changes in oxy- and deoxy-hemoglobin in the brain that result from evoked brain activity during functional experiments. However, the reconstruction of accurate spatial images of hemoglobin changes from DOT data is an ill-posed linearized inverse problem, which requires model regularization to yield appropriate solutions. In this work, we describe and demonstrate the application of a parametric restricted maximum likelihood method (ReML) to incorporate multiple statistical priors into the recovery of optical images. This work is based on similar methods that have been applied to the inverse problem for magnetoencephalography (MEG). Herein, we discuss the adaptation of this model to DOT and demonstrate that this approach provides a means to objectively incorporate reconstruction constraints and demonstrate this approach through a series of simulated numerical examples. PMID:21258532
Modeling Unreliable Observations in Bayesian Networks by Credal Networks
NASA Astrophysics Data System (ADS)
Antonucci, Alessandro; Piatti, Alberto
Bayesian networks are probabilistic graphical models widely employed in AI for the implementation of knowledge-based systems. Standard inference algorithms can update the beliefs about a variable of interest in the network after the observation of some other variables. This is usually achieved under the assumption that the observations could reveal the actual states of the variables in a fully reliable way. We propose a procedure for a more general modeling of the observations, which allows for updating beliefs in different situations, including various cases of unreliable, incomplete, uncertain and also missing observations. This is achieved by augmenting the original Bayesian network with a number of auxiliary variables corresponding to the observations. For a flexible modeling of the observational process, the quantification of the relations between these auxiliary variables and those of the original Bayesian network is done by credal sets, i.e., convex sets of probability mass functions. Without any lack of generality, we show how this can be done by simply estimating the bounds of likelihoods of the observations for the different values of the observed variables. Overall, the Bayesian network is transformed into a credal network, for which a standard updating problem has to be solved. Finally, a number of transformations that might simplify the updating of the resulting credal network is provided.
Empirical evaluation of scoring functions for Bayesian network model selection.
Liu, Zhifa; Malone, Brandon; Yuan, Changhe
2012-01-01
In this work, we empirically evaluate the capability of various scoring functions of Bayesian networks for recovering true underlying structures. Similar investigations have been carried out before, but they typically relied on approximate learning algorithms to learn the network structures. The suboptimal structures found by the approximation methods have unknown quality and may affect the reliability of their conclusions. Our study uses an optimal algorithm to learn Bayesian network structures from datasets generated from a set of gold standard Bayesian networks. Because all optimal algorithms always learn equivalent networks, this ensures that only the choice of scoring function affects the learned networks. Another shortcoming of the previous studies stems from their use of random synthetic networks as test cases. There is no guarantee that these networks reflect real-world data. We use real-world data to generate our gold-standard structures, so our experimental design more closely approximates real-world situations. A major finding of our study suggests that, in contrast to results reported by several prior works, the Minimum Description Length (MDL) (or equivalently, Bayesian information criterion (BIC)) consistently outperforms other scoring functions such as Akaike's information criterion (AIC), Bayesian Dirichlet equivalence score (BDeu), and factorized normalized maximum likelihood (fNML) in recovering the underlying Bayesian network structures. We believe this finding is a result of using both datasets generated from real-world applications rather than from random processes used in previous studies and learning algorithms to select high-scoring structures rather than selecting random models. Other findings of our study support existing work, e.g., large sample sizes result in learning structures closer to the true underlying structure; the BDeu score is sensitive to the parameter settings; and the fNML performs pretty well on small datasets. We also
Empirical evaluation of scoring functions for Bayesian network model selection
2012-01-01
In this work, we empirically evaluate the capability of various scoring functions of Bayesian networks for recovering true underlying structures. Similar investigations have been carried out before, but they typically relied on approximate learning algorithms to learn the network structures. The suboptimal structures found by the approximation methods have unknown quality and may affect the reliability of their conclusions. Our study uses an optimal algorithm to learn Bayesian network structures from datasets generated from a set of gold standard Bayesian networks. Because all optimal algorithms always learn equivalent networks, this ensures that only the choice of scoring function affects the learned networks. Another shortcoming of the previous studies stems from their use of random synthetic networks as test cases. There is no guarantee that these networks reflect real-world data. We use real-world data to generate our gold-standard structures, so our experimental design more closely approximates real-world situations. A major finding of our study suggests that, in contrast to results reported by several prior works, the Minimum Description Length (MDL) (or equivalently, Bayesian information criterion (BIC)) consistently outperforms other scoring functions such as Akaike's information criterion (AIC), Bayesian Dirichlet equivalence score (BDeu), and factorized normalized maximum likelihood (fNML) in recovering the underlying Bayesian network structures. We believe this finding is a result of using both datasets generated from real-world applications rather than from random processes used in previous studies and learning algorithms to select high-scoring structures rather than selecting random models. Other findings of our study support existing work, e.g., large sample sizes result in learning structures closer to the true underlying structure; the BDeu score is sensitive to the parameter settings; and the fNML performs pretty well on small datasets. We also
Model-based hierarchical reinforcement learning and human action control
Botvinick, Matthew; Weinstein, Ari
2014-01-01
Recent work has reawakened interest in goal-directed or ‘model-based’ choice, where decisions are based on prospective evaluation of potential action outcomes. Concurrently, there has been growing attention to the role of hierarchy in decision-making and action control. We focus here on the intersection between these two areas of interest, considering the topic of hierarchical model-based control. To characterize this form of action control, we draw on the computational framework of hierarchical reinforcement learning, using this to interpret recent empirical findings. The resulting picture reveals how hierarchical model-based mechanisms might play a special and pivotal role in human decision-making, dramatically extending the scope and complexity of human behaviour. PMID:25267822
Model-based hierarchical reinforcement learning and human action control.
Botvinick, Matthew; Weinstein, Ari
2014-11-05
Recent work has reawakened interest in goal-directed or 'model-based' choice, where decisions are based on prospective evaluation of potential action outcomes. Concurrently, there has been growing attention to the role of hierarchy in decision-making and action control. We focus here on the intersection between these two areas of interest, considering the topic of hierarchical model-based control. To characterize this form of action control, we draw on the computational framework of hierarchical reinforcement learning, using this to interpret recent empirical findings. The resulting picture reveals how hierarchical model-based mechanisms might play a special and pivotal role in human decision-making, dramatically extending the scope and complexity of human behaviour.
A hierarchical model for the analysis of inter-laboratory comparison data
NASA Astrophysics Data System (ADS)
Forbes, Alistair B.
2016-12-01
This paper discusses the analysis of inter-laboratory comparison (ILC) data where there may be some doubt about the validity of the uncertainty statements. We develop a hierarchical model that treats the stated uncertainties as estimates of parameters representing the variances associated with the reported values of the measurand. The degree of belief in these estimates is modelled by an additional set of constants that can also be treated as parameters in the model. The hierarchical model is motivated by the analysis of repeated measurements drawn from a Gaussian distribution with unknown variance and represents a natural extension of the model underlying standard approaches to the analysis of ILC data based on a weighted least squares approach. Using Bayesian inference, the model provides a natural mechanism for updating the input distributions associated with the values reported by the participating laboratories based on the information available from all the participants. Importantly, the shapes of the input distributions are adjusted, not just their standard deviations. The distribution for the measurand is derived in terms of t-distributions and can be calculated using simple numerical quadrature schemes. The approach is illustrated on a number of data sets available in the literature.
Bayesian latent variable modelling of multivariate spatio-temporal variation in cancer mortality.
Tzala, Evangelia; Best, Nicky
2008-02-01
In this article, three alternative Bayesian hierarchical latent factor models are described for spatially and temporally correlated multivariate health data. The fundamentals of factor analysis with ideas of space- time disease mapping to provide a flexible framework for the joint analysis of multiple-related diseases in space and time with a view to estimating common and disease-specific trends in cancer risk are combined. The models are applied to area-level mortality data on six diet-related cancers for Greece over the 20-year period from 1980 to 1999. The aim of this study is to uncover the spatial and temporal patterns of any latent factor(s) underlying the cancer data that could be interpreted as reflecting some aspects of the habitual diet of the Greek population.
Applying Hierarchical Model Calibration to Automatically Generated Items.
ERIC Educational Resources Information Center
Williamson, David M.; Johnson, Matthew S.; Sinharay, Sandip; Bejar, Isaac I.
This study explored the application of hierarchical model calibration as a means of reducing, if not eliminating, the need for pretesting of automatically generated items from a common item model prior to operational use. Ultimately the successful development of automatic item generation (AIG) systems capable of producing items with highly similar…
The Revised Hierarchical Model: A Critical Review and Assessment
ERIC Educational Resources Information Center
Kroll, Judith F.; van Hell, Janet G.; Tokowicz, Natasha; Green, David W.
2010-01-01
Brysbaert and Duyck (this issue) suggest that it is time to abandon the Revised Hierarchical Model (Kroll and Stewart, 1994) in favor of connectionist models such as BIA+ (Dijkstra and Van Heuven, 2002) that more accurately account for the recent evidence on non-selective access in bilingual word recognition. In this brief response, we first…
Johnson-Neyman Type Technique in Hierarchical Linear Model.
ERIC Educational Resources Information Center
Miyazaki, Yasuo
One of the innovative approaches in the use of hierarchical linear models (HLM) is to use HLM for Slopes as Outcomes models. This implies that the researcher considers that the regression slopes vary from cluster to cluster randomly as well as systematically with certain covariates at the cluster level. Among the covariates, group indicator…
Hierarchical Policy Model for Managing Heterogeneous Security Systems
NASA Astrophysics Data System (ADS)
Lee, Dong-Young; Kim, Minsoo
2007-12-01
The integrated security management becomes increasingly complex as security manager must take heterogeneous security systems, different networking technologies, and distributed applications into consideration. The task of managing these security systems and applications depends on various systems and vender specific issues. In this paper, we present a hierarchical policy model which are derived from the conceptual policy, and specify means to enforce this behavior. The hierarchical policy model consist of five levels which are conceptual policy level, goal-oriented policy level, target policy level, process policy level and low-level policy.
An examination of disparities in cancer incidence in Texas using Bayesian random coefficient models
2015-01-01
Disparities in cancer risk exist between ethnic groups in the United States. These disparities often result from differential access to healthcare, differences in socioeconomic status and differential exposure to carcinogens. This study uses cancer incidence data from the population based Texas Cancer Registry to investigate the disparities in digestive and respiratory cancers from 2000 to 2008. A Bayesian hierarchical regression approach is used. All models are fit using the INLA method of Bayesian model estimation. Specifically, a spatially varying coefficient model of the disparity between Hispanic and Non-Hispanic incidence is used. Results suggest that a spatio-temporal heterogeneity model best accounts for the observed Hispanic disparity in cancer risk. Overall, there is a significant disadvantage for the Hispanic population of Texas with respect to both of these cancers, and this disparity varies significantly over space. The greatest disparities between Hispanics and Non-Hispanics in digestive and respiratory cancers occur in eastern Texas, with patterns emerging as early as 2000 and continuing until 2008. PMID:26421245
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 ...
Lai, Canhai; Xu, Zhijie; Pan, Wenxiao; Sun, Xin; Storlie, Curtis; Marcy, Peter; Dietiker, Jean-François; Li, Tingwen; Spenik, James
2016-01-01
To quantify the predictive confidence of a solid sorbent-based carbon capture design, a hierarchical validation methodology—consisting of basic unit problems with increasing physical complexity coupled with filtered model-based geometric upscaling has been developed and implemented. This paper describes the computational fluid dynamics (CFD) multi-phase reactive flow simulations and the associated data flows among different unit problems performed within the said hierarchical validation approach. The bench-top experiments used in this calibration and validation effort were carefully designed to follow the desired simple-to-complex unit problem hierarchy, with corresponding data acquisition to support model parameters calibrations at each unit problem level. A Bayesian calibration procedure is employed and the posterior model parameter distributions obtained at one unit-problem level are used as prior distributions for the same parameters in the next-tier simulations. Overall, the results have demonstrated that the multiphase reactive flow models within MFIX can be used to capture the bed pressure, temperature, CO2 capture capacity, and kinetics with quantitative accuracy. The CFD modeling methodology and associated uncertainty quantification techniques presented herein offer a solid framework for estimating the predictive confidence in the virtual scale up of a larger carbon capture device.
Bayesian neural network for rainfall-runoff modeling
NASA Astrophysics Data System (ADS)
Khan, Mohammad Sajjad; Coulibaly, Paulin
2006-07-01
In this paper, a Bayesian learning approach is introduced to train a multilayer feed-forward network for daily river flow and reservoir inflow simulation in a cold region river basin in Canada. In Bayesian approach, uncertainty about the relationship between inputs and outputs is initially taken care of by an assumed prior distribution of parameters (weights and biases). This prior distribution is updated to posterior distribution using a likelihood function following Bayes' theorem while data are observed. This posterior distribution is called the objective function of a network in the Bayesian learning approach. The objective function is maximized using a suitable optimization technique. Once the network is trained, the predictive distribution of the network outputs is obtained by integrating over the posterior distribution of weights. In this study, Gaussian prior distribution and a Gaussian noise model are used in defining posterior distribution. The network has been optimized using a scaled conjugate gradient technique. Posterior distribution of weights is approximated to Gaussian during prediction. Prediction performance of the Bayesian neural network (BNN) is compared with the results obtained from a standard artificial neural network (ANN) model and a widely used conceptual rainfall-runoff model, namely, HBV-96. The BNN model outperformed the conceptual model and slightly outperformed the standard ANN model in simulating mean, peak, and low river flows and reservoir inflows. The significant contribution of the Bayesian method over the conventional ANN approach, among others, is the uncertainty estimation of the outputs in the form of confidence intervals which are particularly needed in practical water resources applications. Prediction confidence limits (or intervals) indicate the extent to which one can rely on predictions for decision making. It is shown that the BNN can provide reliable streamflow and reservoir inflow forecasts without a loss in model
Bayesian analysis of structural equation models with dichotomous variables.
Lee, Sik-Yum; Song, Xin-Yuan
2003-10-15
Structural equation modelling has been used extensively in the behavioural and social sciences for studying interrelationships among manifest and latent variables. Recently, its uses have been well recognized in medical research. This paper introduces a Bayesian approach to analysing general structural equation models with dichotomous variables. In the posterior analysis, the observed dichotomous data are augmented with the hypothetical missing values, which involve the latent variables in the model and the unobserved continuous measurements underlying the dichotomous data. An algorithm based on the Gibbs sampler is developed for drawing the parameters values and the hypothetical missing values from the joint posterior distributions. Useful statistics, such as the Bayesian estimates and their standard error estimates, and the highest posterior density intervals, can be obtained from the simulated observations. A posterior predictive p-value is used to test the goodness-of-fit of the posited model. The methodology is applied to a study of hypertensive patient non-adherence to medication.
Bayesian non parametric modelling of Higgs pair production
NASA Astrophysics Data System (ADS)
Scarpa, Bruno; Dorigo, Tommaso
2017-03-01
Statistical classification models are commonly used to separate a signal from a background. In this talk we face the problem of isolating the signal of Higgs pair production using the decay channel in which each boson decays into a pair of b-quarks. Typically in this context non parametric methods are used, such as Random Forests or different types of boosting tools. We remain in the same non-parametric framework, but we propose to face the problem following a Bayesian approach. A Dirichlet process is used as prior for the random effects in a logit model which is fitted by leveraging the Polya-Gamma data augmentation. Refinements of the model include the insertion in the simple model of P-splines to relate explanatory variables with the response and the use of Bayesian trees (BART) to describe the atoms in the Dirichlet process.
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.
Conceptual hierarchical modeling to describe wetland plant community organization
Little, A.M.; Guntenspergen, G.R.; Allen, T.F.H.
2010-01-01
Using multivariate analysis, we created a hierarchical modeling process that describes how differently-scaled environmental factors interact to affect wetland-scale plant community organization in a system of small, isolated wetlands on Mount Desert Island, Maine. We followed the procedure: 1) delineate wetland groups using cluster analysis, 2) identify differently scaled environmental gradients using non-metric multidimensional scaling, 3) order gradient hierarchical levels according to spatiotem-poral scale of fluctuation, and 4) assemble hierarchical model using group relationships with ordination axes and post-hoc tests of environmental differences. Using this process, we determined 1) large wetland size and poor surface water chemistry led to the development of shrub fen wetland vegetation, 2) Sphagnum and water chemistry differences affected fen vs. marsh / sedge meadows status within small wetlands, and 3) small-scale hydrologic differences explained transitions between forested vs. non-forested and marsh vs. sedge meadow vegetation. This hierarchical modeling process can help explain how upper level contextual processes constrain biotic community response to lower-level environmental changes. It creates models with more nuanced spatiotemporal complexity than classification and regression tree procedures. Using this process, wetland scientists will be able to generate more generalizable theories of plant community organization, and useful management models. ?? Society of Wetland Scientists 2009.
Bayesian Estimation of Categorical Dynamic Factor Models
ERIC Educational Resources Information Center
Zhang, Zhiyong; Nesselroade, John R.
2007-01-01
Dynamic factor models have been used to analyze continuous time series behavioral data. We extend 2 main dynamic factor model variations--the direct autoregressive factor score (DAFS) model and the white noise factor score (WNFS) model--to categorical DAFS and WNFS models in the framework of the underlying variable method and illustrate them with…
de la Cruz-Mesía, Rolando; Quintana, Fernando A
2007-04-01
This paper discusses Bayesian statistical methods for the classification of observations into two or more groups based on hierarchical models for nonlinear longitudinal profiles. Parameter estimation for a discriminant model that classifies individuals into distinct predefined groups or populations uses appropriate posterior simulation schemes. The methods are illustrated with data from a study involving 173 pregnant women. The main objective in this study is to predict normal versus abnormal pregnancy outcomes from beta human chorionic gonadotropin data available at early stages of pregnancy.
Application of a predictive Bayesian model to environmental accounting.
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.
Application of the Bayesian dynamic survival model in medicine.
He, Jianghua; McGee, Daniel L; Niu, Xufeng
2010-02-10
The Bayesian dynamic survival model (BDSM), a time-varying coefficient survival model from the Bayesian prospective, was proposed in early 1990s but has not been widely used or discussed. In this paper, we describe the model structure of the BDSM and introduce two estimation approaches for BDSMs: the Markov Chain Monte Carlo (MCMC) approach and the linear Bayesian (LB) method. The MCMC approach estimates model parameters through sampling and is computationally intensive. With the newly developed geoadditive survival models and software BayesX, the BDSM is available for general applications. The LB approach is easier in terms of computations but it requires the prespecification of some unknown smoothing parameters. In a simulation study, we use the LB approach to show the effects of smoothing parameters on the performance of the BDSM and propose an ad hoc method for identifying appropriate values for those parameters. We also demonstrate the performance of the MCMC approach compared with the LB approach and a penalized partial likelihood method available in software R packages. A gastric cancer trial is utilized to illustrate the application of the BDSM.
Johnson-Neyman Type Technique in Hierarchical Linear Models
ERIC Educational Resources Information Center
Miyazaki, Yasuo; Maier, Kimberly S.
2005-01-01
In hierarchical linear models we often find that group indicator variables at the cluster level are significant predictors for the regression slopes. When this is the case, the average relationship between the outcome and a key independent variable are different from group to group. In these settings, a question such as "what range of the…
A hierarchical spatial modelling approach to investigate MRSA transmission in a tertiary hospital
2013-01-01
Background Most hospitals have a hierarchical design with beds positioned within cubicles and cubicles positioned within wards. Transmission of MRSA may be facilitated by patient proximity and thus the spatial arrangements of beds, cubicles and wards could be important in understanding MRSA transmission risk. Identifying high-risk areas of transmission may be useful in the design of more effective, targeted MRSA interventions. Methods Retrospective data on numbers of multi-resistant and non-multiresistant MRSA acquisitions were collected for 52 weeks in 2007 in a tertiary hospital in Brisbane, Australia. A hierarchical Bayesian spatio-temporal modelling approach was used to investigate spatial correlation in the hierarchically arranged datasets. The spatial component of the model decomposes cubicle-level variation into a spatially structured component and a spatially unstructured component, thereby encapsulating the influence of unmeasured predictor variables that themselves are spatially clustered and/or random. A fixed effect for the presence of another patient with the same type of MRSA in the cubicles two weeks prior was included. Results The best-fitting model for non-multiresistant MRSA had an unstructured random effect but no spatially structured random effect. The best-fitting model for multiresistant MRSA incorporated both spatially structured and unstructured random effects. While between-cubicle variability in risk of MRSA acquisition within the hospital was significant, there was only weak evidence to suggest that MRSA is spatially clustered. Presence of another patient with the same type of MRSA in the cubicles two weeks prior was a significant predictor of both types of MRSA in all models. Conclusions We found weak evidence of clustering of MRSA acquisition within the hospital. The presence of an infected patient in the same cubicle two weeks prior may support the importance of environmental contamination as a source of MRSA transmission. PMID
Modeling urban air pollution with optimized hierarchical fuzzy inference system.
Tashayo, Behnam; Alimohammadi, Abbas
2016-10-01
Environmental exposure assessments (EEA) and epidemiological studies require urban air pollution models with appropriate spatial and temporal resolutions. Uncertain available data and inflexible models can limit air pollution modeling techniques, particularly in under developing countries. This paper develops a hierarchical fuzzy inference system (HFIS) to model air pollution under different land use, transportation, and meteorological conditions. To improve performance, the system treats the issue as a large-scale and high-dimensional problem and develops the proposed model using a three-step approach. In the first step, a geospatial information system (GIS) and probabilistic methods are used to preprocess the data. In the second step, a hierarchical structure is generated based on the problem. In the third step, the accuracy and complexity of the model are simultaneously optimized with a multiple objective particle swarm optimization (MOPSO) algorithm. We examine the capabilities of the proposed model for predicting daily and annual mean PM2.5 and NO2 and compare the accuracy of the results with representative models from existing literature. The benefits provided by the model features, including probabilistic preprocessing, multi-objective optimization, and hierarchical structure, are precisely evaluated by comparing five different consecutive models in terms of accuracy and complexity criteria. Fivefold cross validation is used to assess the performance of the generated models. The respective average RMSEs and coefficients of determination (R (2)) for the test datasets using proposed model are as follows: daily PM2.5 = (8.13, 0.78), annual mean PM2.5 = (4.96, 0.80), daily NO2 = (5.63, 0.79), and annual mean NO2 = (2.89, 0.83). The obtained results demonstrate that the developed hierarchical fuzzy inference system can be utilized for modeling air pollution in EEA and epidemiological studies.
Bayesian Inference of High-Dimensional Dynamical Ocean Models
NASA Astrophysics Data System (ADS)
Lin, J.; Lermusiaux, P. F. J.; Lolla, S. V. T.; Gupta, A.; Haley, P. J., Jr.
2015-12-01
This presentation addresses a holistic set of challenges in high-dimension ocean Bayesian nonlinear estimation: i) predict the probability distribution functions (pdfs) of large nonlinear dynamical systems using stochastic partial differential equations (PDEs); ii) assimilate data using Bayes' law with these pdfs; iii) predict the future data that optimally reduce uncertainties; and (iv) rank the known and learn the new model formulations themselves. Overall, we allow the joint inference of the state, equations, geometry, boundary conditions and initial conditions of dynamical models. Examples are provided for time-dependent fluid and ocean flows, including cavity, double-gyre and Strait flows with jets and eddies. The Bayesian model inference, based on limited observations, is illustrated first by the estimation of obstacle shapes and positions in fluid flows. Next, the Bayesian inference of biogeochemical reaction equations and of their states and parameters is presented, illustrating how PDE-based machine learning can rigorously guide the selection and discovery of complex ecosystem models. Finally, the inference of multiscale bottom gravity current dynamics is illustrated, motivated in part by classic overflows and dense water formation sites and their relevance to climate monitoring and dynamics. This is joint work with our MSEAS group at MIT.
Bayesian restoration of ion channel records using hidden Markov models.
Rosales, R; Stark, J A; Fitzgerald, W J; Hladky, S B
2001-03-01
Hidden Markov models have been used to restore recorded signals of single ion channels buried in background noise. Parameter estimation and signal restoration are usually carried out through likelihood maximization by using variants of the Baum-Welch forward-backward procedures. This paper presents an alternative approach for dealing with this inferential task. The inferences are made by using a combination of the framework provided by Bayesian statistics and numerical methods based on Markov chain Monte Carlo stochastic simulation. The reliability of this approach is tested by using synthetic signals of known characteristics. The expectations of the model parameters estimated here are close to those calculated using the Baum-Welch algorithm, but the present methods also yield estimates of their errors. Comparisons of the results of the Bayesian Markov Chain Monte Carlo approach with those obtained by filtering and thresholding demonstrate clearly the superiority of the new methods.
Hierarchical Architectural Considerations in Econometric Modeling of Manufacturing Systems
1981-06-01
the model (e.g. center level as a function of cell level, etc.). Although the current effort was to develop an IDEF o activ- ity model, the...concepts and thoughts on synthesizing existing knowledge toward the objective of developing a hierarchical IDEF o econo- metric model for a large scale...review of the termin- ology and structure of IDEF o (ICAM definition method-version 0) is given in the subsequent paragraphs. Structured analysis
Theory-Based Bayesian Models of Inductive Inference
2010-06-30
Oxford University Press . 28. Griffiths, T. L. and Tenenbaum, J.B. (2007). Two proposals for causal grammar. In A. Gopnik and L. Schulz (eds.). ( ausal Learning. Oxford University Press . 29. Tenenbaum. J. B.. Kemp, C, Shafto. P. (2007). Theory-based Bayesian models for inductive reasoning. In A. Feeney and E. Heit (eds.). Induction. Cambridge University Press. 30. Goodman, N. D., Tenenbaum, J. B., Griffiths. T. L.. & Feldman, J. (2008). Compositionality in rational analysis: Grammar-based induction for concept
Slice sampling technique in Bayesian extreme of gold price modelling
NASA Astrophysics Data System (ADS)
Rostami, Mohammad; Adam, Mohd Bakri; Ibrahim, Noor Akma; Yahya, Mohamed Hisham
2013-09-01
In this paper, a simulation study of Bayesian extreme values by using Markov Chain Monte Carlo via slice sampling algorithm is implemented. We compared the accuracy of slice sampling with other methods for a Gumbel model. This study revealed that slice sampling algorithm offers more accurate and closer estimates with less RMSE than other methods . Finally we successfully employed this procedure to estimate the parameters of Malaysia extreme gold price from 2000 to 2011.
How to Address Measurement Noise in Bayesian Model Averaging
NASA Astrophysics Data System (ADS)
Schöniger, A.; Wöhling, T.; Nowak, W.
2014-12-01
When confronted with the challenge of selecting one out of several competing conceptual models for a specific modeling task, Bayesian model averaging is a rigorous choice. It ranks the plausibility of models based on Bayes' theorem, which yields an optimal trade-off between performance and complexity. With the resulting posterior model probabilities, their individual predictions are combined into a robust weighted average and the overall predictive uncertainty (including conceptual uncertainty) can be quantified. This rigorous framework does, however, not yet explicitly consider statistical significance of measurement noise in the calibration data set. This is a major drawback, because model weights might be instable due to the uncertainty in noisy data, which may compromise the reliability of model ranking. We present a new extension to the Bayesian model averaging framework that explicitly accounts for measurement noise as a source of uncertainty for the weights. This enables modelers to assess the reliability of model ranking for a specific application and a given calibration data set. Also, the impact of measurement noise on the overall prediction uncertainty can be determined. Technically, our extension is built within a Monte Carlo framework. We repeatedly perturb the observed data with random realizations of measurement error. Then, we determine the robustness of the resulting model weights against measurement noise. We quantify the variability of posterior model weights as weighting variance. We add this new variance term to the overall prediction uncertainty analysis within the Bayesian model averaging framework to make uncertainty quantification more realistic and "complete". We illustrate the importance of our suggested extension with an application to soil-plant model selection, based on studies by Wöhling et al. (2013, 2014). Results confirm that noise in leaf area index or evaporation rate observations produces a significant amount of weighting
Bayesian Isotonic Regression Dose-response (BIRD) Model.
Li, Wen; Fu, Haoda
2016-12-21
Understanding dose-response relationship is a crucial step in drug development. There are a few parametric methods to estimate dose-response curves, such as the Emax model and the logistic model. These parametric models are easy to interpret and, hence, widely used. However, these models often require the inclusion of patients on high-dose levels; otherwise, the model parameters cannot be reliably estimated. To have robust estimation, nonparametric models are used. However, these models are not able to estimate certain important clinical parameters, such as ED50 and Emax. Furthermore, in many therapeutic areas, dose-response curves can be assumed as non-decreasing functions. This creates an additional challenge for nonparametric methods. In this paper, we propose a new Bayesian isotonic regression dose-response model which features advantages from both parametric and nonparametric models. The ED50 and Emax can be derived from this model. Simulations are provided to evaluate the Bayesian isotonic regression dose-response model performance against two parametric models. We apply this model to a data set from a diabetes dose-finding study.
Bayesian prediction of placebo analgesia in an instrumental learning model
Jung, Won-Mo; Lee, Ye-Seul; Wallraven, Christian; Chae, Younbyoung
2017-01-01
Placebo analgesia can be primarily explained by the Pavlovian conditioning paradigm in which a passively applied cue becomes associated with less pain. In contrast, instrumental conditioning employs an active paradigm that might be more similar to clinical settings. In the present study, an instrumental conditioning paradigm involving a modified trust game in a simulated clinical situation was used to induce placebo analgesia. Additionally, Bayesian modeling was applied to predict the placebo responses of individuals based on their choices. Twenty-four participants engaged in a medical trust game in which decisions to receive treatment from either a doctor (more effective with high cost) or a pharmacy (less effective with low cost) were made after receiving a reference pain stimulus. In the conditioning session, the participants received lower levels of pain following both choices, while high pain stimuli were administered in the test session even after making the decision. The choice-dependent pain in the conditioning session was modulated in terms of both intensity and uncertainty. Participants reported significantly less pain when they chose the doctor or the pharmacy for treatment compared to the control trials. The predicted pain ratings based on Bayesian modeling showed significant correlations with the actual reports from participants for both of the choice categories. The instrumental conditioning paradigm allowed for the active choice of optional cues and was able to induce the placebo analgesia effect. Additionally, Bayesian modeling successfully predicted pain ratings in a simulated clinical situation that fits well with placebo analgesia induced by instrumental conditioning. PMID:28225816
Comparing Bayesian stable isotope mixing models: Which tools are best for sediments?
NASA Astrophysics Data System (ADS)
Morris, David; Macko, Stephen
2016-04-01
Bayesian stable isotope mixing models have received much attention as a means of coping with multiple sources and uncertainty in isotope ecology (e.g. Phillips et al., 2014), enabling the probabilistic determination of the contributions made by each food source to the total diet of the organism in question. We have applied these techniques to marine sediments for the first time. The sediments of the Chukchi Sea and Beaufort Sea offer an opportunity to utilize these models for organic geochemistry, as there are three likely sources of organic carbon; pelagic phytoplankton, sea ice algae and terrestrial material from rivers and coastal erosion, as well as considerable variation in the marine δ13C values. Bayesian mixing models using bulk δ13C and δ15N data from Shelf Basin Interaction samples allow for the probabilistic determination of the contributions made by each of the sources to the organic carbon budget, and can be compared with existing source contribution estimates based upon biomarker models (e.g. Belicka & Harvey, 2009, Faux, Belicka, & Rodger Harvey, 2011). The δ13C of this preserved material varied from -22.1 to -16.7‰ (mean -19.4±1.3‰), while δ15N varied from 4.1 to 7.6‰ (mean 5.7±1.1‰). Using the SIAR model, we found that water column productivity was the source of between 50 and 70% of the organic carbon buried in this portion of the western Arctic with the remainder mainly supplied by sea ice algal productivity (25-35%) and terrestrial inputs (15%). With many mixing models now available, this study will compare SIAR with MixSIAR and the new FRUITS model. Monte Carlo modeling of the mixing polygon will be used to validate the models, and hierarchical models will be utilised to glean more information from the data set.
Babcock, Chad; Finley, Andrew O.; Bradford, John B.; Kolka, Randall K.; Birdsey, Richard A.; Ryan, Michael G.
2015-01-01
Many studies and production inventory systems have shown the utility of coupling covariates derived from Light Detection and Ranging (LiDAR) data with forest variables measured on georeferenced inventory plots through regression models. The objective of this study was to propose and assess the use of a Bayesian hierarchical modeling framework that accommodates both residual spatial dependence and non-stationarity of model covariates through the introduction of spatial random effects. We explored this objective using four forest inventory datasets that are part of the North American Carbon Program, each comprising point-referenced measures of above-ground forest biomass and discrete LiDAR. For each dataset, we considered at least five regression model specifications of varying complexity. Models were assessed based on goodness of fit criteria and predictive performance using a 10-fold cross-validation procedure. Results showed that the addition of spatial random effects to the regression model intercept improved fit and predictive performance in the presence of substantial residual spatial dependence. Additionally, in some cases, allowing either some or all regression slope parameters to vary spatially, via the addition of spatial random effects, further improved model fit and predictive performance. In other instances, models showed improved fit but decreased predictive performance—indicating over-fitting and underscoring the need for cross-validation to assess predictive ability. The proposed Bayesian modeling framework provided access to pixel-level posterior predictive distributions that were useful for uncertainty mapping, diagnosing spatial extrapolation issues, revealing missing model covariates, and discovering locally significant parameters.
A Bayesian Nonparametric Meta-Analysis Model
ERIC Educational Resources Information Center
Karabatsos, George; Talbott, Elizabeth; Walker, Stephen G.
2015-01-01
In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal effect-size population distribution, conditionally on parameters and covariates. For estimating the mean overall…
Hierarchical Item Response Models for Cognitive Diagnosis
ERIC Educational Resources Information Center
Hansen, Mark Patrick
2013-01-01
Cognitive diagnosis models (see, e.g., Rupp, Templin, & Henson, 2010) have received increasing attention within educational and psychological measurement. The popularity of these models may be largely due to their perceived ability to provide useful information concerning both examinees (classifying them according to their attribute profiles)…
Hierarchical spatial models for predicting pygmy rabbit distribution and relative abundance
Wilson, T.L.; Odei, J.B.; Hooten, M.B.; Edwards, T.C.
2010-01-01
Conservationists routinely use species distribution models to plan conservation, restoration and development actions, while ecologists use them to infer process from pattern. These models tend to work well for common or easily observable species, but are of limited utility for rare and cryptic species. This may be because honest accounting of known observation bias and spatial autocorrelation are rarely included, thereby limiting statistical inference of resulting distribution maps. We specified and implemented a spatially explicit Bayesian hierarchical model for a cryptic mammal species (pygmy rabbit Brachylagus idahoensis). Our approach used two levels of indirect sign that are naturally hierarchical (burrows and faecal pellets) to build a model that allows for inference on regression coefficients as well as spatially explicit model parameters. We also produced maps of rabbit distribution (occupied burrows) and relative abundance (number of burrows expected to be occupied by pygmy rabbits). The model demonstrated statistically rigorous spatial prediction by including spatial autocorrelation and measurement uncertainty. We demonstrated flexibility of our modelling framework by depicting probabilistic distribution predictions using different assumptions of pygmy rabbit habitat requirements. Spatial representations of the variance of posterior predictive distributions were obtained to evaluate heterogeneity in model fit across the spatial domain. Leave-one-out cross-validation was conducted to evaluate the overall model fit. Synthesis and applications. Our method draws on the strengths of previous work, thereby bridging and extending two active areas of ecological research: species distribution models and multi-state occupancy modelling. Our framework can be extended to encompass both larger extents and other species for which direct estimation of abundance is difficult. ?? 2010 The Authors. Journal compilation ?? 2010 British Ecological Society.
3-D model-based Bayesian classification
Soenneland, L.; Tenneboe, P.; Gehrmann, T.; Yrke, O.
1994-12-31
The challenging task of the interpreter is to integrate different pieces of information and combine them into an earth model. The sophistication level of this earth model might vary from the simplest geometrical description to the most complex set of reservoir parameters related to the geometrical description. Obviously the sophistication level also depend on the completeness of the available information. The authors describe the interpreter`s task as a mapping between the observation space and the model space. The information available to the interpreter exists in observation space and the task is to infer a model in model-space. It is well-known that this inversion problem is non-unique. Therefore any attempt to find a solution depend son constraints being added in some manner. The solution will obviously depend on which constraints are introduced and it would be desirable to allow the interpreter to modify the constraints in a problem-dependent manner. They will present a probabilistic framework that gives the interpreter the tools to integrate the different types of information and produce constrained solutions. The constraints can be adapted to the problem at hand.
Bayesian Thurstonian models for ranking data using JAGS.
Johnson, Timothy R; Kuhn, Kristine M
2013-09-01
A Thurstonian model for ranking data assumes that observed rankings are consistent with those of a set of underlying continuous variables. This model is appealing since it renders ranking data amenable to familiar models for continuous response variables-namely, linear regression models. To date, however, the use of Thurstonian models for ranking data has been very rare in practice. One reason for this may be that inferences based on these models require specialized technical methods. These methods have been developed to address computational challenges involved in these models but are not easy to implement without considerable technical expertise and are not widely available in software packages. To address this limitation, we show that Bayesian Thurstonian models for ranking data can be very easily implemented with the JAGS software package. We provide JAGS model files for Thurstonian ranking models for general use, discuss their implementation, and illustrate their use in analyses.
Zhang, Guannan; Webster, Clayton G; Gunzburger, Max D
2012-09-01
Although Bayesian analysis has become vital to the quantification of prediction uncertainty in groundwater modeling, its application has been hindered due to the computational cost associated with numerous model executions needed for exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, we develop a new approach that improves computational efficiency of Bayesian inference by constructing a surrogate system based on an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, we utilize a compactly supported higher-order hierar- chical basis to construct the surrogate system, resulting in a significant reduction in the number of computational simulations required. In addition, we use hierarchical surplus as an error indi- cator to determine adaptive sparse grids. This allows local refinement in the uncertain domain and/or anisotropic detection with respect to the random model parameters, which further improves computational efficiency. Finally, we incorporate a global optimization technique and propose an iterative algorithm for building the surrogate system for the PPDF with multiple significant modes. Once the surrogate system is determined, the PPDF can be evaluated by sampling the surrogate system directly with very little computational cost. The developed method is evaluated first using a simple analytical density function with multiple modes and then using two synthetic groundwater reactive transport models. The groundwater models represent different levels of complexity; the first example involves coupled linear reactions and the second example simulates nonlinear ura- nium surface complexation. The results show that the aSG-hSC is an effective and efficient tool for Bayesian inference in groundwater modeling in comparison with conventional
Predicting coastal cliff erosion using a Bayesian probabilistic model
Hapke, C.; Plant, N.
2010-01-01
Regional coastal cliff retreat is difficult to model due to the episodic nature of failures and the along-shore variability of retreat events. There is a growing demand, however, for predictive models that can be used to forecast areas vulnerable to coastal erosion hazards. Increasingly, probabilistic models are being employed that require data sets of high temporal density to define the joint probability density function that relates forcing variables (e.g. wave conditions) and initial conditions (e.g. cliff geometry) to erosion events. In this study we use a multi-parameter Bayesian network to investigate correlations between key variables that control and influence variations in cliff retreat processes. The network uses Bayesian statistical methods to estimate event probabilities using existing observations. Within this framework, we forecast the spatial distribution of cliff retreat along two stretches of cliffed coast in Southern California. The input parameters are the height and slope of the cliff, a descriptor of material strength based on the dominant cliff-forming lithology, and the long-term cliff erosion rate that represents prior behavior. The model is forced using predicted wave impact hours. Results demonstrate that the Bayesian approach is well-suited to the forward modeling of coastal cliff retreat, with the correct outcomes forecast in 70-90% of the modeled transects. The model also performs well in identifying specific locations of high cliff erosion, thus providing a foundation for hazard mapping. This approach can be employed to predict cliff erosion at time-scales ranging from storm events to the impacts of sea-level rise at the century-scale. ?? 2010.