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 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.
Bayesian hierarchical modeling of drug stability data.
Chen, Jie; Zhong, Jinglin; Nie, Lei
2008-06-15
Stability data are commonly analyzed using linear fixed or random effect model. The linear fixed effect model does not take into account the batch-to-batch variation, whereas the random effect model may suffer from the unreliable shelf-life estimates due to small sample size. Moreover, both methods do not utilize any prior information that might have been available. In this article, we propose a Bayesian hierarchical approach to modeling drug stability data. Under this hierarchical structure, we first use Bayes factor to test the poolability of batches. Given the decision on poolability of batches, we then estimate the shelf-life that applies to all batches. The approach is illustrated with two example data sets and its performance is compared in simulation studies with that of the commonly used frequentist methods. (c) 2008 John Wiley & Sons, Ltd.
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
Bayesian Hierarchical Models to Augment the Mediterranean Forecast System
2016-06-07
Bayesian Hierarchical Models to Augment the Mediterranean Forecast System Ralph F. Milliff Colorado Research Associates Division NorthWest...last year. Our goal is to develop an ensemble ocean forecast methodology, using Bayesian Hierarchical Modelling (BHM) tools. The ocean ensemble...geostrophy model introduced by Royle et al. (1998). The second objective involves the accurate representation of forecast error covariance evolution in
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
Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring
Carlos Carroll; Devin S. Johnson; Jeffrey R. Dunk; William J. Zielinski
2010-01-01
Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their dataâs 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...
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
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 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
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.
Calibrating Subjective Probabilities Using Hierarchical Bayesian Models
NASA Astrophysics Data System (ADS)
Merkle, Edgar C.
A body of psychological research has examined the correspondence between a judge's subjective probability of an event's outcome and the event's actual outcome. The research generally shows that subjective probabilities are noisy and do not match the "true" probabilities. However, subjective probabilities are still useful for forecasting purposes if they bear some relationship to true probabilities. The purpose of the current research is to exploit relationships between subjective probabilities and outcomes to create improved, model-based probabilities for forecasting. Once the model has been trained in situations where the outcome is known, it can then be used in forecasting situations where the outcome is unknown. These concepts are demonstrated using experimental psychology data, and potential applications are discussed.
A Bayesian hierarchical model for climate change detection and attribution
NASA Astrophysics Data System (ADS)
Katzfuss, Matthias; Hammerling, Dorit; Smith, Richard L.
2017-06-01
Regression-based detection and attribution methods continue to take a central role in the study of climate change and its causes. Here we propose a novel Bayesian hierarchical approach to this problem, which allows us to address several open methodological questions. Specifically, we take into account the uncertainties in the true temperature change due to imperfect measurements, the uncertainty in the true climate signal under different forcing scenarios due to the availability of only a small number of climate model simulations, and the uncertainty associated with estimating the climate variability covariance matrix, including the truncation of the number of empirical orthogonal functions (EOFs) in this covariance matrix. We apply Bayesian model averaging to assign optimal probabilistic weights to different possible truncations and incorporate all uncertainties into the inference on the regression coefficients. We provide an efficient implementation of our method in a software package and illustrate its use with a realistic application.
Mapping soil water retention curves via spatial Bayesian hierarchical models
NASA Astrophysics Data System (ADS)
Yang, Wen-Hsi; Clifford, David; Minasny, Budiman
2015-05-01
Soil water retention curves are an important parameter in soil hydrological modeling. These curves are usually represented by the van Genuchten model. Two approaches have previously been taken to predict curves across a field - interpolation of field measurements followed by estimation of the van Genuchten model parameters, or estimation of the parameters according to field measurements followed by interpolation of the estimated parameters. Neither approach is ideal as, due to their two-stage nature, they fail to properly track uncertainty from one stage to the next. In this paper we address this shortcoming through a spatial Bayesian hierarchical model that fits the van Genuchten model and predicts the fields of hydraulic parameters of the van Genuchten model as well as fields of the corresponding soil water retention curves. This approach expands the van Genuchten model to a hierarchical modeling framework. In this framework, soil properties and physical or environmental factors can be treated as covariates to add into the van Genuchten model hierarchically. Consequently, the effects of covariates on the hydraulic parameters of the van Genuchten model can be identified. In addition, our approach takes advantage of Bayesian analysis to account for uncertainty and overcome the shortcomings of other existing methods. The code used to fit these models are available as an appendix to this paper. We apply this approach to data surveyed from part of the alluvial plain of the river Rhône near Yenne in Savoie, France. In this data analysis, we demonstrate how the inclusion of soil type or spatial effects can improve the van Genuchten model's predictions of soil water retention curves.
Analysis of runoff extremes using spatial hierarchical Bayesian modeling
NASA Astrophysics Data System (ADS)
Reza Najafi, Mohammad; Moradkhani, Hamid
2013-10-01
A spatial hierarchical Bayesian method is developed to model the extreme runoffs over two spatial domains in Columbia River Basin, USA. This method combines the limited number of data from different locations. The two spatial domains contain 31 and 20 gage stations, respectively, with daily streamflow records ranging from 30 to over 130 years. The generalized Pareto distribution (GPD) is employed for the analysis of extremes. Temporally independent data are generated using declustering procedure, where runoff extremes are first grouped into clusters and then the maximum of each cluster is retained. The GPD scale parameter is modeled based on a Gaussian geostatistical process and additional variables including the latitude, longitude, elevation, and drainage area are incorporated by means of a hierarchy. Metropolis-Hasting within Gibbs Sampler is used to infer the parameters of the GPD and the geostatistical process to estimate the return levels across the basins. The performance of the hierarchical Bayesian model is evaluated by comparing the estimates of 100 year return level floods with the maximum likelihood estimates at sites that are not used during the parameter inference process. Various prior distributions are used to assess the sensitivity of the posterior distributions. The selected model is then employed to estimate floods with different return levels in time slices of 15 years in order to detect possible trends in runoff extremes. The results show cyclic variations in the spatial average of the 100 year return level floods across the basins with consistent increasing trends distinguishable in some areas.
Inversion of hierarchical Bayesian models using Gaussian processes.
Lomakina, Ekaterina I; Paliwal, Saee; Diaconescu, Andreea O; Brodersen, Kay H; Aponte, Eduardo A; Buhmann, Joachim M; Stephan, Klaas E
2015-09-01
Over the past decade, computational approaches to neuroimaging have increasingly made use of hierarchical Bayesian models (HBMs), either for inferring on physiological mechanisms underlying fMRI data (e.g., dynamic causal modelling, DCM) or for deriving computational trajectories (from behavioural data) which serve as regressors in general linear models. However, an unresolved problem is that standard methods for inverting the hierarchical Bayesian model are either very slow, e.g. Markov Chain Monte Carlo Methods (MCMC), or are vulnerable to local minima in non-convex optimisation problems, such as variational Bayes (VB). This article considers Gaussian process optimisation (GPO) as an alternative approach for global optimisation of sufficiently smooth and efficiently evaluable objective functions. GPO avoids being trapped in local extrema and can be computationally much more efficient than MCMC. Here, we examine the benefits of GPO for inverting HBMs commonly used in neuroimaging, including DCM for fMRI and the Hierarchical Gaussian Filter (HGF). Importantly, to achieve computational efficiency despite high-dimensional optimisation problems, we introduce a novel combination of GPO and local gradient-based search methods. The utility of this GPO implementation for DCM and HGF is evaluated against MCMC and VB, using both synthetic data from simulations and empirical data. Our results demonstrate that GPO provides parameter estimates with equivalent or better accuracy than the other techniques, but at a fraction of the computational cost required for MCMC. We anticipate that GPO will prove useful for robust and efficient inversion of high-dimensional and nonlinear models of neuroimaging data. Copyright © 2015. Published by Elsevier Inc.
A generalizable hierarchical Bayesian model for persistent SAR change detection
NASA Astrophysics Data System (ADS)
Newstadt, Gregory E.; Zelnio, Edmund G.; Hero, Alfred O., III
2012-05-01
This paper proposes a hierarchical Bayesian model for multiple-pass, multiple antenna synthetic aperture radar (SAR) systems with the goal of adaptive change detection. We model the SAR phenomenology directly, including antenna and spatial dependencies, speckle and specular noise, and stationary clutter. We extend previous work1 by estimating the antenna covariance matrix directly, leading to improved performance in high clutter regions. The proposed SAR model is also shown to be easily generalizable when additional prior information is available, such as locations of roads/intersections or smoothness priors on the target motion. The performance of our posterior inference algorithm is analyzed over a large set of measured SAR imagery. It is shown that the proposed algorithm provides competitive or better results to common change detection algorithms with additional benefits such as few tuning parameters and a characterization of the posterior distribution.
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.
Bayesian Hierarchical Modeling for Big Data Fusion in Soil Hydrology
NASA Astrophysics Data System (ADS)
Mohanty, B.; Kathuria, D.; Katzfuss, M.
2016-12-01
Soil moisture datasets from remote sensing (RS) platforms (such as SMOS and SMAP) and reanalysis products from land surface models are typically available on a coarse spatial granularity of several square km. Ground based sensors on the other hand provide observations on a finer spatial scale (meter scale or less) but are sparsely available. Soil moisture is affected by high variability due to complex interactions between geologic, topographic, vegetation and atmospheric variables. Hydrologic processes usually occur at a scale of 1 km or less and therefore spatially ubiquitous and temporally periodic soil moisture products at this scale are required to aid local decision makers in agriculture, weather prediction and reservoir operations. Past literature has largely focused on downscaling RS soil moisture for a small extent of a field or a watershed and hence the applicability of such products has been limited. The present study employs a spatial Bayesian Hierarchical Model (BHM) to derive soil moisture products at a spatial scale of 1 km for the state of Oklahoma by fusing point scale Mesonet data and coarse scale RS data for soil moisture and its auxiliary covariates such as precipitation, topography, soil texture and vegetation. It is seen that the BHM model handles change of support problems easily while performing accurate uncertainty quantification arising from measurement errors and imperfect retrieval algorithms. The computational challenge arising due to the large number of measurements is tackled by utilizing basis function approaches and likelihood approximations. The BHM model can be considered as a complex Bayesian extension of traditional geostatistical prediction methods (such as Kriging) for large datasets in the presence of uncertainties.
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.
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.
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
Wei Wu; James Clark; James Vose
2010-01-01
Hierarchical Bayesian (HB) modeling allows for multiple sources of uncertainty by factoring complex relationships into conditional distributions that can be used to draw inference and make predictions. We applied an HB model to estimate the parameters and state variables of a parsimonious hydrological model â GR4J â by coherently assimilating the uncertainties from the...
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…
Qian, Song S; Craig, J Kevin; Baustian, Melissa M; Rabalais, Nancy N
2009-12-01
We introduce the Bayesian hierarchical modeling approach for analyzing observational data from marine ecological studies using a data set intended for inference on the effects of bottom-water hypoxia on macrobenthic communities in the northern Gulf of Mexico off the coast of Louisiana, USA. We illustrate (1) the process of developing a model, (2) the use of the hierarchical model results for statistical inference through innovative graphical presentation, and (3) a comparison to the conventional linear modeling approach (ANOVA). Our results indicate that the Bayesian hierarchical approach is better able to detect a "treatment" effect than classical ANOVA while avoiding several arbitrary assumptions necessary for linear models, and is also more easily interpreted when presented graphically. These results suggest that the hierarchical modeling approach is a better alternative than conventional linear models and should be considered for the analysis of observational field data from marine systems.
Cross-validation to select Bayesian hierarchical models in phylogenetics.
Duchêne, Sebastián; Duchêne, David A; Di Giallonardo, Francesca; Eden, John-Sebastian; Geoghegan, Jemma L; Holt, Kathryn E; Ho, Simon Y W; Holmes, Edward C
2016-05-26
Recent developments in Bayesian phylogenetic models have increased the range of inferences that can be drawn from molecular sequence data. Accordingly, model selection has become an important component of phylogenetic analysis. Methods of model selection generally consider the likelihood of the data under the model in question. In the context of Bayesian phylogenetics, the most common approach involves estimating the marginal likelihood, which is typically done by integrating the likelihood across model parameters, weighted by the prior. Although this method is accurate, it is sensitive to the presence of improper priors. We explored an alternative approach based on cross-validation that is widely used in evolutionary analysis. This involves comparing models according to their predictive performance. We analysed simulated data and a range of viral and bacterial data sets using a cross-validation approach to compare a variety of molecular clock and demographic models. Our results show that cross-validation can be effective in distinguishing between strict- and relaxed-clock models and in identifying demographic models that allow growth in population size over time. In most of our empirical data analyses, the model selected using cross-validation was able to match that selected using marginal-likelihood estimation. The accuracy of cross-validation appears to improve with longer sequence data, particularly when distinguishing between relaxed-clock models. Cross-validation is a useful method for Bayesian phylogenetic model selection. This method can be readily implemented even when considering complex models where selecting an appropriate prior for all parameters may be difficult.
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
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.
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 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 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 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 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 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 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 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 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.
Bayesian X-ray computed tomography using a three-level hierarchical prior model
NASA Astrophysics Data System (ADS)
Wang, Li; Mohammad-Djafari, Ali; Gac, Nicolas
2017-06-01
In recent decades X-ray Computed Tomography (CT) image reconstruction has been largely developed in both medical and industrial domain. In this paper, we propose using the Bayesian inference approach with a new hierarchical prior model. In the proposed model, a generalised Student-t distribution is used to enforce the Haar transformation of images to be sparse. Comparisons with some state of the art methods are presented. It is shown that by using the proposed model, the sparsity of sparse representation of images is enforced, so that edges of images are preserved. Simulation results are also provided to demonstrate the effectiveness of the new hierarchical model for reconstruction with fewer projections.
Berry, Scott M; Broglio, Kristine R; Groshen, Susan; Berry, Donald A
2015-01-01
Background In oncology, the treatment paradigm is shifting toward personalized medicine, where the goal is to match patients to the treatments most likely to deliver benefit. Treatment effects in various subpopulations may provide some information about treatment effects in other subpopulations. Purpose We compare different approaches to Phase II trial design where a new treatment is being investigated in several groups of patients. We compare considering each group in an independent trial to a single trial with hierarchical modeling of the patient groups. Methods We assume four patient groups with different background response rates and simulate operating characteristics of three trial designs, Simon’s Optimal Two-Stage design, a Bayesian adaptive design with frequent interim analyses, and a Bayesian adaptive design with frequent interim analyses and hierarchical modeling across patient groups. Results Simon’s designs are based on 10% Type I and Type II error rates. The independent Bayesian designs are tuned to have similar error rates, but may have a slightly smaller mean sample size due to more frequent interim analyses. Under the null, the mean sample size is 2–4 patients smaller. A hierarchical model across patient groups can provide additional power and a further reduction in mean sample size. Under the null, the addition of the hierarchical model decreases the mean sample size an additional 4–7 patients in each group. Under the alternative hypothesis, power is increased to at least 98% in all groups. Limitations Hierarchical borrowing can make finding a single group in which the treatment is promising, if there is only one, more difficult. In a scenario where the treatment is uninteresting in all but one group, power for that one group is reduced to 65%. When the drug appears promising in some groups and not in others, there is potential for borrowing to inflate the Type I error rate. Conclusions The Bayesian hierarchical design is more likely to
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.
Shankle, William R; Pooley, James P; Steyvers, Mark; Hara, Junko; Mangrola, Tushar; Reisberg, Barry; Lee, Michael D
2013-01-01
Determining how cognition affects functional abilities is important in Alzheimer disease and related disorders. A total of 280 patients (normal or Alzheimer disease and related disorders) received a total of 1514 assessments using the functional assessment staging test (FAST) procedure and the MCI Screen. A hierarchical Bayesian cognitive processing model was created by embedding a signal detection theory model of the MCI Screen-delayed recognition memory task into a hierarchical Bayesian framework. The signal detection theory model used latent parameters of discriminability (memory process) and response bias (executive function) to predict, simultaneously, recognition memory performance for each patient and each FAST severity group. The observed recognition memory data did not distinguish the 6 FAST severity stages, but the latent parameters completely separated them. The latent parameters were also used successfully to transform the ordinal FAST measure into a continuous measure reflecting the underlying continuum of functional severity. Hierarchical Bayesian cognitive processing models applied to recognition memory data from clinical practice settings accurately translated a latent measure of cognition into a continuous measure of functional severity for both individuals and FAST groups. Such a translation links 2 levels of brain information processing and may enable more accurate correlations with other levels, such as those characterized by biomarkers.
NASA Astrophysics Data System (ADS)
Najafi, M.; Moradkhani, H.
2012-12-01
We investigate the runoff extremes over the Columbia River Basin (CRB) based on available gage data and those obtained at grid cells from distributed hydrologic modeling. The Spatial Hierarchical Bayesian model is used in this study to estimate the parameters of the Generalized Extreme Value (GEV) and Generalized Pareto distributions in order to assess the runoff extremes. Generalized Pareto Distribution (GPD) is employed to model the upper 95% flows during December through March for two regions in CRB having 31 and 20 gauge stations respectively. The covariates including latitude, longitude, elevation and drainage area are used to generate the second stage of the hierarchy. The performance of the Bayesian hierarchical model is evaluated by comparing the estimates of 100- year return level floods with the maximum likelihood estimates at sites that are not used during the parameter inference process. Model selection is also performed based on the Deviance Information Criterion (DIC). Various prior distributions are used to assess the sensitivity of the posterior distributions. The selected model is then employed to assess floods with different return levels in time periods of fifteen years in order to detect possible trends in runoff extremes. The historical variations in flood events are found in time periods of fifteen years. Hydrologic modeling using Variable Infiltration Capacity (VIC) model is then conducted over the entire basin at 1/8 degree resolution. The hydrologic model is driven by Regional climate model simulations from the NARCCAP to obtain the runoff for the periods of 1971-2000 and 2041-2070. The spatial hierarchical model is employed to model the runoff extremes and investigate possible variations as a result of climate change. Markov Chain Monte Carlo (MCMC) method is utilized to infer the parameters. The Spatial Hierarchical Bayesian technique extracts the information content from different locations by pooling data together, while providing an
Analysis of household data on influenza epidemic with Bayesian hierarchical model.
Hsu, C Y; Yen, A M F; Chen, L S; Chen, H H
2015-03-01
Data used for modelling the household transmission of infectious diseases, such as influenza, have inherent multilevel structures and correlated property, which make the widely used conventional infectious disease transmission models (including the Greenwood model and the Reed-Frost model) not directly applicable within the context of a household (due to the crowded domestic condition or socioeconomic status of the household). Thus, at the household level, the effects resulting from individual-level factors, such as vaccination, may be confounded or modified in some way. We proposed the Bayesian hierarchical random-effects (random intercepts and random slopes) model under the context of generalised linear model to capture heterogeneity and variation on the individual, generation, and household levels. It was applied to empirical surveillance data on the influenza epidemic in Taiwan. The parameters of interest were estimated by using the Markov chain Monte Carlo method in conjunction with the Bayesian directed acyclic graphical models. Comparisons between models were made using the deviance information criterion. Based on the result of the random-slope Bayesian hierarchical method under the context of the Reed-Frost transmission model, the regression coefficient regarding the protective effect of vaccination varied statistically significantly from household to household. The result of such a heterogeneity was robust to the use of different prior distributions (including non-informative, sceptical, and enthusiastic ones). By integrating out the uncertainty of the parameters of the posterior distribution, the predictive distribution was computed to forecast the number of influenza cases allowing for random-household effect.
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)
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)
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.
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…
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
Leite, Mauro T.; Zangwill, Linda M.; Weinreb, Robert N.
2011-01-01
Purpose. To present and evaluate a new methodology for combining longitudinal information from structural and functional tests to improve detection of glaucoma progression and estimation of rates of change. Methods. This observational cohort study included 434 eyes of 257 participants observed for an average of 4.2 ± 1.1 years and recruited from the Diagnostic Innovations in Glaucoma Study (DIGS). The subjects were examined annually with standard automated perimetry, optic disc stereophotographs, and scanning laser polarimetry with enhanced corneal compensation. Rates of change over time were measured using the visual field index (VFI) and average retinal nerve fiber layer thickness (TSNIT average). A Bayesian hierarchical model was built to integrate information from the longitudinal measures and classify individual eyes as progressing or not. Estimates of sensitivity and specificity of the Bayesian method were compared with those obtained by the conventional approach of ordinary least-squares (OLS) regression. Results. The Bayesian method identified a significantly higher proportion of the 405 glaucomatous and suspect eyes as having progressed when compared with the OLS method (22.7% vs. 12.8%; P < 0.001), while having the same specificity of 100% in 29 healthy eyes. In addition, the Bayesian method identified a significantly higher proportion of eyes with progression by optic disc stereophotographs compared with the OLS method (74% vs. 37%; P = 0.001). Conclusions. A Bayesian hierarchical modeling approach for combining functional and structural tests performed significantly better than the OLS method for detection of glaucoma progression. (ClinicalTrials.gov number, NCT00221897.) PMID:21693614
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
Bayesian Hierarchical Models to Augment the Mediterranean Forecast System
2008-09-30
respective Gibbs Samplers. The impacts of the first implementations of MFS-Error-BHM are being tested in reforecast experiments at INGV for MFS sub-region 3...Sensitivity tests of this kind are expensive (i.e. reforecast experiments must be run in the full MFS model), but they are proceeding at INGV
Bayesian Hierarchical Models to Augment the Mediterranean Forecast System
2008-09-30
experiments at INGV for MFS sub-region 3 (Gulf of Lyons). Refinements in the data stage inputs and data stage distribution calculations are also...proceeding at INGV nonetheless. 6 MFS-SuperEnsemble-BHM The multi-model form of MFS-SuperEnsemble-BHM development is in initial
Bayesian Hierarchical Models to Augment the Mediterranean Forecast System
2008-09-30
Gibbs Samplers. The impacts of the first implementations of MFS-Error-BHM are being tested in reforecast experiments at INGV for MFS sub-region 3...tests of this kind are expensive (i.e. reforecast experiments must be run in the full MFS model), but they are proceeding at INGV nonetheless. 6
A Hierarchical Bayesian Model for Calibrating Estimates of Species Divergence Times
Heath, Tracy A.
2012-01-01
In Bayesian divergence time estimation methods, incorporating calibrating information from the fossil record is commonly done by assigning prior densities to ancestral nodes in the tree. Calibration prior densities are typically parametric distributions offset by minimum age estimates provided by the fossil record. Specification of the parameters of calibration densities requires the user to quantify his or her prior knowledge of the age of the ancestral node relative to the age of its calibrating fossil. The values of these parameters can, potentially, result in biased estimates of node ages if they lead to overly informative prior distributions. Accordingly, determining parameter values that lead to adequate prior densities is not straightforward. In this study, I present a hierarchical Bayesian model for calibrating divergence time analyses with multiple fossil age constraints. This approach applies a Dirichlet process prior as a hyperprior on the parameters of calibration prior densities. Specifically, this model assumes that the rate parameters of exponential prior distributions on calibrated nodes are distributed according to a Dirichlet process, whereby the rate parameters are clustered into distinct parameter categories. Both simulated and biological data are analyzed to evaluate the performance of the Dirichlet process hyperprior. Compared with fixed exponential prior densities, the hierarchical Bayesian approach results in more accurate and precise estimates of internal node ages. When this hyperprior is applied using Markov chain Monte Carlo methods, the ages of calibrated nodes are sampled from mixtures of exponential distributions and uncertainty in the values of calibration density parameters is taken into account. PMID:22334343
A hierarchical Bayesian model for calibrating estimates of species divergence times.
Heath, Tracy A
2012-10-01
In Bayesian divergence time estimation methods, incorporating calibrating information from the fossil record is commonly done by assigning prior densities to ancestral nodes in the tree. Calibration prior densities are typically parametric distributions offset by minimum age estimates provided by the fossil record. Specification of the parameters of calibration densities requires the user to quantify his or her prior knowledge of the age of the ancestral node relative to the age of its calibrating fossil. The values of these parameters can, potentially, result in biased estimates of node ages if they lead to overly informative prior distributions. Accordingly, determining parameter values that lead to adequate prior densities is not straightforward. In this study, I present a hierarchical Bayesian model for calibrating divergence time analyses with multiple fossil age constraints. This approach applies a Dirichlet process prior as a hyperprior on the parameters of calibration prior densities. Specifically, this model assumes that the rate parameters of exponential prior distributions on calibrated nodes are distributed according to a Dirichlet process, whereby the rate parameters are clustered into distinct parameter categories. Both simulated and biological data are analyzed to evaluate the performance of the Dirichlet process hyperprior. Compared with fixed exponential prior densities, the hierarchical Bayesian approach results in more accurate and precise estimates of internal node ages. When this hyperprior is applied using Markov chain Monte Carlo methods, the ages of calibrated nodes are sampled from mixtures of exponential distributions and uncertainty in the values of calibration density parameters is taken into account.
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.
HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python.
Wiecki, Thomas V; Sofer, Imri; Frank, Michael J
2013-01-01
The diffusion model is a commonly used tool to infer latent psychological processes underlying decision-making, and to link them to neural mechanisms based on response times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of response time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model), which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject/condition than non-hierarchical methods, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g., fMRI) influence decision-making parameters. This paper will first describe the theoretical background of the drift diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the χ(2)-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs/
Altini, Marco; Casale, Pierluigi; Penders, Julien; Amft, Oliver
2015-08-01
Accurate estimation of energy expenditure (EE) and cardiorespiratory fitness (CRF) is a key element in determining the causal relation between aspects of human behavior related to physical activity and health. In this paper we estimate CRF without requiring laboratory protocols and personalize energy expenditure (EE) estimation models that rely on heart rate data, using CRF. CRF influences the relation between heart rate and EE. Thus, EE estimation based on heart rate typically requires individual calibration. Our modeling technique relies on a hierarchical approach using Bayesian modeling for both CRF and EE estimation models. By including CRF level in a hierarchical Bayesian model, we avoid the need for individual calibration or explicit heart rate normalization since CRF accounts for the different relation between heart rate and EE in different individuals. Our method first estimates CRF level from heart rate during low intensity activities of daily living, showing that CRF can be determined without specific protocols. Reference VO2max and EE were collected on a sample of 32 participants with varying CRF level. CRF estimation error could be reduced up to 27.0% compared to other models. Secondly, we show that including CRF as a group level predictor in a hierarchical model for EE estimation accounts for the relation between CRF, heart rate and EE. Thus, reducing EE estimation error by 18.2% on average. Our results provide evidence that hierarchical modeling is a promising technique for generalized CRF estimation from activities of daily living and personalized EE estimation. Copyright © 2015 Elsevier Inc. All rights reserved.
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
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.
Boyd, Heather A; Flanders, W Dana; Addiss, David G; Waller, Lance A
2005-07-01
Analytic methods commonly used in epidemiology do not account for spatial correlation between observations. In regression analyses, this omission can bias parameter estimates and yield incorrect standard error estimates. We present a Bayesian hierarchical model (BHM) approach that accounts for spatial correlation, and illustrate its strengths and weaknesses by applying this modeling approach to data on Wuchereria bancrofti infection in Haiti. A program to eliminate lymphatic filariasis in Haiti assessed prevalence of W. bancrofti infection in 57 schools across Leogane Commune. We analyzed the spatial pattern in the prevalence data using semi-variograms and correlograms. We then modeled the data using (1) standard logistic regression (GLM); (2) non-Bayesian logistic generalized linear mixed models (GLMMs) with school-specific nonspatial random effects; (3) BHMs with school-specific nonspatial random effects; and (4) BHMs with spatial random effects. An exponential semi-variogram with an effective range of 2.15 km best fit the data. GLMM and nonspatial BHM point estimates were comparable and also were generally similar with the marginal GLM point estimates. In contrast, compared with the nonspatial mixed model results, spatial BHM point estimates were markedly attenuated. The clear spatial pattern evident in the Haitian W. bancrofti prevalence data and the observation that point estimates and standard errors differed depending on the modeling approach indicate that it is important to account for residual spatial correlation in analyses of W. bancrofti infection data. Bayesian hierarchical models provide a flexible, readily implementable approach to modeling spatially correlated data. However, our results also illustrate that spatial smoothing must be applied with care.
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
Shankle, William R.; Pooley, James P.; Steyvers, Mark; Hara, Junko; Mangrola, Tushar; Reisberg, Barry; Lee, Michael D.
2012-01-01
Determining how cognition affects functional abilities is important in Alzheimer’s disease and related disorders (ADRD). 280 patients (normal or ADRD) received a total of 1,514 assessments using the Functional Assessment Staging Test (FAST) procedure and the MCI Screen (MCIS). A hierarchical Bayesian cognitive processing (HBCP) model was created by embedding a signal detection theory (SDT) model of the MCIS delayed recognition memory task into a hierarchical Bayesian framework. The SDT model used latent parameters of discriminability (memory process) and response bias (executive function) to predict, simultaneously, recognition memory performance for each patient and each FAST severity group. The observed recognition memory data did not distinguish the six FAST severity stages, but the latent parameters completely separated them. The latent parameters were also used successfully to transform the ordinal FAST measure into a continuous measure reflecting the underlying continuum of functional severity. HBCP models applied to recognition memory data from clinical practice settings accurately translated a latent measure of cognition to a continuous measure of functional severity for both individuals and FAST groups. Such a translation links two levels of brain information processing, and may enable more accurate correlations with other levels, such as those characterized by biomarkers. PMID:22407225
NASA Astrophysics Data System (ADS)
Skataric, Maja; Bose, Sandip; Zeroug, Smaine; Tilke, Peter
2017-02-01
It is not uncommon in the field of non-destructive evaluation that multiple measurements encompassing a variety of modalities are available for analysis and interpretation for determining the underlying states of nature of the materials or parts being tested. Despite and sometimes due to the richness of data, significant challenges arise in the interpretation manifested as ambiguities and inconsistencies due to various uncertain factors in the physical properties (inputs), environment, measurement device properties, human errors, and the measurement data (outputs). Most of these uncertainties cannot be described by any rigorous mathematical means, and modeling of all possibilities is usually infeasible for many real time applications. In this work, we will discuss an approach based on Hierarchical Bayesian Graphical Models (HBGM) for the improved interpretation of complex (multi-dimensional) problems with parametric uncertainties that lack usable physical models. In this setting, the input space of the physical properties is specified through prior distributions based on domain knowledge and expertise, which are represented as Gaussian mixtures to model the various possible scenarios of interest for non-destructive testing applications. Forward models are then used offline to generate the expected distribution of the proposed measurements which are used to train a hierarchical Bayesian network. In Bayesian analysis, all model parameters are treated as random variables, and inference of the parameters is made on the basis of posterior distribution given the observed data. Learned parameters of the posterior distribution obtained after the training can therefore be used to build an efficient classifier for differentiating new observed data in real time on the basis of pre-trained models. We will illustrate the implementation of the HBGM approach to ultrasonic measurements used for cement evaluation of cased wells in the oil industry.
Bayesian Hierarchical Random Intercept Model Based on Three Parameter Gamma Distribution
NASA Astrophysics Data System (ADS)
Wirawati, Ika; Iriawan, Nur; Irhamah
2017-06-01
Hierarchical data structures are common throughout many areas of research. Beforehand, the existence of this type of data was less noticed in the analysis. The appropriate statistical analysis to handle this type of data is the hierarchical linear model (HLM). This article will focus only on random intercept model (RIM), as a subclass of HLM. This model assumes that the intercept of models in the lowest level are varied among those models, and their slopes are fixed. The differences of intercepts were suspected affected by some variables in the upper level. These intercepts, therefore, are regressed against those upper level variables as predictors. The purpose of this paper would demonstrate a proven work of the proposed two level RIM of the modeling on per capita household expenditure in Maluku Utara, which has five characteristics in the first level and three characteristics of districts/cities in the second level. The per capita household expenditure data in the first level were captured by the three parameters Gamma distribution. The model, therefore, would be more complex due to interaction of many parameters for representing the hierarchical structure and distribution pattern of the data. To simplify the estimation processes of parameters, the computational Bayesian method couple with Markov Chain Monte Carlo (MCMC) algorithm and its Gibbs Sampling are employed.
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
Bello, Nora M; Steibel, Juan P; Tempelman, Robert J
2010-06-01
Bivariate mixed effects models are often used to jointly infer upon covariance matrices for both random effects (u) and residuals (e) between two different phenotypes in order to investigate the architecture of their relationship. However, these (co)variances themselves may additionally depend upon covariates as well as additional sets of exchangeable random effects that facilitate borrowing of strength across a large number of clusters. We propose a hierarchical Bayesian extension of the classical bivariate mixed effects model by embedding additional levels of mixed effects modeling of reparameterizations of u-level and e-level (co)variances between two traits. These parameters are based upon a recently popularized square-root-free Cholesky decomposition and are readily interpretable, each conveniently facilitating a generalized linear model characterization. Using Markov Chain Monte Carlo methods, we validate our model based on a simulation study and apply it to a joint analysis of milk yield and calving interval phenotypes in Michigan dairy cows. This analysis indicates that the e-level relationship between the two traits is highly heterogeneous across herds and depends upon systematic herd management factors.
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
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.
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.
Prion Amplification and Hierarchical Bayesian Modeling Refine Detection of Prion Infection
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
2015-01-01
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. PMID:25665713
Coley, Rebecca Yates; Brown, Elizabeth R
2016-07-10
Inconsistent results in recent HIV prevention trials of pre-exposure prophylactic interventions may be due to heterogeneity in risk among study participants. Intervention effectiveness is most commonly estimated with the Cox model, which compares event times between populations. When heterogeneity is present, this population-level measure underestimates intervention effectiveness for individuals who are at risk. We propose a likelihood-based Bayesian hierarchical model that estimates the individual-level effectiveness of candidate interventions by accounting for heterogeneity in risk with a compound Poisson-distributed frailty term. This model reflects the mechanisms of HIV risk and allows that some participants are not exposed to HIV and, therefore, have no risk of seroconversion during the study. We assess model performance via simulation and apply the model to data from an HIV prevention trial. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Conesa, D; Martínez-Beneito, M A; Amorós, R; López-Quílez, A
2015-04-01
Considerable effort has been devoted to the development of statistical algorithms for the automated monitoring of influenza surveillance data. In this article, we introduce a framework of models for the early detection of the onset of an influenza epidemic which is applicable to different kinds of surveillance data. In particular, the process of the observed cases is modelled via a Bayesian Hierarchical Poisson model in which the intensity parameter is a function of the incidence rate. The key point is to consider this incidence rate as a normal distribution in which both parameters (mean and variance) are modelled differently, depending on whether the system is in an epidemic or non-epidemic phase. To do so, we propose a hidden Markov model in which the transition between both phases is modelled as a function of the epidemic state of the previous week. Different options for modelling the rates are described, including the option of modelling the mean at each phase as autoregressive processes of order 0, 1 or 2. Bayesian inference is carried out to provide the probability of being in an epidemic state at any given moment. The methodology is applied to various influenza data sets. The results indicate that our methods outperform previous approaches in terms of sensitivity, specificity and timeliness. © The Author(s) 2011 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.
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.
Spatial Bayesian hierarchical modeling of precipitation extremes over a large domain
NASA Astrophysics Data System (ADS)
Bracken, C.; Rajagopalan, B.; Cheng, L.; Kleiber, W.; Gangopadhyay, S.
2016-08-01
We propose a Bayesian hierarchical model for spatial extremes on a large domain. In the data layer a Gaussian elliptical copula having generalized extreme value (GEV) marginals is applied. Spatial dependence in the GEV parameters is captured with a latent spatial regression with spatially varying coefficients. Using a composite likelihood approach, we are able to efficiently incorporate a large precipitation data set, which includes stations with missing data. The model is demonstrated by application to fall precipitation extremes at approximately 2600 stations covering the western United States, -125°E to -100°E longitude and 30°N-50°N latitude. The hierarchical model provides GEV parameters on a 1/8° grid and, consequently, maps of return levels and associated uncertainty. The model results indicate that return levels and their associated uncertainty have a well-defined spatial structure. Maps of return levels provide information about the spatial variations of the risk of extreme precipitation in the western US and is expected to be useful for infrastructure planning.
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.
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.
A Bayesian Hierarchical Framework for Spatial Modeling of fMRI Data
Bowman, F. DuBois; Caffo, Brian; Bassett, Susan Spear; Kilts, Clinton
2007-01-01
Applications of functional magnetic resonance imaging (fMRI) have provided novel insights into the neuropathophysiology of major psychiatric, neurological, and substance abuse disorders and their treatments. Modern activation studies often compare localized task-induced changes in brain activity between experimental groups. Complementary approaches consider the ensemble of voxels constituting an anatomically defined region of interest (ROI) or summary statistics, such as means or quantiles, of the ROI. In this work we present a Bayesian extension of voxel-level analyses that offers several notable benefits. Among these, it combines whole-brain voxel-by-voxel modeling and ROI analyses within a unified framework. Secondly, an unstructured variance/covariance matrix for regional mean parameters allows for the study of inter-regional (long-range) correlations, and the model employs an exchangeable correlation structure to capture intra-regional (short-range) correlations. Estimation is performed using Markov Chain Monte Carlo (MCMC) techniques implemented via Gibbs sampling. We apply our Bayesian hierarchical model to two novel fMRI data sets: one considering inhibitory control in cocaine-dependent men and the second considering verbal memory in subjects at high risk for Alzheimer's disease. PMID:17936016
A Bayesian Hierarchical Model for Estimation of Abundance and Spatial Density of Aedes aegypti
Villela, Daniel A. M.; Codeço, Claudia T.; Figueiredo, Felipe; Garcia, Gabriela A.; Maciel-de-Freitas, Rafael; Struchiner, Claudio J.
2015-01-01
Strategies to minimize dengue transmission commonly rely on vector control, which aims to maintain Ae. aegypti density below a theoretical threshold. Mosquito abundance is traditionally estimated from mark-release-recapture (MRR) experiments, which lack proper analysis regarding accurate vector spatial distribution and population density. Recently proposed strategies to control vector-borne diseases involve replacing the susceptible wild population by genetically modified individuals’ refractory to the infection by the pathogen. Accurate measurements of mosquito abundance in time and space are required to optimize the success of such interventions. In this paper, we present a hierarchical probabilistic model for the estimation of population abundance and spatial distribution from typical mosquito MRR experiments, with direct application to the planning of these new control strategies. We perform a Bayesian analysis using the model and data from two MRR experiments performed in a neighborhood of Rio de Janeiro, Brazil, during both low- and high-dengue transmission seasons. The hierarchical model indicates that mosquito spatial distribution is clustered during the winter (0.99 mosquitoes/premise 95% CI: 0.80–1.23) and more homogeneous during the high abundance period (5.2 mosquitoes/premise 95% CI: 4.3–5.9). The hierarchical model also performed better than the commonly used Fisher-Ford’s method, when using simulated data. The proposed model provides a formal treatment of the sources of uncertainty associated with the estimation of mosquito abundance imposed by the sampling design. Our approach is useful in strategies such as population suppression or the displacement of wild vector populations by refractory Wolbachia-infected mosquitoes, since the invasion dynamics have been shown to follow threshold conditions dictated by mosquito abundance. The presence of spatially distributed abundance hotspots is also formally addressed under this modeling framework and
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
Wynton, Sarah K A; Anglim, Jeromy
2017-04-10
While researchers have often sought to understand the learning curve in terms of multiple component processes, few studies have measured and mathematically modeled these processes on a complex task. In particular, there remains a need to reconcile how abrupt changes in strategy use can co-occur with gradual changes in task completion time. Thus, the current study aimed to assess the degree to which strategy change was abrupt or gradual, and whether strategy aggregation could partially explain gradual performance change. It also aimed to show how Bayesian methods could be used to model the effect of practice on strategy use. To achieve these aims, 162 participants completed 15 blocks of practice on a complex computer-based task-the Wynton-Anglim booking (WAB) task. The task allowed for multiple component strategies (i.e., memory retrieval, information reduction, and insight) that could also be aggregated to a global measure of strategy use. Bayesian hierarchical models were used to compare abrupt and gradual functions of component and aggregate strategy use. Task completion time was well-modeled by a power function, and global strategy use explained substantial variance in performance. Change in component strategy use tended to be abrupt, whereas change in global strategy use was gradual and well-modeled by a power function. Thus, differential timing of component strategy shifts leads to gradual changes in overall strategy efficiency, and this provides one reason for why smooth learning curves can co-occur with abrupt changes in strategy use. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
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
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.
2011-01-01
The term structure of interest rates is used to price defaultable bonds and credit derivatives, as well as to infer the quality of bonds for risk management purposes. We introduce a model that jointly estimates term structures by means of a Bayesian hierarchical model with a prior probability model based on Dirichlet process mixtures. The modeling methodology borrows strength across term structures for purposes of estimation. The main advantage of our framework is its ability to produce reliable estimators at the company level even when there are only a few bonds per company. After describing the proposed model, we discuss an empirical application in which the term structure of 197 individual companies is estimated. The sample of 197 consists of 143 companies with only one or two bonds. In-sample and out-of-sample tests are used to quantify the improvement in accuracy that results from approximating the term structure of corporate bonds with estimators by company rather than by credit rating, the latter being a popular choice in the financial literature. A complete description of a Markov chain Monte Carlo (MCMC) scheme for the proposed model is available as Supplementary Material. PMID:21765566
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.
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).
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
Bayesian hierarchical models for regional climate reconstructions of the last glacial maximum
NASA Astrophysics Data System (ADS)
Weitzel, Nils; Hense, Andreas; Ohlwein, Christian
2017-04-01
Spatio-temporal reconstructions of past climate are important for the understanding of the long term behavior of the climate system and the sensitivity to forcing changes. Unfortunately, they are subject to large uncertainties, have to deal with a complex proxy-climate structure, and a physically reasonable interpolation between the sparse proxy observations is difficult. Bayesian Hierarchical Models (BHMs) are a class of statistical models that is well suited for spatio-temporal reconstructions of past climate because they permit the inclusion of multiple sources of information (e.g. records from different proxy types, uncertain age information, output from climate simulations) and quantify uncertainties in a statistically rigorous way. BHMs in paleoclimatology typically consist of three stages which are modeled individually and are combined using Bayesian inference techniques. The data stage models the proxy-climate relation (often named transfer function), the process stage models the spatio-temporal distribution of the climate variables of interest, and the prior stage consists of prior distributions of the model parameters. For our BHMs, we translate well-known proxy-climate transfer functions for pollen to a Bayesian framework. In addition, we can include Gaussian distributed local climate information from preprocessed proxy records. The process stage combines physically reasonable spatial structures from prior distributions with proxy records which leads to a multivariate posterior probability distribution for the reconstructed climate variables. The prior distributions that constrain the possible spatial structure of the climate variables are calculated from climate simulation output. We present results from pseudoproxy tests as well as new regional reconstructions of temperatures for the last glacial maximum (LGM, ˜ 21,000 years BP). These reconstructions combine proxy data syntheses with information from climate simulations for the LGM that were
Epigenetic change detection and pattern recognition via Bayesian hierarchical hidden Markov models
Wang, Xinlei; Zang, Miao; Xiao, Guanghua
2014-01-01
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. PMID:23097332
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
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
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
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.
Extreme Rainfall Analysis using Bayesian Hierarchical Modeling in the Willamette River Basin, Oregon
NASA Astrophysics Data System (ADS)
Love, C. A.; Skahill, B. E.; AghaKouchak, A.; Karlovits, G. S.; England, J. F.; Duren, A. M.
2016-12-01
We present preliminary results of ongoing research directed at evaluating the worth of including various covariate data to support extreme rainfall analysis in the Willamette River basin using Bayesian hierarchical modeling (BHM). We also compare the BHM derived extreme rainfall estimates with their respective counterparts obtained from a traditional regional frequency analysis (RFA) using the same set of rain gage extreme rainfall data. The U.S. Army Corps of Engineers (USACE) Portland District operates thirteen dams in the 11,478 square mile Willamette River basin (WRB) located in northwestern Oregon, a major tributary of the Columbia River whose 187 miles long main stem, the Willamette River, flows northward between the Coastal and Cascade Ranges. The WRB contains approximately two-thirds of Oregon's population and 20 of the 25 most populous cities in the state. Extreme rainfall estimates are required to support risk-informed hydrologic analyses for these projects as part of the USACE Dam Safety Program. We analyze daily annual rainfall maxima data for the WRB utilizing the spatial BHM R package "spatial.gev.bma", which has been shown to be efficient in developing coherent maps of extreme rainfall by return level. Our intent is to profile for the USACE an alternate methodology to a RFA which was developed in 2008 due to the lack of an official NOAA Atlas 14 update for the state of Oregon. Unlike RFA, the advantage of a BHM-based analysis of hydrometeorological extremes is its ability to account for non-stationarity while providing robust estimates of uncertainty. BHM also allows for the inclusion of geographical and climatological factors which we show for the WRB influence regional rainfall extremes. Moreover, the Bayesian framework permits one to combine additional data types into the analysis; for example, information derived via elicitation and causal information expansion data, both being additional opportunities for future related research.
NASA Astrophysics Data System (ADS)
Norros, Veera; Laine, Marko; Lignell, Risto; Thingstad, Frede
2017-10-01
Methods for extracting empirically and theoretically sound parameter values are urgently needed in aquatic ecosystem modelling to describe key flows and their variation in the system. Here, we compare three Bayesian formulations for mechanistic model parameterization that differ in their assumptions about the variation in parameter values between various datasets: 1) global analysis - no variation, 2) separate analysis - independent variation and 3) hierarchical analysis - variation arising from a shared distribution defined by hyperparameters. We tested these methods, using computer-generated and empirical data, coupled with simplified and reasonably realistic plankton food web models, respectively. While all methods were adequate, the simulated example demonstrated that a well-designed hierarchical analysis can result in the most accurate and precise parameter estimates and predictions, due to its ability to combine information across datasets. However, our results also highlighted sensitivity to hyperparameter prior distributions as an important caveat of hierarchical analysis. In the more complex empirical example, hierarchical analysis was able to combine precise identification of parameter values with reasonably good predictive performance, although the ranking of the methods was less straightforward. We conclude that hierarchical Bayesian analysis is a promising tool for identifying key ecosystem-functioning parameters and their variation from empirical datasets.
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
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.
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.
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
A hierarchical Bayesian model for flexible module discovery in three-way time-series data
Amar, David; Yekutieli, Daniel; Maron-Katz, Adi; Hendler, Talma; Shamir, Ron
2015-01-01
Motivation: Detecting modules of co-ordinated activity is fundamental in the analysis of large biological studies. For two-dimensional data (e.g. genes × patients), this is often done via clustering or biclustering. More recently, studies monitoring patients over time have added another dimension. Analysis is much more challenging in this case, especially when time measurements are not synchronized. New methods that can analyze three-way data are thus needed. Results: We present a new algorithm for finding coherent and flexible modules in three-way data. Our method can identify both core modules that appear in multiple patients and patient-specific augmentations of these core modules that contain additional genes. Our algorithm is based on a hierarchical Bayesian data model and Gibbs sampling. The algorithm outperforms extant methods on simulated and on real data. The method successfully dissected key components of septic shock response from time series measurements of gene expression. Detected patient-specific module augmentations were informative for disease outcome. In analyzing brain functional magnetic resonance imaging time series of subjects at rest, it detected the pertinent brain regions involved. Availability and implementation: R code and data are available at http://acgt.cs.tau.ac.il/twigs/. Contact: rshamir@tau.ac.il Supplementary information: Supplementary data are available at Bioinformatics online. PMID:26072479
A hierarchical Bayesian model for flexible module discovery in three-way time-series data.
Amar, David; Yekutieli, Daniel; Maron-Katz, Adi; Hendler, Talma; Shamir, Ron
2015-06-15
Detecting modules of co-ordinated activity is fundamental in the analysis of large biological studies. For two-dimensional data (e.g. genes × patients), this is often done via clustering or biclustering. More recently, studies monitoring patients over time have added another dimension. Analysis is much more challenging in this case, especially when time measurements are not synchronized. New methods that can analyze three-way data are thus needed. We present a new algorithm for finding coherent and flexible modules in three-way data. Our method can identify both core modules that appear in multiple patients and patient-specific augmentations of these core modules that contain additional genes. Our algorithm is based on a hierarchical Bayesian data model and Gibbs sampling. The algorithm outperforms extant methods on simulated and on real data. The method successfully dissected key components of septic shock response from time series measurements of gene expression. Detected patient-specific module augmentations were informative for disease outcome. In analyzing brain functional magnetic resonance imaging time series of subjects at rest, it detected the pertinent brain regions involved. R code and data are available at http://acgt.cs.tau.ac.il/twigs/. © The Author 2015. Published by Oxford University Press.
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
Wheeler, David C; Hickson, Demarc A; Waller, Lance A
2010-06-01
Many diagnostic tools and goodness-of-fit measures, such as the Akaike information criterion (AIC) and the Bayesian deviance information criterion (DIC), are available to evaluate the overall adequacy of linear regression models. In addition, visually assessing adequacy in models has become an essential part of any regression analysis. In this paper, we focus on a spatial consideration of the local DIC measure for model selection and goodness-of-fit evaluation. We use a partitioning of the DIC into the local DIC, leverage, and deviance residuals to assess local model fit and influence for both individual observations and groups of observations in a Bayesian framework. We use visualization of the local DIC and differences in local DIC between models to assist in model selection and to visualize the global and local impacts of adding covariates or model parameters. We demonstrate the utility of the local DIC in assessing model adequacy using HIV prevalence data from pregnant women in the Butare province of Rwanda during 1989-1993 using a range of linear model specifications, from global effects only to spatially varying coefficient models, and a set of covariates related to sexual behavior. Results of applying the diagnostic visualization approach include more refined model selection and greater understanding of the models as applied to the data.
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
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
Xia, Yongqiu; Weller, Donald E; Williams, Meghan N; Jordan, Thomas E; Yan, Xiaoyuan
2016-11-15
Export coefficient models (ECMs) are often used to predict nutrient sources and sinks in watersheds because ECMs can flexibly incorporate processes and have minimal data requirements. However, ECMs do not quantify uncertainties in model structure, parameters, or predictions; nor do they account for spatial and temporal variability in land characteristics, weather, and management practices. We applied Bayesian hierarchical methods to address these problems in ECMs used to predict nitrate concentration in streams. We compared four model formulations, a basic ECM and three models with additional terms to represent competing hypotheses about the sources of error in ECMs and about spatial and temporal variability of coefficients: an ADditive Error Model (ADEM), a SpatioTemporal Parameter Model (STPM), and a Dynamic Parameter Model (DPM). The DPM incorporates a first-order random walk to represent spatial correlation among parameters and a dynamic linear model to accommodate temporal correlation. We tested the modeling approach in a proof of concept using watershed characteristics and nitrate export measurements from watersheds in the Coastal Plain physiographic province of the Chesapeake Bay drainage. Among the four models, the DPM was the best--it had the lowest mean error, explained the most variability (R(2) = 0.99), had the narrowest prediction intervals, and provided the most effective tradeoff between fit complexity (its deviance information criterion, DIC, was 45.6 units lower than any other model, indicating overwhelming support for the DPM). The superiority of the DPM supports its underlying hypothesis that the main source of error in ECMs is their failure to account for parameter variability rather than structural error. Analysis of the fitted DPM coefficients for cropland export and instream retention revealed some of the factors controlling nitrate concentration: cropland nitrate exports were positively related to stream flow and watershed average slope
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
Yu, Wenxi; Liu, Yang; Ma, Zongwei; Bi, Jun
2017-08-01
Using satellite-based aerosol optical depth (AOD) measurements and statistical models to estimate ground-level PM2.5 is a promising way to fill the areas that are not covered by ground PM2.5 monitors. The statistical models used in previous studies are primarily Linear Mixed Effects (LME) and Geographically Weighted Regression (GWR) models. In this study, we developed a new regression model between PM2.5 and AOD using Gaussian processes in a Bayesian hierarchical setting. Gaussian processes model the stochastic nature of the spatial random effects, where the mean surface and the covariance function is specified. The spatial stochastic process is incorporated under the Bayesian hierarchical framework to explain the variation of PM2.5 concentrations together with other factors, such as AOD, spatial and non-spatial random effects. We evaluate the results of our model and compare them with those of other, conventional statistical models (GWR and LME) by within-sample model fitting and out-of-sample validation (cross validation, CV). The results show that our model possesses a CV result (R(2) = 0.81) that reflects higher accuracy than that of GWR and LME (0.74 and 0.48, respectively). Our results indicate that Gaussian process models have the potential to improve the accuracy of satellite-based PM2.5 estimates.
ERIC Educational Resources Information Center
Boedeker, Peter
2017-01-01
Hierarchical linear modeling (HLM) is a useful tool when analyzing data collected from groups. There are many decisions to be made when constructing and estimating a model in HLM including which estimation technique to use. Three of the estimation techniques available when analyzing data with HLM are maximum likelihood, restricted maximum…
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
Mapping Brucellosis Increases Relative to Elk Density Using Hierarchical Bayesian Models
Cross, Paul C.; Heisey, Dennis M.; Scurlock, Brandon M.; Edwards, William H.; Ebinger, Michael R.; Brennan, Angela
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. PMID:20428240
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.
NASA Astrophysics Data System (ADS)
Ahn, Kuk-Hyun; Palmer, Richard; Steinschneider, Scott
2017-01-01
This study presents a regional, probabilistic framework for seasonal forecasts of extreme low summer flows in the northeastern United States conditioned on antecedent climate and hydrologic conditions. The model is developed to explore three innovations in hierarchical modeling for seasonal forecasting at ungaged sites: (1) predictive climate teleconnections are inferred directly from ocean fields instead of predefined climate indices, (2) a parsimonious modeling structure is introduced to allow climate teleconnections to vary spatially across streamflow gages, and (3) climate teleconnections and antecedent hydrologic conditions are considered jointly for regional forecast development. The proposed model is developed and calibrated in a hierarchical Bayesian framework to pool regional information across sites and enhance regionalization skill. The model is validated in a cross-validation framework along with five simpler nested formulations to test specific hypotheses embedded in the full model structure. Results indicate that each of the three innovations improve out-of-sample summer low-flow forecasts, with the greatest benefits derived from the spatially heterogeneous effect of climate teleconnections. We conclude with a discussion of possible model improvements from a better representation of antecedent hydrologic conditions at ungaged sites.
Parker, Aimée; Pin, Carmen; Carding, Simon R.; Watson, Alastair J. M.; Byrne, Helen M.
2017-01-01
Our work addresses two key challenges, one biological and one methodological. First, we aim to understand how proliferation and cell migration rates in the intestinal epithelium are related under healthy, damaged (Ara-C treated) and recovering conditions, and how these relations can be used to identify mechanisms of repair and regeneration. We analyse new data, presented in more detail in a companion paper, in which BrdU/IdU cell-labelling experiments were performed under these respective conditions. Second, in considering how to more rigorously process these data and interpret them using mathematical models, we use a probabilistic, hierarchical approach. This provides a best-practice approach for systematically modelling and understanding the uncertainties that can otherwise undermine the generation of reliable conclusions—uncertainties in experimental measurement and treatment, difficult-to-compare mathematical models of underlying mechanisms, and unknown or unobserved parameters. Both spatially discrete and continuous mechanistic models are considered and related via hierarchical conditional probability assumptions. We perform model checks on both in-sample and out-of-sample datasets and use them to show how to test possible model improvements and assess the robustness of our conclusions. We conclude, for the present set of experiments, that a primarily proliferation-driven model suffices to predict labelled cell dynamics over most time-scales. PMID:28753601
Maclaren, Oliver J; Parker, Aimée; Pin, Carmen; Carding, Simon R; Watson, Alastair J M; Fletcher, Alexander G; Byrne, Helen M; Maini, Philip K
2017-07-01
Our work addresses two key challenges, one biological and one methodological. First, we aim to understand how proliferation and cell migration rates in the intestinal epithelium are related under healthy, damaged (Ara-C treated) and recovering conditions, and how these relations can be used to identify mechanisms of repair and regeneration. We analyse new data, presented in more detail in a companion paper, in which BrdU/IdU cell-labelling experiments were performed under these respective conditions. Second, in considering how to more rigorously process these data and interpret them using mathematical models, we use a probabilistic, hierarchical approach. This provides a best-practice approach for systematically modelling and understanding the uncertainties that can otherwise undermine the generation of reliable conclusions-uncertainties in experimental measurement and treatment, difficult-to-compare mathematical models of underlying mechanisms, and unknown or unobserved parameters. Both spatially discrete and continuous mechanistic models are considered and related via hierarchical conditional probability assumptions. We perform model checks on both in-sample and out-of-sample datasets and use them to show how to test possible model improvements and assess the robustness of our conclusions. We conclude, for the present set of experiments, that a primarily proliferation-driven model suffices to predict labelled cell dynamics over most time-scales.
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 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
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.
Moore, Jonathan W.; Darimont, Chris T.
2009-01-01
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. PMID:19587790
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.
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
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
Yu, Jiyang; Silva, Jose; Califano, Andrea
2016-01-15
Functional genomics (FG) screens, using RNAi or CRISPR technology, have become a standard tool for systematic, genome-wide loss-of-function studies for therapeutic target discovery. As in many large-scale assays, however, off-target effects, variable reagents' potency and experimental noise must be accounted for appropriately control for false positives. Indeed, rigorous statistical analysis of high-throughput FG screening data remains challenging, particularly when integrative analyses are used to combine multiple sh/sgRNAs targeting the same gene in the library. We use large RNAi and CRISPR repositories that are publicly available to evaluate a novel meta-analysis approach for FG screens via Bayesian hierarchical modeling, Screening Bayesian Evaluation and Analysis Method (ScreenBEAM). Results from our analysis show that the proposed strategy, which seamlessly combines all available data, robustly outperforms classical algorithms developed for microarray data sets as well as recent approaches designed for next generation sequencing technologies. Remarkably, the ScreenBEAM algorithm works well even when the quality of FG screens is relatively low, which accounts for about 80-95% of the public datasets. R package and source code are available at: https://github.com/jyyu/ScreenBEAM. ac2248@columbia.edu, jose.silva@mssm.edu, yujiyang@gmail.com Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
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
2014-09-01
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.
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
Bayesian hierarchical modeling of means and covariances of gene expression data within families.
Pique-Regi, Roger; Morrison, John; Thomas, Duncan C
2007-01-01
We describe a hierarchical Bayes model for the influence of constitutional genotypes from a linkage scan on the expression of a large number of genes. The model comprises linear regression models for the means in relation to genotypes and for the covariances between pairs of related individuals in relation to their identity-by-descent estimates. The matrices of regression coefficients for all possible pairs of single-nucleotide polymorphisms (SNPs) by all possible expressed genes are in turn modeled as a mixture of null values and a normal distribution of non-null values, with probabilities and means given by a third-level model of SNP and trait random effects and a spatial regression on the distance between the SNP and the expressed gene. The latter provides a way of testing for cis and trans effects. The method was applied to data on 116 SNPs and 189 genes on chromosome 11, for which Morley et al. (Nature 2004, 430: 743-747) had previously reported linkage. We were able to confirm the association of the expression of HSD17B12 with a SNP in the same region reported by Morley et al., and also detected a SNP that appeared to affect the expression of many genes on this chromosome. The approach appears to be a promising way to address the huge multiple comparisons problem for relating genome-wide genotype x expression data.
Buhule, O D; Wahed, A S; Youk, A O
2017-08-22
Modeling of correlated biomarkers jointly has been shown to improve the efficiency of parameter estimates, leading to better clinical decisions. In this paper, we employ a joint modeling approach to a unique diabetes dataset, where blood glucose (continuous) and urine glucose (ordinal) measures of disease severity for diabetes are known to be correlated. The postulated joint model assumes that the outcomes are from distributions that are in the exponential family and hence modeled as multivariate generalized linear mixed effects model associated through correlated and/or shared random effects. The Markov chain Monte Carlo Bayesian approach is used to approximate posterior distribution and draw inference on the parameters. This proposed methodology provides a flexible framework to account for the hierarchical structure of the highly unbalanced data as well as the association between the 2 outcomes. The results indicate improved efficiency of parameter estimates when blood glucose and urine glucose are modeled jointly. Moreover, the simulation studies show that estimates obtained from the joint model are consistently less biased and more efficient than those in the separate models. Copyright © 2017 John Wiley & Sons, Ltd.
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
Schmid, Volker J; Whitcher, Brandon; Padhani, Anwar R; Taylor, N Jane; Yang, Guang-Zhong
2009-01-01
Imaging in clinical oncology trials provides a wealth of information that contributes to the drug development process, especially in early phase studies. This article focuses on kinetic modeling in DCE-MRI, inspired by mixed-effects models that are frequently used in the analysis of clinical trials. Instead of summarizing each scanning session as a single kinetic parameter--such as median k(trans) across all voxels in the tumor ROI-we propose to analyze all voxel time courses from all scans and across all subjects simultaneously in a single model. The kinetic parameters from the usual nonlinear regression model are decomposed into unique components associated with factors from the longitudinal study; e.g., treatment, patient, and voxel effects. A Bayesian hierarchical model provides the framework to construct a data model, a parameter model, as well as prior distributions. The posterior distribution of the kinetic parameters is estimated using Markov chain Monte Carlo (MCMC) methods. Hypothesis testing at the study level for an overall treatment effect is straightforward and the patient- and voxel-level parameters capture random effects that provide additional information at various levels of resolution to allow a thorough evaluation of the clinical trial. The proposed method is validated with a breast cancer study, where the subjects were imaged before and after two cycles of chemotherapy, demonstrating the clinical potential of this method to longitudinal oncology studies.
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
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
Choi, Leena; Caffo, Brian S; Kohli, Utkarsh; Pandharipande, Pratik; Kurnik, Daniel; Ely, E Wesley; Stein, C Michael
2011-10-01
The purpose of this study is to develop a statistical methodology to handle a large proportion of artifactual outliers in a population pharmacokinetic (PK) modeling. The motivating PK data were obtained from a population PK study to examine associations between PK parameters such as clearance of dexmedetomidine (DEX) and cytochrome P450 2A6 phenotypes. The blood samples were sparsely sampled from patients in intensive care units (ICUs) while different doses of DEX were continuously infused. Conventional population PK analysis of these data revealed several challenges and intricacies. Especially, there was strong evidence that some plasma drug concentrations were artifactually high and likely contaminated with the infused drug due to blood sampling processes that are sometimes unavoidable in an ICU setting. If not addressed, or if arbitrarily excluded, these outlying values could lead to biased estimates of PK parameters and miss important relationships between PK parameters and covariates due to increased variability. We propose a novel population PK model, a Bayesian hierarchical nonlinear mixture model, to accommodate the artifactual outliers using a finite mixture as the residual error model. Our results showed that the proposed model handles the outliers well. We also conducted simulation studies with a varying proportion of the outliers. These simulation results showed that the proposed model can accommodate the outliers well so that the estimated PK parameters are less biased.
Bello, Nora M; Steibel, Juan P; Tempelman, Robert J
2012-03-01
The augmentation of categorical outcomes with underlying Gaussian variables in bivariate generalized mixed effects models has facilitated the joint modeling of continuous and binary response variables. These models typically assume that random effects and residual effects (co)variances are homogeneous across all clusters and subjects, respectively. Motivated by conflicting evidence about the association between performance outcomes in dairy production systems, we consider the situation where these (co)variance parameters may themselves be functions of systematic and/or random effects. We present a hierarchical Bayesian extension of bivariate generalized linear models whereby functions of the (co)variance matrices are specified as linear combinations of fixed and random effects following a square-root-free Cholesky reparameterization that ensures necessary positive semidefinite constraints. We test the proposed model by simulation and apply it to the analysis of a dairy cattle data set in which the random herd-level and residual cow-level effects (co)variances between a continuous production trait and binary reproduction trait are modeled as functions of fixed management effects and random cluster effects. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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
Buscot, Marie-Jeanne; Wotherspoon, Simon S; Magnussen, Costan G; Juonala, Markus; Sabin, Matthew A; Burgner, David P; Lehtimäki, Terho; Viikari, Jorma S A; Hutri-Kähönen, Nina; Raitakari, Olli T; Thomson, Russell J
2017-06-06
Bayesian hierarchical piecewise regression (BHPR) modeling has not been previously formulated to detect and characterise the mechanism of trajectory divergence between groups of participants that have longitudinal responses with distinct developmental phases. These models are useful when participants in a prospective cohort study are grouped according to a distal dichotomous health outcome. Indeed, a refined understanding of how deleterious risk factor profiles develop across the life-course may help inform early-life interventions. Previous techniques to determine between-group differences in risk factors at each age may result in biased estimate of the age at divergence. We demonstrate the use of Bayesian hierarchical piecewise regression (BHPR) to generate a point estimate and credible interval for the age at which trajectories diverge between groups for continuous outcome measures that exhibit non-linear within-person response profiles over time. We illustrate our approach by modeling the divergence in childhood-to-adulthood body mass index (BMI) trajectories between two groups of adults with/without type 2 diabetes mellitus (T2DM) in the Cardiovascular Risk in Young Finns Study (YFS). Using the proposed BHPR approach, we estimated the BMI profiles of participants with T2DM diverged from healthy participants at age 16 years for males (95% credible interval (CI):13.5-18 years) and 21 years for females (95% CI: 19.5-23 years). These data suggest that a critical window for weight management intervention in preventing T2DM might exist before the age when BMI growth rate is naturally expected to decrease. Simulation showed that when using pairwise comparison of least-square means from categorical mixed models, smaller sample sizes tended to conclude a later age of divergence. In contrast, the point estimate of the divergence time is not biased by sample size when using the proposed BHPR method. BHPR is a powerful analytic tool to model long-term non
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.
DiMaggio, Charlie; Galea, Sandro; Vlahov, David
2009-01-01
To illustrate how spatial modeling methods may provide insight about the relation between proximity to mass trauma and substance use, we examined the role of proximity to a terrorist event in determining risk of substance use related diagnoses. Previous analyses that have assessed changes in substance use following mass traumas such as terrorist attacks have produced conflicting results. We used Bayesian hierarchical modeling methods to assess whether distance from the World Trade Center (WTC) site in the aftermath of the September 11, 2001 terrorist attacks was associated with risk of substance use related diagnoses. In analyses controlling for age, gender, median household income, and employment-related exposure to the terrorist attacks, we found that each two mile increment in distance away from the WTC site was associated with 18% more substance use related diagnoses in the population we studied; this relation between distance from the WTC and substance use related disorder was the opposite of the relations observed one year before the same attacks in the same area. By accounting for spatial relationships that may influence the population risk of substance use health disorder, this approach helps explain some of the conflicting observations in the extant literature. These methods hold promise for the characterization of disease risk where spatial patterning of exposures and outcomes may matter.
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.
Godsland, Ian F; Agbaje, Olorunsola F; Hovorka, Roman
2006-07-01
Minimal model analysis of intravenous glucose tolerance test (IVGTT) glucose and insulin concentrations offers a validated approach to measuring insulin sensitivity, but model identification is not always successful. Improvements may be achieved by using alternative settings in the modeling process, although results may differ according to setting, and care must be exercised in combining results. IVGTT data (12 samples, regular test) from 533 men without diabetes was modeled by the traditional nonlinear regression (NLR) approach, using five different permutations of settings. Results were evaluated with reference to the more robust Bayesian hierarchical (BH) approach to model identification and to the proportion of variance they explained in known correlates of insulin sensitivity (age, BMI, blood pressure, fasting glucose and insulin, serum triglyceride, HDL cholesterol, and uric acid concentration). BH analysis was successful in all cases. With NLR analysis, between 17 and 35 IVGTTs were associated with parameter coefficients of variation (PCVs) for minimal model parameters S(I) (insulin sensitivity) and S(G) (glucose effectiveness) of >100%. Systematic use of each different approach in combination reduced this number to five. Mean (interquartile range) S(I)(NLR) was then 3.14 (2.29-4.63) min(-1).mU(-1).l x 10(-4) and 2.56 (1.74-3.83) min(-1).mU(-1).l x 10(-4) for S(I)(BH) (correlation 0.86, P < 0.0001). S(I)(NLR) explained, on average, 10.6% of the variance in known correlates of insulin sensitivity, whereas S(I)(BH) explained 8.5%. In a large body of data, which BH analysis demonstrated could be fully identified, use of alternative modeling settings in NLR analysis could substantially reduce the number of analyses with PCVs >100%. S(I)(NLR) compared favorably with S(I)(BH) in the proportion of variance explained in known correlates of insulin sensitivity.
Li, Lianfa; Laurent, Olivier; Wu, Jun
2016-02-05
Epidemiological studies suggest that air pollution is adversely associated with pregnancy outcomes. Such associations may be modified by spatially-varying factors including socio-demographic characteristics, land-use patterns and unaccounted exposures. Yet, few studies have systematically investigated the impact of these factors on spatial variability of the air pollution's effects. This study aimed to examine spatial variability of the effects of air pollution on term birth weight across Census tracts and the influence of tract-level factors on such variability. We obtained over 900,000 birth records from 2001 to 2008 in Los Angeles County, California, USA. Air pollution exposure was modeled at individual level for nitrogen dioxide (NO2) and nitrogen oxides (NOx) using spatiotemporal models. Two-stage Bayesian hierarchical non-linear models were developed to (1) quantify the associations between air pollution exposure and term birth weight within each tract; and (2) examine the socio-demographic, land-use, and exposure-related factors contributing to the between-tract variability of the associations between air pollution and term birth weight. Higher air pollution exposure was associated with lower term birth weight (average posterior effects: -14.7 (95 % CI: -19.8, -9.7) g per 10 ppb increment in NO2 and -6.9 (95 % CI: -12.9, -0.9) g per 10 ppb increment in NOx). The variation of the association across Census tracts was significantly influenced by the tract-level socio-demographic, exposure-related and land-use factors. Our models captured the complex non-linear relationship between these factors and the associations between air pollution and term birth weight: we observed the thresholds from which the influence of the tract-level factors was markedly exacerbated or attenuated. Exacerbating factors might reflect additional exposure to environmental insults or lower socio-economic status with higher vulnerability, whereas attenuating factors might indicate reduced
NASA Astrophysics Data System (ADS)
Mandel, Kaisey S.; Scolnic, Daniel M.; Shariff, Hikmatali; Foley, Ryan J.; Kirshner, Robert P.
2017-06-01
Conventional Type Ia supernova (SN Ia) cosmology analyses currently use a simplistic linear regression of magnitude versus color and light curve shape, which does not model intrinsic SN Ia variations and host galaxy dust as physically distinct effects, resulting in low color-magnitude slopes. We construct a probabilistic generative model for the dusty distribution of extinguished absolute magnitudes and apparent colors as the convolution of an intrinsic SN Ia color-magnitude distribution and a host galaxy dust reddening-extinction distribution. If the intrinsic color-magnitude (M B versus B - V) slope {β }{int} differs from the host galaxy dust law R B , this convolution results in a specific curve of mean extinguished absolute magnitude versus apparent color. The derivative of this curve smoothly transitions from {β }{int} in the blue tail to R B in the red tail of the apparent color distribution. The conventional linear fit approximates this effective curve near the average apparent color, resulting in an apparent slope {β }{app} between {β }{int} and R B . We incorporate these effects into a hierarchical Bayesian statistical model for SN Ia light curve measurements, and analyze a data set of SALT2 optical light curve fits of 248 nearby SNe Ia at z< 0.10. The conventional linear fit gives {β }{app}≈ 3. Our model finds {β }{int}=2.3+/- 0.3 and a distinct dust law of {R}B=3.8+/- 0.3, consistent with the average for Milky Way dust, while correcting a systematic distance bias of ˜0.10 mag in the tails of the apparent color distribution. Finally, we extend our model to examine the SN Ia luminosity-host mass dependence in terms of intrinsic and dust components.
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.
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.
Wu, Zhen; Liu, Yong; Liang, Zhongyao; Wu, Sifeng; Guo, Huaicheng
2017-06-01
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. Copyright © 2017 Elsevier Ltd. All rights reserved.
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.
Dura-Bernal, Salvador; Wennekers, Thomas; Denham, Susan L.
2012-01-01
Hierarchical generative models, such as Bayesian networks, and belief propagation have been shown to provide a theoretical framework that can account for perceptual processes, including feedforward recognition and feedback modulation. The framework explains both psychophysical and physiological experimental data and maps well onto the hierarchical distributed cortical anatomy. However, the complexity required to model cortical processes makes inference, even using approximate methods, very computationally expensive. Thus, existing object perception models based on this approach are typically limited to tree-structured networks with no loops, use small toy examples or fail to account for certain perceptual aspects such as invariance to transformations or feedback reconstruction. In this study we develop a Bayesian network with an architecture similar to that of HMAX, a biologically-inspired hierarchical model of object recognition, and use loopy belief propagation to approximate the model operations (selectivity and invariance). Crucially, the resulting Bayesian network extends the functionality of HMAX by including top-down recursive feedback. Thus, the proposed model not only achieves successful feedforward recognition invariant to noise, occlusions, and changes in position and size, but is also able to reproduce modulatory effects such as illusory contour completion and attention. Our novel and rigorous methodology covers key aspects such as learning using a layerwise greedy algorithm, combining feedback information from multiple parents and reducing the number of operations required. Overall, this work extends an established model of object recognition to include high-level feedback modulation, based on state-of-the-art probabilistic approaches. The methodology employed, consistent with evidence from the visual cortex, can be potentially generalized to build models of hierarchical perceptual organization that include top-down and bottom-up interactions, for
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
Storz, Jay F; Beaumont, Mark A; Alberts, Susan C
2002-11-01
The purpose of this study was to test for evidence that savannah baboons (Papio cynocephalus) underwent a population expansion in concert with a hypothesized expansion of African human and chimpanzee populations during the late Pleistocene. The rationale is that any type of environmental event sufficient to cause simultaneous population expansions in African humans and chimpanzees would also be expected to affect other codistributed mammals. To test for genetic evidence of population expansion or contraction, we performed a coalescent analysis of multilocus microsatellite data using a hierarchical Bayesian model. Markov chain Monte Carlo (MCMC) simulations were used to estimate the posterior probability density of demographic and genealogical parameters. The model was designed to allow interlocus variation in mutational and demographic parameters, which made it possible to detect aberrant patterns of variation at individual loci that could result from heterogeneity in mutational dynamics or from the effects of selection at linked sites. Results of the MCMC simulations were consistent with zero variance in demographic parameters among loci, but there was evidence for a 10- to 20-fold difference in mutation rate between the most slowly and most rapidly evolving loci. Results of the model provided strong evidence that savannah baboons have undergone a long-term historical decline in population size. The mode of the highest posterior density for the joint distribution of current and ancestral population size indicated a roughly eightfold contraction over the past 1,000 to 250,000 years. These results indicate that savannah baboons apparently did not share a common demographic history with other codistributed primate species.
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
NASA Astrophysics Data System (ADS)
Wahl, E. R.
2008-12-01
as much information as the multi-taxonomic MAT in well-selected regions, the ratio inverse model is used as the starting point for developing a temperature-pollen forward model. Such a forward model can be directly incorporated into a Bayesian hierarchical model (BHM) framework: the reason for seeking a taxonomically simplified pollen model is itself driven by computational considerations within the BHM. The BHM framework thus allows pollen- derived climate information to contribute multi-decadal to centennial information into a simultaneous reconstruction framework that also incorporates annually-resolved climate information from tree ring sources and centennial to multi-centennial information from borehole reconstructions. In the forward model, the pine and oak pollen counts are treated as binomial random variables with expected values (p) and (1-p), conditional on the calibration temperature values and the total counts (n) used to determine the ratios. Model parameters and (p) values have been estimated using a binomial logistic form of the generalized linear model. Comparison of the estimated conditional expected (p) values with the associated calibration ratio/temperature relationships shows good performance for the SW N American test case, with little (but non- 0) bias and good overall tracking (R2 = 0.79). (4) The results from (3) indicate that appropriate forward models can be developed for a suite of sites in North America with temporally dense, well-dated fossil pollen records over the past 2ka, and then incorporated into the BHM. Modeling results for the suite of sites will be presented.
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
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
Guo, Ying; Bowman, F. DuBois; Kilts, Clinton
2009-01-01
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 non-response 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 pre-treatment 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 (EM) 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
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…
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 Bayesian Hierarchical Selection Model for Academic Growth with Missing Data
ERIC Educational Resources Information Center
Allen, Jeff
2017-01-01
Using a sample of schools testing annually in grades 9-11 with a vertically linked series of assessments, a latent growth curve model is used to model test scores with student intercepts and slopes nested within school. Missed assessments can occur because of student mobility, student dropout, absenteeism, and other reasons. Missing data…
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 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…
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
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...
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.
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.
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.
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.
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
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.
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.
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.
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. Copyright © 2013 Elsevier Ltd. All rights reserved.
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
Introduction to Bayesian modelling in dental research.
Gilthorpe, M S; Maddick, I H; Petrie, A
2000-12-01
To explain the concepts and application of Bayesian modelling and how it can be applied to the analysis of dental research data. Methodological in nature, this article introduces Bayesian modelling through hypothetical dental examples. The synthesis of RCT results with previous evidence, including expert opinion, is used to illustrate full Bayesian modelling. Meta-analysis, in the form of empirical Bayesian modelling, is introduced. An example of full Bayesian modelling is described for the synthesis of evidence from several studies that investigate the success of root canal treatment. Hierarchical (Bayesian) modelling is demonstrated for a survey of childhood caries, where surface data is nested within subjects. Bayesian methods enhance interpretation of research evidence through the synthesis of information from multiple sources. Bayesian modelling is now readily accessible to clinical researchers and is able to augment the application of clinical decision making in the development of guidelines and clinical practice.
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
2011-01-01
Background Previous research has documented heterogeneity in the effects of maternal education on adverse birth outcomes by nativity and Hispanic subgroup in the United States. In this article, we considered the risk of preterm birth (PTB) using 9 years of vital statistics birth data from New York City. We employed finer categorizations of exposure than used previously and estimated the risk dose-response across the range of education by nativity and ethnicity. Methods Using Bayesian random effects logistic regression models with restricted quadratic spline terms for years of completed maternal education, we calculated and plotted the estimated posterior probabilities of PTB (gestational age < 37 weeks) for each year of education by ethnic and nativity subgroups adjusted for only maternal age, as well as with more extensive covariate adjustments. We then estimated the posterior risk difference between native and foreign born mothers by ethnicity over the continuous range of education exposures. Results The risk of PTB varied substantially by education, nativity and ethnicity. Native born groups showed higher absolute risk of PTB and declining risk associated with higher levels of education beyond about 10 years, as did foreign-born Puerto Ricans. For most other foreign born groups, however, risk of PTB was flatter across the education range. For Mexicans, Central Americans, Dominicans, South Americans and "Others", the protective effect of foreign birth diminished progressively across the educational range. Only for Puerto Ricans was there no nativity advantage for the foreign born, although small numbers of foreign born Cubans limited precision of estimates for that group. Conclusions Using flexible Bayesian regression models with random effects allowed us to estimate absolute risks without strong modeling assumptions. Risk comparisons for any sub-groups at any exposure level were simple to calculate. Shrinkage of posterior estimates through the use of random
Inferring on the Intentions of Others by Hierarchical Bayesian Learning
Diaconescu, Andreea O.; Mathys, Christoph; Weber, Lilian A. E.; Daunizeau, Jean; Kasper, Lars; Lomakina, Ekaterina I.; Fehr, Ernst; Stephan, Klaas E.
2014-01-01
Inferring on others' (potentially time-varying) intentions is a fundamental problem during many social transactions. To investigate the underlying mechanisms, we applied computational modeling to behavioral data from an economic game in which 16 pairs of volunteers (randomly assigned to “player” or “adviser” roles) interacted. The player performed a probabilistic reinforcement learning task, receiving information about a binary lottery from a visual pie chart. The adviser, who received more predictive information, issued an additional recommendation. Critically, the game was structured such that the adviser's incentives to provide helpful or misleading information varied in time. Using a meta-Bayesian modeling framework, we found that the players' behavior was best explained by the deployment of hierarchical learning: they inferred upon the volatility of the advisers' intentions in order to optimize their predictions about the validity of their advice. Beyond learning, volatility estimates also affected the trial-by-trial variability of decisions: participants were more likely to rely on their estimates of advice accuracy for making choices when they believed that the adviser's intentions were presently stable. Finally, our model of the players' inference predicted the players' interpersonal reactivity index (IRI) scores, explicit ratings of the advisers' helpfulness and the advisers' self-reports on their chosen strategy. Overall, our results suggest that humans (i) employ hierarchical generative models to infer on the changing intentions of others, (ii) use volatility estimates to inform decision-making in social interactions, and (iii) integrate estimates of advice accuracy with non-social sources of information. The Bayesian framework presented here can quantify individual differences in these mechanisms from simple behavioral readouts and may prove useful in future clinical studies of maladaptive social cognition. PMID:25187943
Inferring on the intentions of others by hierarchical Bayesian learning.
Diaconescu, Andreea O; Mathys, Christoph; Weber, Lilian A E; Daunizeau, Jean; Kasper, Lars; Lomakina, Ekaterina I; Fehr, Ernst; Stephan, Klaas E
2014-09-01
Inferring on others' (potentially time-varying) intentions is a fundamental problem during many social transactions. To investigate the underlying mechanisms, we applied computational modeling to behavioral data from an economic game in which 16 pairs of volunteers (randomly assigned to "player" or "adviser" roles) interacted. The player performed a probabilistic reinforcement learning task, receiving information about a binary lottery from a visual pie chart. The adviser, who received more predictive information, issued an additional recommendation. Critically, the game was structured such that the adviser's incentives to provide helpful or misleading information varied in time. Using a meta-Bayesian modeling framework, we found that the players' behavior was best explained by the deployment of hierarchical learning: they inferred upon the volatility of the advisers' intentions in order to optimize their predictions about the validity of their advice. Beyond learning, volatility estimates also affected the trial-by-trial variability of decisions: participants were more likely to rely on their estimates of advice accuracy for making choices when they believed that the adviser's intentions were presently stable. Finally, our model of the players' inference predicted the players' interpersonal reactivity index (IRI) scores, explicit ratings of the advisers' helpfulness and the advisers' self-reports on their chosen strategy. Overall, our results suggest that humans (i) employ hierarchical generative models to infer on the changing intentions of others, (ii) use volatility estimates to inform decision-making in social interactions, and (iii) integrate estimates of advice accuracy with non-social sources of information. The Bayesian framework presented here can quantify individual differences in these mechanisms from simple behavioral readouts and may prove useful in future clinical studies of maladaptive social cognition.
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.
Rahimi, Azar; Sapp, John; Xu, Jingjia; Bajorski, Peter; Horacek, Milan; Wang, Linwei
2015-01-01
Noninvasive cardiac electrophysiological (EP) imaging aims to mathematically reconstruct the spatiotemporal dynamics of cardiac sources from body-surface electrocardiographic (ECG) data. This ill-posed problem is often regularized by a fixed constraining model. However, a fixed-model approach enforces the source distribution to follow a pre-assumed structure that does not always match the varying spatiotemporal distribution of actual sources. To understand the model-data relation and examine the impact of prior models, we present a multiple-model approach for volumetric cardiac EP imaging where multiple prior models are included and automatically picked by the available ECG data. Multiple models are incorporated as an Lp-norm prior for sources, where p is an unknown hyperparameter with a prior uniform distribution. To examine how different combinations of models may be favored by different measurement data, the posterior distribution of cardiac sources and hyperparameter p is calculated using a Markov Chain Monte Carlo (MCMC) technique. The importance of multiple-model prior was assessed in two sets of synthetic and real-data experiments, compared to fixed-model priors (using Laplace and Gaussian priors). The results showed that the posterior combination of models (the posterior distribution of p) as determined by the ECG data differed substantially when reconstructing sources with different sizes and structures. While the use of fixed models is best suited in situations where the prior assumption fits the actual source structures, the use of an automatically adaptive set of models may have the ability to better address model-data mismatch and to provide consistent performance in reconstructing sources with different properties. PMID:26259018
Rahimi, Azar; Sapp, John; Xu, Jingjia; Bajorski, Peter; Horacek, Milan; Wang, Linwei
2016-01-01
Noninvasive cardiac electrophysiological (EP) imaging aims to mathematically reconstruct the spatiotemporal dynamics of cardiac sources from body-surface electrocardiographic (ECG) data. This ill-posed problem is often regularized by a fixed constraining model. However, a fixed-model approach enforces the source distribution to follow a pre-assumed structure that does not always match the varying spatiotemporal distribution of actual sources. To understand the model-data relation and examine the impact of prior models, we present a multiple-model approach for volumetric cardiac EP imaging where multiple prior models are included and automatically picked by the available ECG data. Multiple models are incorporated as an Lp-norm prior for sources, where p is an unknown hyperparameter with a prior uniform distribution. To examine how different combinations of models may be favored by different measurement data, the posterior distribution of cardiac sources and hyperparameter p is calculated using a Markov Chain Monte Carlo (MCMC) technique. The importance of multiple-model prior was assessed in two sets of synthetic and real-data experiments, compared to fixed-model priors (using Laplace and Gaussian priors). The results showed that the posterior combination of models (the posterior distribution of p) as determined by the ECG data differed substantially when reconstructing sources with different sizes and structures. While the use of fixed models is best suited in situations where the prior assumption fits the actual source structures, the use of an automatically adaptive set of models may have the ability to better address model-data mismatch and to provide consistent performance in reconstructing sources with different properties.
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.
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
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
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.
NASA Astrophysics Data System (ADS)
Schlef, K.; Spence, C. M.; Brown, C.
2016-12-01
Riverine flooding in West Africa has recently caused devastating damages, yet there is limited information on historical flooding and projections of future flooding under non-stationary climate are highly uncertain. The purpose of this study is twofold: first, to identify key oceanic-atmospheric mechanisms that drive flood events in West Africa, and second, to build a non-stationary model of future regional flooding conditioned on the expected evolution of those mechanisms under climate change. We identify climate covariates, such as the West African Monsoon Index, that are based on large-scale atmospheric processes with a demonstrated mechanistic link to flood events. We then develop a hierarchical Bayesian framework that is conditioned on climate and basin-specific covariates. A peaks-over-threshold method is used to identify flood event magnitude and frequency, which are represented by Generalized Pareto and Poisson distributions, respectively. Poor data quality is mitigated by incorporating censored information. After the model is validated using historical climate and streamflow data, projections of the climate covariates from general circulation models are used to develop estimates of future flooding and corresponding uncertainty bounds. This study improves understanding of the causes of floods, and uses novel methods to develop estimates of future flooding in West Africa, thus providing an essential step towards building flood resilience.
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.
Lee, Whanhee; Hwang, Sung-Hee; Choi, Hayoung; Kim, Ho
2017-01-01
Smoking and passive smoking have been extensively reported as risk factors of cardiovascular morbidity and mortality. Despite the biological mechanisms underlying the impact of hazardous chemical substances contained in tobacco in cardiovascular diseases (CVD), studies investigating the association between smoking and passive smoking with morbidity are at an inchoate stage in Korea. Therefore, this study aimed to estimate the risks of smoking and passive smoking on cardiovascular morbidity at the national and regional levels. This study calculated sex-standardized and age-standardized prevalence of CVD and smoking indices in 253 community health centers (si/gun/gu) in Korea using the 2008-2013 Korea Community Health Survey data. Furthermore, a Bayesian hierarchical model was used to estimate the association of smoking and passive smoking with the prevalence of CVD from the national and regional community health centers. At the national level, smoking was significantly associated with stroke (relative risk [RR], 1.060) and hypertension (RR, 1.016) prevalence, whilst passive smoking at home and work were also significantly associated with prevalence of stroke (RR, 1.037/1.013), angina (RR, 1.016/1.006), and hypertension (RR, 1.010/1.004). Furthermore, the effects of smoking and passive smoking were greater in urban-industrial areas than in rural areas. The findings of this study would provide grounds for national policies that limit smoking and passive smoking, as well as regionally serve as the basis for region-specific healthcare policies in populations with high CVD vulnerability.
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.
Xie, Meiquan; Cheng, Wen; Gill, Gurdiljot Singh; Zhou, Jiao; Jia, Xudong; Choi, Simon
2017-08-24
Most of the extensive research dedicated to identifying the influential factors of hit-and-run (HR) crashes has utilized the typical Maximum Likelihood Estimation Binary Logit models, and none of them have employed the real-time traffic data. To fill this gap, this study focused on investigating contributing factors of HR crashes, as well as the severity levels of HR. This study analyzed four-year crash and real time loop detector data by employing the hierarchical Bayesian models with random effects within a sequential Logit structure. Along with the evaluation of impact of random effects on model fitness and complexity, the prediction capability of the models was also examined. Stepwise incremental sensitivity and specificity were calculated and ROC (Receiver Operating Characteristic) curve was utilized to graphically illustrate the predictive performance of the model. Among the real-time flow variables, the average occupancy and speed from upstream detector was observed to be positively correlated with HR crash possibility. The average upstream speed and speed difference of upstream and downstream speed were correlated with the occurrence of severe HR crashes. Apart from real-time factors, the other variables found influential for HR and severe HR crashes were length of segment, adverse weather conditions, dark lighting conditions with malfunctioning street light, driving under influence of alcohol, width of inner shoulder, and night time. This study suggests the potential traffic conditions of HR and severe HR occurrence, which refer to relatively congested upstream traffic conditions with high upstream speed and significant speed deviations on long segments. The above findings suggest that traffic enforcement should be directed towards mitigating the risky driving under the aforementioned traffic conditions. Moreover, the enforcement agencies may employ alcohol checkpoints to counter DUI during the night time. As per the engineering improvements, wider inner
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.
Shin, Hwashin Hyun; Stieb, Dave; Burnett, Rick; Takahara, Glen; Jessiman, Barry
2012-03-01
The association between daily variations in urban air quality and mortality has been well documented using time series statistical methods. This approach assumes a constant association over time. We develop a space-time dynamic model that relaxes this assumption, thus more directly examining the hypothesis that improvements in air quality translate into improvements in public health. We postulate a Bayesian hierarchical two-level model to estimate annual mortality risks at regional and national levels and to track both risk and heterogeneity of risk within and between regions over time. We illustrate our methods using daily nitrogen dioxide concentrations (NO2) and nonaccidental mortality data collected for 1984-2004 in 24 Canadian cities. Estimates of risk and heterogeneity are compared by cause of mortality (cardio-pulmonary [CP] versus non-CP) and season, respectively. Over the entire period, the NO2 risk for CP mortality was slightly lower but with a narrower credible interval than that for non-CP mortality, mainly due to an unusually low risk for a single year (1998). Warm season NO2 risk was higher than cold season risk for both CP and non-CP mortality. For 21 years overall there were no significant differences detected among the four regional NO2 risks. We found overall that there was no strong evidence for time trends in NO2 risk at national or regional levels. However, an increasing linear time trend in the annual between-region heterogeneities was detected, which suggests the differences in risk among the four regions are getting larger, and further studies are necessary to understand the increasing heterogeneity. © 2011 Society for Risk Analysis.
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
Peripheral nerve segmentation using Nonparametric Bayesian Hierarchical Clustering.
Giraldo, Juan J; Álvarez, Mauricio A; Orozco, Álvaro A
2015-01-01
Several cases related to chronic pain, due to accidents, illness or surgical interventions, depend on anesthesiology procedures. These procedures are assisted with ultrasound images. Although, the ultrasound images are a useful instrument in order to guide the specialist in anesthesiology, the lack of intelligibility due to speckle noise, makes the clinical intervention a difficult task. In a similar manner, some artifacts are introduced in the image capturing process, challenging the expertise of anesthesiologists for not confusing the true nerve structures. Accordingly, an assistance methodology using image processing can improve the accuracy in the anesthesia practice. This paper proposes a peripheral nerve segmentation method in medical ultrasound images, based on Nonparametric Bayesian Hierarchical Clustering. The experimental results show segmentation performances with a Mean Squared Error performance of 1.026 ± 0.379 pixels for ulnar nerve, 0.704 ± 0.233 pixels for median nerve and 1.698 ± 0.564 pixels for peroneal nerve. Likewise, the model allows to emphasize other soft structures like muscles and aqueous tissues, that might be useful for an anesthesiologist.
Bayesian Variable Selection for Hierarchical Gene-Environment and Gene-Gene Interactions
Liu, Changlu; Ma, Jianzhong; Amos, Christopher I.
2014-01-01
We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions and gene by environment interactions in the same model. Our approach incorporates the natural hierarchical structure between the main effects and interaction effects into a mixture model, such that our methods tend to remove the irrelevant interaction effects more effectively, resulting in more robust and parsimonious models. We consider both strong and weak hierarchical models. For a strong hierarchical model, both of the main effects between interacting factors must be present for the interactions to be considered in the model development, while for a weak hierarchical model, only one of the two main effects is required to be present for the interaction to be evaluated. Our simulation results show that the proposed strong and weak hierarchical mixture models work well in controlling false positive rates and provide a powerful approach for identifying the predisposing effects and interactions in gene-environment interaction studies, in comparison with the naive model that does not impose this hierarchical constraint in most of the scenarios simulated. We illustrated our approach using data for lung cancer and cutaneous melanoma. PMID:25154630
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.
When mechanism matters: Bayesian forecasting using models of ecological diffusion
Hefley, Trevor J.; Hooten, Mevin B.; Russell, Robin E.; Walsh, Daniel P.; Powell, James A.
2017-01-01
Ecological diffusion is a theory that can be used to understand and forecast spatio-temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white-tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression-based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.
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.
Flexible Bayesian Human Fecundity Models.
Kim, Sungduk; Sundaram, Rajeshwari; Buck Louis, Germaine M; Pyper, Cecilia
2012-12-01
Human fecundity is an issue of considerable interest for both epidemiological and clinical audiences, and is dependent upon a couple's biologic capacity for reproduction coupled with behaviors that place a couple at risk for pregnancy. Bayesian hierarchical models have been proposed to better model the conception probabilities by accounting for the acts of intercourse around the day of ovulation, i.e., during the fertile window. These models can be viewed in the framework of a generalized nonlinear model with an exponential link. However, a fixed choice of link function may not always provide the best fit, leading to potentially biased estimates for probability of conception. Motivated by this, we propose a general class of models for fecundity by relaxing the choice of the link function under the generalized nonlinear model framework. We use a sample from the Oxford Conception Study (OCS) to illustrate the utility and fit of this general class of models for estimating human conception. Our findings reinforce the need for attention to be paid to the choice of link function in modeling conception, as it may bias the estimation of conception probabilities. Various properties of the proposed models are examined and a Markov chain Monte Carlo sampling algorithm was developed for implementing the Bayesian computations. The deviance information criterion measure and logarithm of pseudo marginal likelihood are used for guiding the choice of links. The supplemental material section contains technical details of the proof of the theorem stated in the paper, and contains further simulation results and analysis.
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.
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.
Chad Babcock; Hans Andersen; Andrew O. Finley; Bruce D. Cook
2015-01-01
Models leveraging repeat LiDAR and field collection campaigns may be one possible mechanism to monitor carbon flux in remote forested regions. Here, we look to the spatio-temporally data-rich Kenai Peninsula in Alaska, USA to examine the potential for Bayesian spatio-temporal mapping of terrestrial forest carbon storage and uncertainty.
Blakely, Tony; Richardson, Ken; Young, Jim; Callister, Paul; Didham, Robert
2009-12-11
BACKGROUND Pacific mortality rates are traditionally presented for all Pacific people combined, yet there is likely heterogeneity between separate Pacific ethnic groups. We aimed to determine mortality rates for Samoan, Cook Island Māori, Tongan, and Niuean ethnic groups (living in New Zealand). METHODS We used New Zealand Census-Mortality Study (NZCMS) data for 2001-04, for 380,000 person years of follow-up of 0-74 year olds in the 2001-04 cohort for which there was complete data on sex, age, ethnicity (total counts), natality, and household income. Given sparse data, we used hierarchical Bayesian (HB) regression modelling, with: a prior covariate structure specified for sex, age, natality (New Zealand/Overseas born), and household income; and smoothing of rates using shrinkage. The posterior mortality rate estimates were then directly standardised.RESULTS Standardising for sex, age, income, and natality, all-cause mortality rate ratios compared to Samoan were: 1.21 (95% credibility interval 1.05 to 1.42) for Cook Island Māori; 0.93 (0.77 to 1.10) for Tongan; and 1.07 (0.88 to 1.29) for Niuean. Cardiovascular disease (CVD) mortality rate ratios showed greater heterogeneity: 1.66 (1.26 to 2.13) for Cook Island Māori; 1.11 (0.72 to 1.58) for Niuean; and 0.86 (0.58 to 1.20) for Tongan. Results were little different standardising for just sex and age. We conducted a range of sensitivity analyses about a plausible range of (differential) return migration by Pacific people when terminally ill, and a plausible range of census undercounting of Pacific people. Our findings, in particular the elevated CVD mortality among Cook Island Māori, appeared robust. CONCLUSIONS To our knowledge, this project is the first time in New Zealand that clear (and marked in the case of CVD) differences in mortality have been demonstrated between different Pacific ethnic groups. Future health research and policy should, wherever possible and practicable, evaluate and incorporate
NASA Astrophysics Data System (ADS)
Eadie, Gwendolyn M.; Springford, Aaron; Harris, William E.
2017-02-01
We present a hierarchical Bayesian method for estimating the total mass and mass profile of the Milky Way Galaxy. The new hierarchical Bayesian approach further improves the framework presented by Eadie et al. and Eadie and Harris and builds upon the preliminary reports by Eadie et al. The method uses a distribution function f({ E },L) to model the Galaxy and kinematic data from satellite objects, such as globular clusters (GCs), to trace the Galaxy’s gravitational potential. A major advantage of the method is that it not only includes complete and incomplete data simultaneously in the analysis, but also incorporates measurement uncertainties in a coherent and meaningful way. We first test the hierarchical Bayesian framework, which includes measurement uncertainties, using the same data and power-law model assumed in Eadie and Harris and find the results are similar but more strongly constrained. Next, we take advantage of the new statistical framework and incorporate all possible GC data, finding a cumulative mass profile with Bayesian credible regions. This profile implies a mass within 125 kpc of 4.8× {10}11{M}⊙ with a 95% Bayesian credible region of (4.0{--}5.8)× {10}11{M}⊙ . Our results also provide estimates of the true specific energies of all the GCs. By comparing these estimated energies to the measured energies of GCs with complete velocity measurements, we observe that (the few) remote tracers with complete measurements may play a large role in determining a total mass estimate of the Galaxy. Thus, our study stresses the need for more remote tracers with complete velocity measurements.
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, ...
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, ...
Zhai, Jingbo; Cao, Hongbo; Ren, Ming; Mu, Wei; Lv, Sisi; Si, Jinhua; Wang, Hui; Chen, Jing; Shang, Hongcai
2016-08-01
N-of-1 trials can be aggregated to estimate population treatment effects using hierarchical Bayesian models. It is very important to report core items in hierarchical Bayesian analysis. In this study, we assessed reporting of items in hierarchical Bayesian analysis for aggregating N-of-1 trials to estimate population treatment effects. This was a systematic literature review of aggregating N-of-1 trials by hierarchical Bayesian models to estimate population treatment effects. A comprehensive search was performed to collect eligible articles. Pilot studies, formal N-of-1 trials and reports in which the data were reanalyzed using hierarchical Bayesian methods, were included. The information of reported items related with hierarchical Bayesian analysis was extracted by two independent reviewers. The guideline "ROBUST," developed for reporting Bayesian analysis of clinical studies, was published in Journal of Clinical Epidemiology in 2005. We assessed the included reports using ROBUST criteria and 18 other important items. After careful screening, 11 studies were identified to be eligible for inclusion. There were three pilot studies, four formal trials, and four reports in which the data were reanalyzed using hierarchical Bayesian methods. The number of reported items in ROBUST criteria ranged from six to seven, with a median number of six. Five of eleven included articles reported all items of the ROBUST criteria. But for justification and sensitivity analysis in prior distribution items, other items were reported in all of the included articles. Software and analysis data set items were reported the most frequently in additional items excluded from the ROBUST criteria. Less than half of the studies reported the other additional items. Reporting of core items in hierarchical Bayesian analysis for aggregating N-of-1 trials to estimate population treatment effects is suboptimal. A PRISMA-like guidance on reviews of Bayesian N-of-1 trials may be required in the future
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.
A Rasch Hierarchical Measurement Model.
ERIC Educational Resources Information Center
Maier, Kimberly S.
This paper describes a model that integrates an item response theory (IRT) Rasch model and a hierarchical linear model and presents a method of estimating model parameter values that does not rely on large-sample theory and normal approximations. The model resulting from the integration of a hierarchical linear model and the Rasch model allows one…
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.
An agglomerative hierarchical approach to visualization in Bayesian clustering problems.
Dawson, K J; Belkhir, K
2009-07-01
Clustering problems (including the clustering of individuals into outcrossing populations, hybrid generations, full-sib families and selfing lines) have recently received much attention in population genetics. In these clustering problems, the parameter of interest is a partition of the set of sampled individuals--the sample partition. In a fully Bayesian approach to clustering problems of this type, our knowledge about the sample partition is represented by a probability distribution on the space of possible sample partitions. As the number of possible partitions grows very rapidly with the sample size, we cannot visualize this probability distribution in its entirety, unless the sample is very small. As a solution to this visualization problem, we recommend using an agglomerative hierarchical clustering algorithm, which we call the exact linkage algorithm. This algorithm is a special case of the maximin clustering algorithm that we introduced previously. The exact linkage algorithm is now implemented in our software package PartitionView. The exact linkage algorithm takes the posterior co-assignment probabilities as input and yields as output a rooted binary tree, or more generally, a forest of such trees. Each node of this forest defines a set of individuals, and the node height is the posterior co-assignment probability of this set. This provides a useful visual representation of the uncertainty associated with the assignment of individuals to categories. It is also a useful starting point for a more detailed exploration of the posterior distribution in terms of the co-assignment probabilities.
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
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
NASA Astrophysics Data System (ADS)
Huang, Yong; Beck, James L.; Li, Hui
2017-05-01
The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse Bayesian learning model from our previous work, we propose two Gibbs sampling algorithms. The algorithms differ in their strategies to deal with the posterior uncertainty of the equation-error precision parameter, but both sample from the conditional posterior probability density functions (PDFs) for the structural stiffness parameters and system modal parameters. The effective dimension for the Gibbs sampling is low because iterative sampling is done from only three conditional posterior PDFs that correspond to three parameter groups, along with sampling of the equation-error precision parameter from another conditional posterior PDF in one of the algorithms where it is not integrated out as a "nuisance" parameter. A nice feature from a computational perspective is that it is not necessary to solve a nonlinear eigenvalue problem of a structural model. The effectiveness and robustness of the proposed algorithms are illustrated by applying them to the IASE-ASCE Phase II simulated and experimental benchmark studies. The goal is to use incomplete modal data identified before and after possible damage to detect and assess spatially-sparse stiffness reductions induced by any damage. Our past and current focus on meeting challenges arising from Bayesian inference of structural stiffness serve to strengthen the capability of vibration-based structural system identification but our methods also have much broader applicability for inverse problems in science and technology where system matrices are to be inferred from noisy partial information about their eigenquantities.
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
Hierarchical Modeling for Spatial Data Problems
Gelfand, Alan E.
2013-01-01
This short paper is centered on hierarchical modeling for problems in spatial and spatio-temporal statistics. It draws its motivation from the interdisciplinary research work of the author in terms of applications in the environmental sciences - ecological processes, environmental exposure, and weather modeling. The paper briefly reviews hierarchical modeling specification, adopting a Bayesian perspective with full inference and associated uncertainty within the specification, while achieving exact inference to avoid what may be uncomfortable asymptotics. It focuses on point-referenced (geo-statistical) and point pattern spatial settings. It looks in some detail at problems involving data fusion, species distributions, and large spatial datasets. It also briefly describes four further examples arising from the author's recent research projects. PMID:24010050
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. PMID:28269842
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.
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
Nummenmaa, Aapo; Auranen, Toni; Hämäläinen, Matti S; Jääskeläinen, Iiro P; Lampinen, Jouko; Sams, Mikko; Vehtari, Aki
2007-04-01
Magnetoencephalography (MEG) provides millisecond-scale temporal resolution for noninvasive mapping of human brain functions, but the problem of reconstructing the underlying source currents from the extracranial data has no unique solution. Several distributed source estimation methods based on different prior assumptions have been suggested for the resolution of this inverse problem. Recently, a hierarchical Bayesian generalization of the traditional minimum norm estimate (MNE) was proposed, in which the variance of distributed current at each cortical location is considered as a random variable and estimated from the data using the variational Bayesian (VB) framework. Here, we introduce an alternative scheme for performing Bayesian inference in the context of this hierarchical model by using Markov chain Monte Carlo (MCMC) strategies. In principle, the MCMC method is capable of numerically representing the true posterior distribution of the currents whereas the VB approach is inherently approximative. We point out some potential problems related to hyperprior selection in the previous work and study some possible solutions. A hyperprior sensitivity analysis is then performed, and the structure of the posterior distribution as revealed by the MCMC method is investigated. We show that the structure of the true posterior is rather complex with multiple modes corresponding to different possible solutions to the source reconstruction problem. We compare the results from the VB algorithm to those obtained from the MCMC simulation under different hyperparameter settings. The difficulties in using a unimodal variational distribution as a proxy for a truly multimodal distribution are also discussed. Simulated MEG data with realistic sensor and source geometries are used in performing the analyses.
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
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)
Bracken, C.; Holman, K. D.; Rajagopalan, B.; Moradkhani, H.
2016-12-01
Nonstationary analysis of hydrologic extremes is crucial for accurately estimating risk in a changing climate. Traditional hydrologic frequency analysis is conducted independently for each variable of interest, such as precipitation, streamflow, and reservoir level. However, these variables are closely related by physical processes animated by large scale climate drivers - El Nino Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), and Atlantic Multidecadal Oscillation (AMO). Specifically, these climate connections modulate the seasonal precipitation extremes, driving the hydrologic extremes and consequently, the extremes in reservoir levels and the infrastructure risk. The climate drivers impact nonstationarity in the hydrologic extremes and also in the infrastructure risk. We present a Bayesian hierarchical framework for conducting nonstationary frequency analysis of multiple hydrologic variables. A Gaussian elliptical copula is used to model the joint distribution of all variables, while allowing the marginal distributions to remain as Generalized Extreme Value (GEV). We demonstrate the utility of this framework with a joint frequency analysis model of annual peak snow water equivalent (SWE), annual peak flow, and annual peak reservoir elevation at Taylor Park dam in Colorado, USA. Aforementioned indices of large scale climate drivers are used as covariates to model temporal nonstationarity. The Bayesian framework provides the posterior distribution of the model parameters and, consequently, the return levels. Results show that performing a joint frequency analysis reduces the uncertainty in the return level estimates and better captures the multivariate dependence, compared to an independent model.
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.
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.
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.
Hierarchical Bayesian inference of galaxy redshift distributions from photometric surveys
NASA Astrophysics Data System (ADS)
Leistedt, Boris; Mortlock, Daniel J.; Peiris, Hiranya V.
2016-08-01
Accurately characterizing the redshift distributions of galaxies is essential for analysing deep photometric surveys and testing cosmological models. We present a technique to simultaneously infer redshift distributions and individual redshifts from photometric galaxy catalogues. Our model constructs a piecewise constant representation (effectively a histogram) of the distribution of galaxy types and redshifts, the parameters of which are efficiently inferred from noisy photometric flux measurements. This approach can be seen as a generalization of template-fitting photometric redshift methods and relies on a library of spectral templates to relate the photometric fluxes of individual galaxies to their redshifts. We illustrate this technique on simulated galaxy survey data, and demonstrate that it delivers correct posterior distributions on the underlying type and redshift distributions, as well as on the individual types and redshifts of galaxies. We show that even with uninformative priors, large photometric errors and parameter degeneracies, the redshift and type distributions can be recovered robustly thanks to the hierarchical nature of the model, which is not possible with common photometric redshift estimation techniques. As a result, redshift uncertainties can be fully propagated in cosmological analyses for the first time, fulfilling an essential requirement for the current and future generations of surveys.
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.
Bayesian analysis of CCDM models
NASA Astrophysics Data System (ADS)
Jesus, J. F.; Valentim, R.; Andrade-Oliveira, F.
2017-09-01
Creation of Cold Dark Matter (CCDM), in the context of Einstein Field Equations, produces a negative pressure term which can be used to explain the accelerated expansion of the Universe. In this work we tested six different spatially flat models for matter creation using statistical criteria, in light of SNe Ia data: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Bayesian Evidence (BE). These criteria allow to compare models considering goodness of fit and number of free parameters, penalizing excess of complexity. We find that JO model is slightly favoured over LJO/ΛCDM model, however, neither of these, nor Γ = 3αH0 model can be discarded from the current analysis. Three other scenarios are discarded either because poor fitting or because of the excess of free parameters. A method of increasing Bayesian evidence through reparameterization in order to reducing parameter degeneracy is also developed.
Hierarchical Bayesian method for mapping biogeochemical hot spots using induced polarization imaging
NASA Astrophysics Data System (ADS)
Wainwright, Haruko M.; Flores Orozco, Adrian; Bücker, Matthias; Dafflon, Baptiste; Chen, Jinsong; Hubbard, Susan S.; Williams, Kenneth H.
2016-01-01
In floodplain environments, a naturally reduced zone (NRZ) is considered to be a common biogeochemical hot spot, having distinct microbial and geochemical characteristics. Although important for understanding their role in mediating floodplain biogeochemical processes, mapping the subsurface distribution of NRZs over the dimensions of a floodplain is challenging, as conventional wellbore data are typically spatially limited and the distribution of NRZs is heterogeneous. In this study, we present an innovative methodology for the probabilistic mapping of NRZs within a three-dimensional (3-D) subsurface domain using induced polarization imaging, which is a noninvasive geophysical technique. Measurements consist of surface geophysical surveys and drilling-recovered sediments at the U.S. Department of Energy field site near Rifle, CO (USA). Inversion of surface time domain-induced polarization (TDIP) data yielded 3-D images of the complex electrical resistivity, in terms of magnitude and phase, which are associated with mineral precipitation and other lithological properties. By extracting the TDIP data values colocated with wellbore lithological logs, we found that the NRZs have a different distribution of resistivity and polarization from the other aquifer sediments. To estimate the spatial distribution of NRZs, we developed a Bayesian hierarchical model to integrate the geophysical and wellbore data. In addition, the resistivity images were used to estimate hydrostratigraphic interfaces under the floodplain. Validation results showed that the integration of electrical imaging and wellbore data using a Bayesian hierarchical model was capable of mapping spatially heterogeneous interfaces and NRZ distributions thereby providing a minimally invasive means to parameterize a hydrobiogeochemical model of the floodplain.
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.…
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.…
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.
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.
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 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…
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 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 model reduction and empirical Bayes for group (DCM) studies.
Friston, Karl J; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E; van Wijk, Bernadette C M; Ziegler, Gabriel; Zeidman, Peter
2016-03-01
This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level - e.g., dynamic causal models - and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.
Bayesian model reduction and empirical Bayes for group (DCM) studies
Friston, Karl J.; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E.; van Wijk, Bernadette C.M.; Ziegler, Gabriel; Zeidman, Peter
2016-01-01
This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level – e.g., dynamic causal models – and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. PMID:26569570
Combining information from multiple flood projections in a hierarchical Bayesian framework
NASA Astrophysics Data System (ADS)
Le Vine, Nataliya
2016-04-01
This study demonstrates, in the context of flood frequency analysis, the potential of a recently proposed hierarchical Bayesian approach to combine information from multiple models. The approach explicitly accommodates shared multimodel discrepancy as well as the probabilistic nature of the flood estimates, and treats the available models as a sample from a hypothetical complete (but unobserved) set of models. The methodology is applied to flood estimates from multiple hydrological projections (the Future Flows Hydrology data set) for 135 catchments in the UK. The advantages of the approach are shown to be: (1) to ensure adequate "baseline" with which to compare future changes; (2) to reduce flood estimate uncertainty; (3) to maximize use of statistical information in circumstances where multiple weak predictions individually lack power, but collectively provide meaningful information; (4) to diminish the importance of model consistency when model biases are large; and (5) to explicitly consider the influence of the (model performance) stationarity assumption. Moreover, the analysis indicates that reducing shared model discrepancy is the key to further reduction of uncertainty in the flood frequency analysis. The findings are of value regarding how conclusions about changing exposure to flooding are drawn, and to flood frequency change attribution studies.
Bayesian modeling of differential gene expression.
Lewin, Alex; Richardson, Sylvia; Marshall, Clare; Glazier, Anne; Aitman, Tim
2006-03-01
We present a Bayesian hierarchical model for detecting differentially expressing genes that includes simultaneous estimation of array effects, and show how to use the output for choosing lists of genes for further investigation. We give empirical evidence that expression-level dependent array effects are needed, and explore different nonlinear functions as part of our model-based approach to normalization. The model includes gene-specific variances but imposes some necessary shrinkage through a hierarchical structure. Model criticism via posterior predictive checks is discussed. Modeling the array effects (normalization) simultaneously with differential expression gives fewer false positive results. To choose a list of genes, we propose to combine various criteria (for instance, fold change and overall expression) into a single indicator variable for each gene. The posterior distribution of these variables is used to pick the list of genes, thereby taking into account uncertainty in parameter estimates. In an application to mouse knockout data, Gene Ontology annotations over- and underrepresented among the genes on the chosen list are consistent with biological expectations.
Bayesian kinematic earthquake source models
NASA Astrophysics Data System (ADS)
Minson, S. E.; Simons, M.; Beck, J. L.; Genrich, J. F.; Galetzka, J. E.; Chowdhury, F.; Owen, S. E.; Webb, F.; Comte, D.; Glass, B.; Leiva, C.; Ortega, F. H.
2009-12-01
Most coseismic, postseismic, and interseismic slip models are based on highly regularized optimizations which yield one solution which satisfies the data given a particular set of regularizing constraints. This regularization hampers our ability to answer basic questions such as whether seismic and aseismic slip overlap or instead rupture separate portions of the fault zone. We present a Bayesian methodology for generating kinematic earthquake source models with a focus on large subduction zone earthquakes. Unlike classical optimization approaches, Bayesian techniques sample the ensemble of all acceptable models presented as an a posteriori probability density function (PDF), and thus we can explore the entire solution space to determine, for example, which model parameters are well determined and which are not, or what is the likelihood that two slip distributions overlap in space. Bayesian sampling also has the advantage that all a priori knowledge of the source process can be used to mold the a posteriori ensemble of models. Although very powerful, Bayesian methods have up to now been of limited use in geophysical modeling because they are only computationally feasible for problems with a small number of free parameters due to what is called the "curse of dimensionality." However, our methodology can successfully sample solution spaces of many hundreds of parameters, which is sufficient to produce finite fault kinematic earthquake models. Our algorithm is a modification of the tempered Markov chain Monte Carlo (tempered MCMC or TMCMC) method. In our algorithm, we sample a "tempered" a posteriori PDF using many MCMC simulations running in parallel and evolutionary computation in which models which fit the data poorly are preferentially eliminated in favor of models which better predict the data. We present results for both synthetic test problems as well as for the 2007 Mw 7.8 Tocopilla, Chile earthquake, the latter of which is constrained by InSAR, local high
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.
Ojajärvi, Anneli; Partanen, Timo; Ahlbom, Anders; Hakulinen, Timo; Kauppinen, Timo; Weiderpass, Elisabete; Wesseling, Catharina
2007-10-01
The study demonstrates the application of a hierarchical Bayesian meta-analysis of epidemiologic studies that show an association between pancreatic cancer risk and job titles, using a job-exposure matrix to estimate risks for occupational exposure agents. Altogether 261 studies published from 1969 through 1998 on pancreatic cancer and job titles were identified. When proportional studies are excluded, 77 studies were informative for 9 selected occupational agents. These studies included more than 3799 observed pancreatic cancer cases. Hierarchical Bayesian models were used for job titles (lower-level data) and agents (higher-level data), the latter from a Finnish job-exposure matrix. Non-Bayesian random effects models were applied for job titles to check consistency with the Bayesian results. The results suggest that occupational exposures to chlorinated hydrocarbon compounds may increase the risk of pancreatic cancer; the meta-relative risk (MRR) was 2.21 [95% credible interval (CrI) 1.31-3.68]. A suggestive weak excess was found for exposure to insecticides (MRR 1.95, 95% CrI 0.51-7.41). Hierarchical models are applicable in meta-analyses when studies addressing the agent(s) under study are lacking or are very few, but several studies address job titles with potential exposure to these agents. Hierarchical meta-analytic models involving durations and intensities of exposure to occupational agents from a job-exposure matrix should be developed.
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.
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.
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.
Frequentist tests for Bayesian models
NASA Astrophysics Data System (ADS)
Lucy, L. B.
2016-04-01
Analogues of the frequentist chi-square and F tests are proposed for testing goodness-of-fit and consistency for Bayesian models. Simple examples exhibit these tests' detection of inconsistency between consecutive experiments with identical parameters, when the first experiment provides the prior for the second. In a related analysis, a quantitative measure is derived for judging the degree of tension between two different experiments with partially overlapping parameter vectors.
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.
Bayesian population receptive field modelling.
Zeidman, Peter; Silson, Edward Harry; Schwarzkopf, Dietrich Samuel; Baker, Chris Ian; Penny, Will
2017-09-08
We introduce a probabilistic (Bayesian) framework and associated software toolbox for mapping population receptive fields (pRFs) based on fMRI data. This generic approach is intended to work with stimuli of any dimension and is demonstrated and validated in the context of 2D retinotopic mapping. The framework enables the experimenter to specify generative (encoding) models of fMRI timeseries, in which experimental stimuli enter a pRF model of neural activity, which in turns drives a nonlinear model of neurovascular coupling and Blood Oxygenation Level Dependent (BOLD) response. The neuronal and haemodynamic parameters are estimated together on a voxel-by-voxel or region-of-interest basis using a Bayesian estimation algorithm (variational Laplace). This offers several novel contributions to receptive field modelling. The variance/covariance of parameters are estimated, enabling receptive fields to be plotted while properly representing uncertainty about pRF size and location. Variability in the haemodynamic response across the brain is accounted for. Furthermore, the framework introduces formal hypothesis testing to pRF analysis, enabling competing models to be evaluated based on their log model evidence (approximated by the variational free energy), which represents the optimal tradeoff between accuracy and complexity. Using simulations and empirical data, we found that parameters typically used to represent pRF size and neuronal scaling are strongly correlated, which is taken into account by the Bayesian methods we describe when making inferences. We used the framework to compare the evidence for six variants of pRF model using 7 T functional MRI data and we found a circular Difference of Gaussians (DoG) model to be the best explanation for our data overall. We hope this framework will prove useful for mapping stimulus spaces with any number of dimensions onto the anatomy of the brain. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.
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
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.
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)
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)
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.
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
Chowdhury, Rasheda Arman; Lina, Jean Marc; Kobayashi, Eliane; Grova, Christophe
2013-01-01
Localizing the generators of epileptic activity in the brain using Electro-EncephaloGraphy (EEG) or Magneto-EncephaloGraphy (MEG) signals is of particular interest during the pre-surgical investigation of epilepsy. Epileptic discharges can be detectable from background brain activity, provided they are associated with spatially extended generators. Using realistic simulations of epileptic activity, this study evaluates the ability of distributed source localization methods to accurately estimate the location of the generators and their sensitivity to the spatial extent of such generators when using MEG data. Source localization methods based on two types of realistic models have been investigated: (i) brain activity may be modeled using cortical parcels and (ii) brain activity is assumed to be locally smooth within each parcel. A Data Driven Parcellization (DDP) method was used to segment the cortical surface into non-overlapping parcels and diffusion-based spatial priors were used to model local spatial smoothness within parcels. These models were implemented within the Maximum Entropy on the Mean (MEM) and the Hierarchical Bayesian (HB) source localization frameworks. We proposed new methods in this context and compared them with other standard ones using Monte Carlo simulations of realistic MEG data involving sources of several spatial extents and depths. Detection accuracy of each method was quantified using Receiver Operating Characteristic (ROC) analysis and localization error metrics. Our results showed that methods implemented within the MEM framework were sensitive to all spatial extents of the sources ranging from 3 cm(2) to 30 cm(2), whatever were the number and size of the parcels defining the model. To reach a similar level of accuracy within the HB framework, a model using parcels larger than the size of the sources should be considered.
Chowdhury, Rasheda Arman; Lina, Jean Marc; Kobayashi, Eliane; Grova, Christophe
2013-01-01
Localizing the generators of epileptic activity in the brain using Electro-EncephaloGraphy (EEG) or Magneto-EncephaloGraphy (MEG) signals is of particular interest during the pre-surgical investigation of epilepsy. Epileptic discharges can be detectable from background brain activity, provided they are associated with spatially extended generators. Using realistic simulations of epileptic activity, this study evaluates the ability of distributed source localization methods to accurately estimate the location of the generators and their sensitivity to the spatial extent of such generators when using MEG data. Source localization methods based on two types of realistic models have been investigated: (i) brain activity may be modeled using cortical parcels and (ii) brain activity is assumed to be locally smooth within each parcel. A Data Driven Parcellization (DDP) method was used to segment the cortical surface into non-overlapping parcels and diffusion-based spatial priors were used to model local spatial smoothness within parcels. These models were implemented within the Maximum Entropy on the Mean (MEM) and the Hierarchical Bayesian (HB) source localization frameworks. We proposed new methods in this context and compared them with other standard ones using Monte Carlo simulations of realistic MEG data involving sources of several spatial extents and depths. Detection accuracy of each method was quantified using Receiver Operating Characteristic (ROC) analysis and localization error metrics. Our results showed that methods implemented within the MEM framework were sensitive to all spatial extents of the sources ranging from 3 cm2 to 30 cm2, whatever were the number and size of the parcels defining the model. To reach a similar level of accuracy within the HB framework, a model using parcels larger than the size of the sources should be considered. PMID:23418485
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…
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…
Zhao, Xing; Cao, Mingqin; Feng, Hai-Huan; Fan, Heng; Chen, Fei; Feng, Zijian; Li, Xiaosong; Zhou, Xiao-Hua
2014-01-01
It is valuable to study the spatiotemporal pattern of Japanese encephalitis (JE) and its association with the contextual risk factors in southwest China, which is the most endemic area in China. Using data from 2004 to 2009, we applied GISmapping and spatial autocorrelation analysis to analyze reported incidence data of JE in 438 counties in southwest China, finding that JE cases were not randomly distributed, and a Bayesian hierarchical spatiotemporal model identified the east part of southwest China as a high risk area. Meanwhile, the Bayesian hierarchical spatial model in 2006 demonstrated a statistically significant association between JE and the agricultural and climatic variables, including the proportion of rural population, the pig-to-human ratio, the monthly precipitation and the monthly mean minimum and maximum temperatures. Particular emphasis was placed on the time-lagged effect for climatic factors. The regression method and the Spearman correlation analysis both identified a two-month lag for the precipitation, while the regression method found a one-month lag for temperature. The results show that the high risk area in the east part of southwest China may be connected to the agricultural and climatic factors. The routine surveillance and the allocation of health resources should be given more attention in this area. Moreover, the meteorological variables might be considered as possible predictors of JE in southwest China. PMID:24739769
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.
Multivariate Bayesian Models of Extreme Rainfall
NASA Astrophysics Data System (ADS)
Rahill-Marier, B.; Devineni, N.; Lall, U.; Farnham, D.
2013-12-01
Accounting for spatial heterogeneity in extreme rainfall has important ramifications in hydrological design and climate models alike. Traditional methods, including areal reduction factors and kriging, are sensitive to catchment shape assumptions and return periods, and do not explicitly model spatial dependence between between data points. More recent spatially dense rainfall simulators depend on newer data sources such as radar and may struggle to reproduce extremes because of physical assumptions in the model and short historical records. Rain gauges offer the longest historical record, key when considering rainfall extremes and changes over time, and particularly relevant in today's environment of designing for climate change. In this paper we propose a probabilistic approach of accounting for spatial dependence using the lengthy but spatially disparate hourly rainfall network in the greater New York City area. We build a hierarchical Bayesian model allowing extremes at one station to co-vary with concurrent rainfall fields occurring at other stations. Subsequently we pool across the extreme rainfall fields of all stations, and demonstrate that the expected catchment-wide events are significantly lower when considering spatial fields instead of maxima-only fields. We additionally demonstrate the importance of using concurrent spatial fields, rather than annual maxima, in producing covariance matrices that describe true storm dynamics. This approach is also unique in that it considers short duration storms - from one hour to twenty-four hours - rather than the daily values typically derived from rainfall gauges. The same methodology can be extended to include the radar fields available in the past decade. The hierarchical multilevel approach lends itself easily to integration of long-record parameters and short-record parameters at a station or regional level. In addition climate covariates can be introduced to support the relationship of spatial covariance with
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
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.
Hierarchical spatiotemporal matrix models for characterizing invasions.
Hooten, Mevin B; Wikle, Christopher K; Dorazio, Robert M; Royle, J Andrew
2007-06-01
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.
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.
Extended hierarchical Bayesian diffuse optical tomography for removing scalp artifact
Shimokawa, Takeaki; Kosaka, Takashi; Yamashita, Okito; Hiroe, Nobuo; Amita, Takashi; Inoue, Yoshihiro; Sato, Masa-aki
2013-01-01
Functional near-infrared spectroscopy (fNIRS) can non-invasively measure hemodynamic responses in the cerebral cortex with a portable apparatus. However, the observation signal in fNIRS measurements is contaminated by the artifact signal from the hemodynamic response in the scalp. In this paper, we propose a method to separate the signals from the cortex and the scalp by estimating both hemodynamic changes by diffuse optical tomography (DOT). In the inverse problem of DOT, we introduce smooth regularization to the hemodynamic change in the scalp and sparse regularization to that in the cortex based on the nature of the hemodynamic responses. These appropriate regularization models, with the spatial information of optical paths of many measurement channels, allow three-dimensional reconstruction of both hemodynamic changes. We validate our proposed method through two-layer phantom experiments and MRI-based head-model simulations. In both experiments, the proposed method simultaneously estimates the superficial smooth activity in the scalp area and the deep localized activity in the cortical area. PMID:24298404
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.
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.
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.
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.
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.
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…
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…
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…
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.
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.
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. PMID:28082825
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.
Vieilledent, Ghislain; Courbaud, Benoît; Kunstler, Georges; Dhôte, Jean-François; Clark, James S
2010-07-01
Tree species differences in crown size and shape are often highlighted as key characteristics determining light interception strategies and successional dynamics. The phenotypic plasticity of species in response to light and space availability suggests that intraspecific variability can have potential consequences on light interception and community dynamics. Species crown size varies depending on site characteristics and other factors at the individual level which differ from competition for light and space. These factors, such as individual genetic characteristics, past disturbances or environmental micro-site effects, combine with competition-related phenotypic plasticity to determine the individual variability in crown size. Site and individual variability are typically ignored when considering crown size and light interception by trees, and residual variability is relegated to a residual error term, which is then ignored when studying ecological processes. In the present study, we structured and quantified variability at the species, site, and individual levels for three frequently used tree allometric relations using fixed and random effects in a hierarchical Bayesian framework. We focused on two species: Abies alba (silver fir) and Picea abies (Norway spruce) in nine forest stands of the western Alps. We demonstrated that species had different allometric relations from site to site and that individual variability accounted for a large part of the variation in allometric relations. Using a spatially explicit radiation transmission model on real stands, we showed that individual variability in tree allometry had a substantial impact on light resource allocation in the forest. Individual variability in tree allometry modulates species' light-intercepting ability. It generates heterogeneous light conditions under the canopy, with high light micro-habitats that may promote the regeneration of light-demanding species and slow down successional dynamics.
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.
Sparse Bayesian infinite factor models
Bhattacharya, A.; Dunson, D. B.
2011-01-01
We focus on sparse modelling of high-dimensional covariance matrices using Bayesian latent factor models. We propose a multiplicative gamma process shrinkage prior on the factor loadings which allows introduction of infinitely many factors, with the loadings increasingly shrunk towards zero as the column index increases. We use our prior on a parameter-expanded loading matrix to avoid the order dependence typical in factor analysis models and develop an efficient Gibbs sampler that scales well as data dimensionality increases. The gain in efficiency is achieved by the joint conjugacy property of the proposed prior, which allows block updating of the loadings matrix. We propose an adaptive Gibbs sampler for automatically truncating the infinite loading matrix through selection of the number of important factors. Theoretical results are provided on the support of the prior and truncation approximation bounds. A fast algorithm is proposed to produce approximate Bayes estimates. Latent factor regression methods are developed for prediction and variable selection in applications with high-dimensional correlated predictors. Operating characteristics are assessed through simulation studies, and the approach is applied to predict survival times from gene expression data. PMID:23049129
Hierarchical model for distributed seismicity
Tejedor, Alejandro; Gomez, Javier B.; Pacheco, Amalio F.
2010-07-15
A cellular automata model for the interaction between seismic faults in an extended region is presented. Faults are represented by boxes formed by a different number of sites and located in the nodes of a fractal tree. Both the distribution of box sizes and the interaction between them is assumed to be hierarchical. Load particles are randomly added to the system, simulating the action of external tectonic forces. These particles fill the sites of the boxes progressively. When a box is full it topples, some of the particles are redistributed to other boxes and some of them are lost. A box relaxation simulates the occurrence of an earthquake in the region. The particle redistributions mostly occur upwards (to larger faults) and downwards (to smaller faults) in the hierarchy producing new relaxations. A simple and efficient bookkeeping of the information allows the running of systems with more than fifty million faults. This model is consistent with the definition of magnitude, i.e., earthquakes of magnitude m take place in boxes with a number of sites ten times bigger than those boxes responsible for earthquakes with a magnitude m-1 which are placed in the immediate lower level of the hierarchy. The three parameters of the model have a geometrical nature: the height or number of levels of the fractal tree, the coordination of the tree and the ratio of areas between boxes in two consecutive levels. Besides reproducing several seismicity properties and regularities, this model is used to test the performance of some precursory patterns.
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
NASA Astrophysics Data System (ADS)
Rupa, Chandra; Mujumdar, Pradeep
2016-04-01
In urban areas, quantification of extreme precipitation is important in the design of storm water drains and other infrastructure. Intensity Duration Frequency (IDF) relationships are generally used to obtain design return level for a given duration and return period. Due to lack of availability of extreme precipitation data for sufficiently large number of years, estimating the probability of extreme events is difficult. Typically, a single station data is used to obtain the design return levels for various durations and return periods, which are used in the design of urban infrastructure for the entire city. In an urban setting, the spatial variation of precipitation can be high; the precipitation amounts and patterns often vary within short distances of less than 5 km. Therefore it is crucial to study the uncertainties in the spatial variation of return levels for various durations. In this work, the extreme precipitation is modeled spatially using the Bayesian hierarchical analysis and the spatial variation of return levels is studied. The analysis is carried out with Block Maxima approach for defining the extreme precipitation, using Generalized Extreme Value (GEV) distribution for Bangalore city, Karnataka state, India. Daily data for nineteen stations in and around Bangalore city is considered in the study. The analysis is carried out for summer maxima (March - May), monsoon maxima (June - September) and the annual maxima rainfall. In the hierarchical analysis, the statistical model is specified in three layers. The data layer models the block maxima, pooling the extreme precipitation from all the stations. In the process layer, the latent spatial process characterized by geographical and climatological covariates (lat-lon, elevation, mean temperature etc.) which drives the extreme precipitation is modeled and in the prior level, the prior distributions that govern the latent process are modeled. Markov Chain Monte Carlo (MCMC) algorithm (Metropolis Hastings
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
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.
Bayesian Methods for High Dimensional Linear Models
Mallick, Himel; Yi, Nengjun
2013-01-01
In this article, we present a selective overview of some recent developments in Bayesian model and variable selection methods for high dimensional linear models. While most of the reviews in literature are based on conventional methods, we focus on recently developed methods, which have proven to be successful in dealing with high dimensional variable selection. First, we give a brief overview of the traditional model selection methods (viz. Mallow’s Cp, AIC, BIC, DIC), followed by a discussion on some recently developed methods (viz. EBIC, regularization), which have occupied the minds of many statisticians. Then, we review high dimensional Bayesian methods with a particular emphasis on Bayesian regularization methods, which have been used extensively in recent years. We conclude by briefly addressing the asymptotic behaviors of Bayesian variable selection methods for high dimensional linear models under different regularity conditions. PMID:24511433
Chad Babcock; Andrew O. Finley; John B. Bradford; Randy Kolka; Richard Birdsey; Michael G. Ryan
2015-01-01
Many studies and production inventory systems have shown the utility of coupling covariates derived from Light Detection and Ranging (LiDAR) data with forest variables measured on georeferenced inventory plots through regression models. The objective of this study was to propose and assess the use of a Bayesian hierarchical modeling framework that accommodates both...
Bayesian Modeling of a Human MMORPG Player
NASA Astrophysics Data System (ADS)
Synnaeve, Gabriel; Bessière, Pierre
2011-03-01
This paper describes an application of Bayesian programming to the control of an autonomous avatar in a multiplayer role-playing game (the example is based on World of Warcraft). We model a particular task, which consists of choosing what to do and to select which target in a situation where allies and foes are present. We explain the model in Bayesian programming and show how we could learn the conditional probabilities from data gathered during human-played sessions.
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
Bayesian methods for assessing system reliability: models and computation.
Graves, T. L.; Hamada, Michael,
2004-01-01
There are many challenges with assessing the reliability of a system today. These challenges arise because a system may be aging and full system tests may be too expensive or can no longer be performed. Without full system testing, one must integrate (1) all science and engineering knowledge, models and simulations, (2) information and data at various levels of the system, e.g., subsystems and components and (3) information and data from similar systems, subsystems and components. The analyst must work with various data types and how the data are collected, account for measurement bias and uncertainty, deal with model and simulation uncertainty and incorporate expert knowledge. Bayesian hierarchical modeling provides a rigorous way to combine information from multiple sources and different types of information. However, an obstacle to applying Bayesian methods is the need to develop new software to analyze novel statistical models. We discuss a new statistical modeling environment, YADAS, that facilitates the development of Bayesian statistical analyses. It includes classes that help analysts specify new models, as well as classes that support the creation of new analysis algorithms. We illustrate these concepts using several examples.
Bayesian multi-scale modeling for aggregated disease mapping data.
Aregay, Mehreteab; Lawson, Andrew B; Faes, Christel; Kirby, Russell S
2015-09-29
In disease mapping, a scale effect due to an aggregation of data from a finer resolution level to a coarser level is a common phenomenon. This article addresses this issue using a hierarchical Bayesian modeling framework. We propose four different multiscale models. The first two models use a shared random effect that the finer level inherits from the coarser level. The third model assumes two independent convolution models at the finer and coarser levels. The fourth model applies a convolution model at the finer level, but the relative risk at the coarser level is obtained by aggregating the estimates at the finer level. We compare the models using the deviance information criterion (DIC) and Watanabe-Akaike information criterion (WAIC) that are applied to real and simulated data. The results indicate that the models with shared random effects outperform the other models on a range of criteria.
Mano, Shuhei; Suto, Yumiko
2014-11-01
The dicentric chromosome assay (DCA) is one of the most sensitive and reliable methods of inferring doses of radiation exposure in patients. In DCA, one calibration curve is prepared in advance by in vitro irradiation to blood samples from one or sometimes multiple healthy donors in considering possible inter-individual variability. Although the standard method has been demonstrated to be quite accurate for actual dose estimates, it cannot account for random effects, which come from such as the blood donor used to prepare the calibration curve, the radiation-exposed patient, and the examiners. To date, it is unknown how these random effects impact on the standard method of dose estimation. We propose a novel Bayesian hierarchical method that incorporates random effects into the dose estimation. To demonstrate dose estimation by the proposed method and to assess the impact of inter-individual variability in samples from multiple donors on the estimation, peripheral blood samples from 13 occupationally non-exposed, non-smoking, healthy individuals were collected and irradiated with gamma rays. The results clearly showed significant inter-individual variability and the standard method using a sample from a single donor gave anti-conservative confidence interval of the irradiated dose. In contrast, the Bayesian credible interval for irradiated dose calculated by the proposed method using samples from multiple donors properly covered the actual doses. Although the classical confidence interval of calibration curve with accounting inter-individual variability in samples from multiple donors was roughly coincident with the Bayesian credible interval, the proposed method has better reasoning and potential for extensions.
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 Models for Astrophysical Data Using R, JAGS, Python, and Stan
NASA Astrophysics Data System (ADS)
Hilbe, Joseph M.; de Souza, Rafael S.; Ishida, Emille E. O.
2017-05-01
This comprehensive guide to Bayesian methods in astronomy enables hands-on work by supplying complete R, JAGS, Python, and Stan code, to use directly or to adapt. It begins by examining the normal model from both frequentist and Bayesian perspectives and then progresses to a full range of Bayesian generalized linear and mixed or hierarchical models, as well as additional types of models such as ABC and INLA. The book provides code that is largely unavailable elsewhere and includes details on interpreting and evaluating Bayesian models. Initial discussions offer models in synthetic form so that readers can easily adapt them to their own data; later the models are applied to real astronomical data. The consistent focus is on hands-on modeling, analysis of data, and interpretations that address scientific questions. A must-have for astronomers, its concrete approach will also be attractive to researchers in the sciences more generally.
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
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…
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…
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…
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…
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…
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.
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…
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…
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…
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
Bayesian modeling of flexible cognitive control.
Jiang, Jiefeng; Heller, Katherine; Egner, Tobias
2014-10-01
"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. Copyright © 2014 Elsevier Ltd. All rights reserved.
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.
A Bayesian, generalized frailty model for comet assays.
Ghebretinsae, Aklilu Habteab; Faes, Christel; Molenberghs, Geert; De Boeck, Marlies; Geys, Helena
2013-05-01
This paper proposes a flexible modeling approach for so-called comet assay data regularly encountered in preclinical research. While such data consist of non-Gaussian outcomes in a multilevel hierarchical structure, traditional analyses typically completely or partly ignore this hierarchical nature by summarizing measurements within a cluster. Non-Gaussian outcomes are often modeled using exponential family models. This is true not only for binary and count data, but also for, example, time-to-event outcomes. Two important reasons for extending this family are for (1) the possible occurrence of overdispersion, meaning that the variability in the data may not be adequately described by the models, which often exhibit a prescribed mean-variance link, and (2) the accommodation of a hierarchical structure in the data, owing to clustering in the data. The first issue is dealt with through so-called overdispersion models. Clustering is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. In the case of time-to-event data, one encounters, for example, the gamma frailty model (Duchateau and Janssen, 2007 ). While both of these issues may occur simultaneously, models combining both are uncommon. Molenberghs et al. ( 2010 ) proposed a broad class of generalized linear models accommodating overdispersion and clustering through two separate sets of random effects. Here, we use this method to model data from a comet assay with a three-level hierarchical structure. Although a conjugate gamma random effect is used for the overdispersion random effect, both gamma and normal random effects are considered for the hierarchical random effect. Apart from model formulation, we place emphasis on Bayesian estimation. Our proposed method has an upper hand over the traditional analysis in that it (1) uses the appropriate distribution stipulated in the literature; (2) deals
Heterogeneous Factor Analysis Models: A Bayesian Approach.
ERIC Educational Resources Information Center
Ansari, Asim; Jedidi, Kamel; Dube, Laurette
2002-01-01
Developed Markov Chain Monte Carlo procedures to perform Bayesian inference, model checking, and model comparison in heterogeneous factor analysis. Tested the approach with synthetic data and data from a consumption emotion study involving 54 consumers. Results show that traditional psychometric methods cannot fully capture the heterogeneity in…
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
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.
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.
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…
Accelerating Bayesian hierarchical clustering of time series data with a randomised algorithm.
Darkins, Robert; Cooke, Emma J; Ghahramani, Zoubin; Kirk, Paul D W; Wild, David L; Savage, Richard S
2013-01-01
We live in an era of abundant data. This has necessitated the development of new and innovative statistical algorithms to get the most from experimental data. For example, faster algorithms make practical the analysis of larger genomic data sets, allowing us to extend the utility of cutting-edge statistical methods. We present a randomised algorithm that accelerates the clustering of time series data using the Bayesian Hierarchical Clustering (BHC) statistical method. BHC is a general method for clustering any discretely sampled time series data. In this paper we focus on a particular application to microarray gene expression data. We define and analyse the randomised algorithm, before presenting results on both synthetic and real biological data sets. We show that the randomised algorithm leads to substantial gains in speed with minimal loss in clustering quality. The randomised time series BHC algorithm is available as part of the R package BHC, which is available for download from Bioconductor (version 2.10 and above) via http://bioconductor.org/packages/2.10/bioc/html/BHC.html. We have also made available a set of R scripts which can be used to reproduce the analyses carried out in this paper. These are available from the following URL. https://sites.google.com/site/randomisedbhc/.
Bayesian modeling in virtual high throughput screening.
Klon, Anthony E
2009-06-01
Naïve Bayesian classifiers are a relatively recent addition to the arsenal of tools available to computational chemists. These classifiers fall into a class of algorithms referred to broadly as machine learning algorithms. Bayesian classifiers may be used in conjunction with classical modeling techniques to assist in the rapid virtual screening of large compound libraries in a systematic manner with a minimum of human intervention. This approach allows computational scientists to concentrate their efforts on their core strengths of model building. Bayesian classifiers have an added advantage of being able to handle a variety of numerical or binary data such as physicochemical properties or molecular fingerprints, making the addition of new parameters to existing models a relatively straightforward process. As a result, during a drug discovery project these classifiers can better evolve with the needs of the projects from general models in the lead finding stages to increasingly precise models in the lead optimization stages that are of particular interest to a specific medicinal chemistry team. Although other machine learning algorithms abound, Bayesian classifiers have been shown to compare favorably under most working conditions and have been shown to be tolerant of noisy experimental data.
Statistical label fusion with hierarchical performance models
Asman, Andrew J.; Dagley, Alexander S.; Landman, Bennett A.
2014-01-01
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. PMID:24817809
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.
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 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 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.
Hierarchical models and chaotic spin glasses
NASA Astrophysics Data System (ADS)
Berker, A. Nihat; McKay, Susan R.
1984-09-01
Renormalization-group studies in position space have led to the discovery of hierarchical models which are exactly solvable, exhibiting nonclassical critical behavior at finite temperature. Position-space renormalization-group approximations that had been widely and successfully used are in fact alternatively applicable as exact solutions of hierarchical models, this realizability guaranteeing important physical requirements. For example, a hierarchized version of the Sierpiriski gasket is presented, corresponding to a renormalization-group approximation which has quantitatively yielded the multicritical phase diagrams of submonolayers on graphite. Hierarchical models are now being studied directly as a testing ground for new concepts. For example, with the introduction of frustration, chaotic renormalization-group trajectories were obtained for the first time. Thus, strong and weak correlations are randomly intermingled at successive length scales, and a new microscopic picture and mechanism for a spin glass emerges. An upper critical dimension occurs via a boundary crisis mechanism in cluster-hierarchical variants developed to have well-behaved susceptibilities.
Managing clustered data using hierarchical linear modeling.
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 assumption and lead to correct analysis of data, yet it is rarely used in nutrition research. The purpose of this viewpoint is to illustrate the benefits of hierarchical linear modeling within a nutrition research context. Copyright © 2012 Society for Nutrition Education and Behavior. Published by Elsevier Inc. All rights reserved.
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.
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.
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
Wen, Xiaoquan
2015-10-01
We consider the problems of hypothesis testing and model comparison under a flexible Bayesian linear regression model whose formulation is closely connected with the linear mixed effect model and the parametric models for Single Nucleotide Polymorphism (SNP) set analysis in genetic association studies. We derive a class of analytic approximate Bayes factors and illustrate their connections with a variety of frequentist test statistics, including the Wald statistic and the variance component score statistic. Taking advantage of Bayesian model averaging and hierarchical modeling, we demonstrate some distinct advantages and flexibilities in the approaches utilizing the derived Bayes factors in the context of genetic association studies. We demonstrate our proposed methods using real or simulated numerical examples in applications of single SNP association testing, multi-locus fine-mapping and SNP set association testing. © The Author 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
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
An Integrative Bayesian Modeling Approach to Imaging Genetics
Stingo, Francesco C.; Guindani, Michele; Vannucci, Marina; Calhoun, Vince D.
2013-01-01
In this paper we present a Bayesian hierarchical modeling approach for imaging genetics, where the interest lies in linking brain connectivity across multiple individuals to their genetic information. We have available data from a functional magnetic resonance (fMRI) study on schizophrenia. Our goals are to identify brain regions of interest (ROIs) with discriminating activation patterns between schizophrenic patients and healthy controls, and to relate the ROIs’ activations with available genetic information from single nucleotide polymorphisms (SNPs) on the subjects. For this task we develop a hierarchical mixture model that includes several innovative characteristics: it incorporates the selection of ROIs that discriminate the subjects into separate groups; it allows the mixture components to depend on selected covariates; it includes prior models that capture structural dependencies among the ROIs. Applied to the schizophrenia data set, the model leads to the simultaneous selection of a set of discriminatory ROIs and the relevant SNPs, together with the reconstruction of the correlation structure of the selected regions. To the best of our knowledge, our work represents the first attempt at a rigorous modeling strategy for imaging genetics data that incorporates all such features. PMID:24298194
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. © 2016 by the Ecological Society of America.
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.
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…
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…
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
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.
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.
A Bayesian Approach for Summarizing and Modeling Time-Series Exposure Data with Left Censoring.
Houseman, E Andres; Virji, M Abbas
2017-08-01
Direct reading instruments are valuable tools for measuring exposure as they provide real-time measurements for rapid decision making. However, their use is limited to general survey applications in part due to issues related to their performance. Moreover, statistical analysis of real-time data is complicated by autocorrelation among successive measurements, non-stationary time series, and the presence of left-censoring due to limit-of-detection (LOD). A Bayesian framework is proposed that accounts for non-stationary autocorrelation and LOD issues in exposure time-series data in order to model workplace factors that affect exposure and estimate summary statistics for tasks or other covariates of interest. A spline-based approach is used to model non-stationary autocorrelation with relatively few assumptions about autocorrelation structure. Left-censoring is addressed by integrating over the left tail of the distribution. The model is fit using Markov-Chain Monte Carlo within a Bayesian paradigm. The method can flexibly account for hierarchical relationships, random effects and fixed effects of covariates. The method is implemented using the rjags package in R, and is illustrated by applying it to real-time exposure data. Estimates for task means and covariates from the Bayesian model are compared to those from conventional frequentist models including linear regression, mixed-effects, and time-series models with different autocorrelation structures. Simulations studies are also conducted to evaluate method performance. Simulation studies with percent of measurements below the LOD ranging from 0 to 50% showed lowest root mean squared errors for task means and the least biased standard deviations from the Bayesian model compared to the frequentist models across all levels of LOD. In the application, task means from the Bayesian model were similar to means from the frequentist models, while the standard deviations were different. Parameter estimates for covariates
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.
Paddock, Susan M
2014-06-01
Examine how widely used statistical benchmarks of health care provider performance compare with histogram-based statistical benchmarks obtained via hierarchical Bayesian modeling. Publicly available data from 3,240 hospitals during April 2009-March 2010 on two process-of-care measures reported on the Medicare Hospital Compare website. Secondary data analyses of two process-of-care measures comparing statistical benchmark estimates and threshold exceedance determinations under various combinations of hospital performance measure estimates and benchmarking approaches. Statistical benchmarking approaches for determining top 10 percent performance varied with respect to which hospitals exceeded the performance benchmark; such differences were not found at the 50 percent threshold. Benchmarks derived from the histogram of provider performance under hierarchical Bayesian modeling provide a compromise between benchmarks based on direct (raw) estimates, which are overdispersed relative to the true distribution of provider performance and prone to high variance for small providers, and posterior mean provider performance, for which over-shrinkage and under-dispersion relative to the true provider performance distribution is a concern. Given the rewards and penalties associated with characterizing top performance, the ability of statistical benchmarks to summarize key features of the provider performance distribution should be examined. © Published 2014. This article is a U.S. Government work and is in the public domain in the U.S.A.
Paddock, Susan M
2014-01-01
Objective Examine how widely used statistical benchmarks of health care provider performance compare with histogram-based statistical benchmarks obtained via hierarchical Bayesian modeling. Data Sources Publicly available data from 3,240 hospitals during April 2009–March 2010 on two process-of-care measures reported on the Medicare Hospital Compare website. Study Design Secondary data analyses of two process-of-care measures comparing statistical benchmark estimates and threshold exceedance determinations under various combinations of hospital performance measure estimates and benchmarking approaches. Principal Findings Statistical benchmarking approaches for determining top 10 percent performance varied with respect to which hospitals exceeded the performance benchmark; such differences were not found at the 50 percent threshold. Benchmarks derived from the histogram of provider performance under hierarchical Bayesian modeling provide a compromise between benchmarks based on direct (raw) estimates, which are overdispersed relative to the true distribution of provider performance and prone to high variance for small providers, and posterior mean provider performance, for which over-shrinkage and under-dispersion relative to the true provider performance distribution is a concern. Conclusions Given the rewards and penalties associated with characterizing top performance, the ability of statistical benchmarks to summarize key features of the provider performance distribution should be examined. PMID:24461071
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.
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.
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 generative model for learning semantic hierarchies.
Mittelman, Roni; Sun, Min; Kuipers, Benjamin; Savarese, Silvio
2014-01-01
Building fine-grained visual recognition systems that are capable of recognizing tens of thousands of categories, has received much attention in recent years. The well known semantic hierarchical structure of categories and concepts, has been shown to provide a key prior which allows for optimal predictions. The hierarchical organization of various domains and concepts has been subject to extensive research, and led to the development of the WordNet domains hierarchy (Fellbaum, 1998), which was also used to organize the images in the ImageNet (Deng et al., 2009) dataset, in which the category count approaches the human capacity. Still, for the human visual system, the form of the hierarchy must be discovered with minimal use of supervision or innate knowledge. In this work, we propose a new Bayesian generative model for learning such domain hierarchies, based on semantic input. Our model is motivated by the super-subordinate organization of domain labels and concepts that characterizes WordNet, and accounts for several important challenges: maintaining context information when progressing deeper into the hierarchy, learning a coherent semantic concept for each node, and modeling uncertainty in the perception process.
Bayesian Recurrent Neural Network for Language Modeling.
Chien, Jen-Tzung; Ku, Yuan-Chu
2016-02-01
A language model (LM) is calculated as the probability of a word sequence that provides the solution to word prediction for a variety of information systems. A recurrent neural network (RNN) is powerful to learn the large-span dynamics of a word sequence in the continuous space. However, the training of the RNN-LM is an ill-posed problem because of too many parameters from a large dictionary size and a high-dimensional hidden layer. This paper presents a Bayesian approach to regularize the RNN-LM and apply it for continuous speech recognition. We aim to penalize the too complicated RNN-LM by compensating for the uncertainty of the estimated model parameters, which is represented by a Gaussian prior. The objective function in a Bayesian classification network is formed as the regularized cross-entropy error function. The regularized model is constructed not only by calculating the regularized parameters according to the maximum a posteriori criterion but also by estimating the Gaussian hyperparameter by maximizing the marginal likelihood. A rapid approximation to a Hessian matrix is developed to implement the Bayesian RNN-LM (BRNN-LM) by selecting a small set of salient outer-products. The proposed BRNN-LM achieves a sparser model than the RNN-LM. Experiments on different corpora show the robustness of system performance by applying the rapid BRNN-LM under different conditions.
Hierarchical phylogenetic models for analyzing multipartite sequence data.
Suchard, Marc A; Kitchen, Christina M R; Sinsheimer, Janet S; Weiss, Robert E
2003-10-01
Debate exists over how to incorporate information from multipartite sequence data in phylogenetic analyses. Strict combined-data approaches argue for concatenation of all partitions and estimation of one evolutionary history, maximizing the explanatory power of the data. Consensus/independence approaches endorse a two-step procedure where partitions are analyzed independently and then a consensus is determined from the multiple results. Mixtures across the model space of a strict combined-data approach and a priori independent parameters are popular methods to integrate these methods. We propose an alternative middle ground by constructing a Bayesian hierarchical phylogenetic model. Our hierarchical framework enables researchers to pool information across data partitions to improve estimate precision in individual partitions while permitting estimation and testing of tendencies in across-partition quantities. Such across-partition quantities include the distribution from which individual topologies relating the sequences within a partition are drawn. We propose standard hierarchical priors on continuous evolutionary parameters across partitions, while the structure on topologies varies depending on the research problem. We illustrate our model with three examples. We first explore the evolutionary history of the guinea pig (Cavia porcellus) using alignments of 13 mitochondrial genes. The hierarchical model returns substantially more precise continuous parameter estimates than an independent parameter approach without losing the salient features of the data. Second, we analyze the frequency of horizontal gene transfer using 50 prokaryotic genes. We assume an unknown species-level topology and allow individual gene topologies to differ from this with a small estimable probability. Simultaneously inferring the species and individual gene topologies returns a transfer frequency of 17%. We also examine HIV sequences longitudinally sampled from HIV+ patients. We ask
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 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.
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…
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…
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
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.
Hierarchical Boltzmann simulations and model error estimation
NASA Astrophysics Data System (ADS)
Torrilhon, Manuel; Sarna, Neeraj
2017-08-01
A hierarchical simulation approach for Boltzmann's equation should provide a single numerical framework in which a coarse representation can be used to compute gas flows as accurately and efficiently as in computational fluid dynamics, but a subsequent refinement allows to successively improve the result to the complete Boltzmann result. We use Hermite discretization, or moment equations, for the steady linearized Boltzmann equation for a proof-of-concept of such a framework. All representations of the hierarchy are rotationally invariant and the numerical method is formulated on fully unstructured triangular and quadrilateral meshes using a implicit discontinuous Galerkin formulation. We demonstrate the performance of the numerical method on model problems which in particular highlights the relevance of stability of boundary conditions on curved domains. The hierarchical nature of the method allows also to provide model error estimates by comparing subsequent representations. We present various model errors for a flow through a curved channel with obstacles.
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.
Three case studies in the Bayesian analysis of cognitive models.
Lee, Michael D
2008-02-01
Bayesian statistical inference offers a principled and comprehensive approach for relating psychological models to data. This article presents Bayesian analyses of three influential psychological models: multidimensional scaling models of stimulus representation, the generalized context model of category learning, and a signal detection theory model of decision making. In each case, the model is recast as a probabilistic graphical model and is evaluated in relation to a previously considered data set. In each case, it is shown that Bayesian inference is able to provide answers to important theoretical and empirical questions easily and coherently. The generality of the Bayesian approach and its potential for the understanding of models and data in psychology 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.
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
NASA Astrophysics Data System (ADS)
Jeong, S.; Hsu, Y.; Newman, S.; Zhang, J.; Andrews, A. E.; Bianco, L.; Bagley, J.; Cui, X.; Graven, H. D.; Kim, J.; Salameh, P.; LaFranchi, B. W.; Priest, C.; Campos-Pineda, M.; Novakovskaia, E.; Sloop, C.; Michelsen, H. A.; Bambha, R.; Weiss, R. F.; Keeling, R. F.; Fischer, M. L.
2015-12-01
We present an analysis of annual state total methane (CH4) and nitrous oxide (N2O) emissions from California using atmospheric observations from thirteen sites (six sites for N2O) in California during June 2013 - May 2014. A hierarchical Bayesian inversion (HBI) method is used to estimate CH4 and N2O emissions for spatial regions (0.3 degree pixels) by comparing measured mixing ratios with transport model (WRF-STILT) predictions. Using the multi-site measurements across California, the HBI analysis constrains a significant portion of expected emissions for both CH4 and N2O in the Central Valley and southern California. Based on the HBI analysis, we estimate a likely range of the state's annual CH4 emissions is 2.4 - 2.7 Tg CH4/yr (at 68% confidence), which is 1.4 - 1.6 times the total estimated by the California Air Resources Board (CARB). Similarly, we estimate the state's annual N2O emissions to be 77 - 95 Gg N2O/yr (at 68% confidence), which are 1.6 - 2.0 times CARB's state total. These results suggest that the combined total of CH4 and N2O emissions from the HBI analysis would comprise 18 - 21% of state total greenhouse gas (GHG) emissions, higher than 12% estimated in the current state inventory. Additionally, we expand previous evaluations of possible systematic bias in annual emission estimates due to transport model error by comparing measured and predicted carbon monoxide (CO) for four of the sites. These results highlight the need for multiple independent methods to estimate non-CO2 GHG emissions, and offer insight into opportunities for non-CO2 GHG emission mitigation efforts towards achieving California's GHG emission goals.
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.
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. Copyright © 2016 John Wiley & Sons, Ltd.
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
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
A hierarchical nest survival model integrating incomplete temporally varying covariates