Bayesian Hierarchical Models (bayesian + hierarchical_models)

Distribution by Scientific Domains


Selected Abstracts


Evaluation of Bayesian models for focused clustering in health data

ENVIRONMETRICS, Issue 8 2007
Bo Ma
Abstract This paper examines the ability of Bayesian hierarchical models to recover evidence of disease risk excess around a fixed location. This location can be a putative source of health hazard, such as an incinerator, mobile phone mast or dump site. While Bayesian models are convenient to use for modeling, it is useful to consider how well these models perform in the true risk scenarios. In what follows, we evaluate the ability of these models to recover the true risk under simulation. It is surprising that the resulting posterior parameters estimates are heavily biased. Using the credible intervals for distance decline parameter to assess ,coverage or power' of detecting distance effect, the ,power' decreases with increasing correlation in the background population effect. The inclusion of correlated heterogeneity in models does affect the ability of the models to detect the stronger distance decline scenarios. The uncorrelated heterogeneity seems little affect this ability however. Copyright 2007 John Wiley & Sons, Ltd. [source]


Analyzing weather effects on airborne particulate matter with HGLM

ENVIRONMETRICS, Issue 7 2003
Yoon Dong Lee
Abstract Particulate matter is one of the six constituent air pollutants regulated by the United States Environmental Protection Agency. In analyzing such data, Bayesian hierarchical models have often been used. In this article we propose the use of hierarchical generalized linear models, which use likelihood inference and have well developed model-checking procedures. Comparisons are made between analyses from hierarchical generalized linear models and Daniels et al.'s (2001) Bayesian models. Model-checking procedure indicates that Daniels et al.'s model can be improved by use of the log-transformation of wind speed and precipitation covariates. Copyright 2003 John Wiley & Sons, Ltd. [source]


Bayesian hierarchical models in ecological studies of health,environment effects

ENVIRONMETRICS, Issue 2 2003
Sylvia Richardson
Abstract We describe Bayesian hierarchical models and illustrate their use in epidemiological studies of the effects of environment on health. The framework of Bayesian hierarchical models refers to a generic model building strategy in which unobserved quantities (e.g. statistical parameters, missing or mismeasured data, random effects, etc.) are organized into a small number of discrete levels with logically distinct and scientifically interpretable functions, and probabilistic relationships between them that capture inherent features of the data. It has proved to be successful for analysing many types of complex epidemiological and biomedical data. The general applicability of Bayesian hierarchical models has been enhanced by advances in computational algorithms, notably those belonging to the family of stochastic algorithms based on Markov chain Monte Carlo techniques. In this article, we review different types of design commonly used in studies of environment and health, give details on how to incorporate the hierarchical structure into the different components of the model (baseline risk, exposure) and discuss the model specification at the different levels of the hierarchy with particular attention to the problem of aggregation (ecological) bias. Copyright 2003 John Wiley & Sons, Ltd. [source]


Assessing sources of variability in measurement of ambient particulate matter

ENVIRONMETRICS, Issue 6 2001
Michael J. Daniels
Abstract Particulate matter (PM), a component of ambient air pollution, has been the subject of United States Environmental Protection Agency regulation in part due to many epidemiological studies examining its connection with health. Better understanding the PM measurement process and its dependence on location, time, and other factors is important for both modifying regulations and better understanding its effects on health. In light of this, in this paper, we will explore sources of variability in measuring PM including spatial, temporal and meteorological effects. In addition, we will assess the degree to which there is heterogeneity in the variability of the micro-scale processes, which may suggest important unmeasured processes, and the degree to which there is unexplained heterogeneity in space and time. We use Bayesian hierarchical models and restrict attention to the greater Pittsburgh (USA) area in 1996. The analyses indicated no spatial dependence after accounting for other sources of variability and also indicated heterogeneity in the variability of the micro-scale processes over time and space. Weather and temporal effects were very important and there was substantial heterogeneity in these effects across sites. Copyright 2001 John Wiley & Sons, Ltd. [source]


Hierarchical Spatial Modeling of Additive and Dominance Genetic Variance for Large Spatial Trial Datasets

BIOMETRICS, Issue 2 2009
Andrew O. Finley
Summary This article expands upon recent interest in Bayesian hierarchical models in quantitative genetics by developing spatial process models for inference on additive and dominance genetic variance within the context of large spatially referenced trial datasets. Direct application of such models to large spatial datasets are, however, computationally infeasible because of cubic-order matrix algorithms involved in estimation. The situation is even worse in Markov chain Monte Carlo (MCMC) contexts where such computations are performed for several iterations. Here, we discuss approaches that help obviate these hurdles without sacrificing the richness in modeling. For genetic effects, we demonstrate how an initial spectral decomposition of the relationship matrices negate the expensive matrix inversions required in previously proposed MCMC methods. For spatial effects, we outline two approaches for circumventing the prohibitively expensive matrix decompositions: the first leverages analytical results from Ornstein,Uhlenbeck processes that yield computationally efficient tridiagonal structures, whereas the second derives a modified predictive process model from the original model by projecting its realizations to a lower-dimensional subspace, thereby reducing the computational burden. We illustrate the proposed methods using a synthetic dataset with additive, dominance, genetic effects and anisotropic spatial residuals, and a large dataset from a Scots pine (Pinus sylvestris L.) progeny study conducted in northern Sweden. Our approaches enable us to provide a comprehensive analysis of this large trial, which amply demonstrates that, in addition to violating basic assumptions of the linear model, ignoring spatial effects can result in downwardly biased measures of heritability. [source]