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399
An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants
 Biometrika
, 2006
"... Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method i ..."
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Cited by 86 (3 self)
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Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value. The proposal distribution is constructed so that the normalising constant cancels from the Metropolis–Hastings ratio. The method is illustrated by producing posterior samples for parameters of the Ising model given a particular lattice realisation.
Hierarchical SpatioTemporal Mapping of Disease Rates
 Journal of the American Statistical Association
, 1996
"... Maps of regional morbidity and mortality rates are useful tools in determining spatial patterns of disease. Combined with sociodemographic census information, they also permit assessment of environmental justice, i.e., whether certain subgroups suffer disproportionately from certain diseases or oth ..."
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Cited by 75 (7 self)
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Maps of regional morbidity and mortality rates are useful tools in determining spatial patterns of disease. Combined with sociodemographic census information, they also permit assessment of environmental justice, i.e., whether certain subgroups suffer disproportionately from certain diseases or other adverse effects of harmful environmental exposures. Bayes and empirical Bayes methods have proven useful in smoothing crude maps of disease risk, eliminating the instability of estimates in lowpopulation areas while maintaining geographic resolution. In this paper we extend existing hierarchical spatial models to account for temporal effects and spatiotemporal interactions. Fitting the resulting highlyparametrized models requires careful implementation of Markov chain Monte Carlo (MCMC) methods, as well as novel techniques for model evaluation and selection. We illustrate our approach using a dataset of countyspecific lung cancer rates in the state of Ohio during the period 19681988...
Poisson/gamma random field models for spatial statistics
 BIOMETRIKA
, 1998
"... Doubly stochastic Bayesian hierarchical models are introduced to account for uncertainty and spatial variation in the underlying intensity measure for point process models. Inhomogeneous gamma process random fields and, more generally, Markov random fields with infinitely divisible distributions are ..."
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Cited by 66 (14 self)
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Doubly stochastic Bayesian hierarchical models are introduced to account for uncertainty and spatial variation in the underlying intensity measure for point process models. Inhomogeneous gamma process random fields and, more generally, Markov random fields with infinitely divisible distributions are used to construct positively autocorrelated intensity measures for spatial Poisson point processes; these in turn are used to model the number and location of individual events. A data augmentation scheme and Markov chain Monte Carlo numerical methods are employed to generate samples from Bayesian posterior and predictive distributions. The methods are developed in both continuous and discrete settings, and are applied to a problem in forest ecology.
Bayesian Detection of Clusters and Discontinuities in Disease Maps
 Biometrics
, 2000
"... An interesting epidemiological problem is the analysis of geographical variation in rates of disease incidence or mortality. One goal of such an analysis is to detect clusters of elevated (or lowered) risk in order to identify unknown risk factors regarding the disease. We propose a nonparametric Ba ..."
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Cited by 63 (4 self)
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An interesting epidemiological problem is the analysis of geographical variation in rates of disease incidence or mortality. One goal of such an analysis is to detect clusters of elevated (or lowered) risk in order to identify unknown risk factors regarding the disease. We propose a nonparametric Bayesian approach for the detection of such clusters based on Green's (1995) reversible jump MCMC methodology. The prior model assumes that geographical regions can be combined in clusters with constant relative risk within a cluster. The number of clusters, the location of the clusters and the risk within each cluster is unknown. This specification can be seen as a changepoint problem of variable dimension in irregular, discrete space. We illustrate our method through an analysis of oral cavity cancer mortality rates in Germany and compare the results with those obtained by the commonly used Bayesian disease mapping method of Besag, York and Molli'e (1991). Key words: Cancer atlas; Clusterin...
The Rhythmic Structure
, 1960
"... additive regression for spacetime data: A mixed model approach ..."
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Cited by 57 (1 self)
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additive regression for spacetime data: A mixed model approach
Spatial Poisson Regression for Health and Exposure Data Measured at Disparate Resolutions
 Journal of the American Statistical Association
, 2000
"... This paper presents a spatial regression analysis of the effect of traffic pollution on respiratory disorders in children. The analysis features data measured at disparate, nonnested scales, including spatially varying covariates, latent spatially varying risk factors, and casespecific individual ..."
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Cited by 53 (10 self)
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This paper presents a spatial regression analysis of the effect of traffic pollution on respiratory disorders in children. The analysis features data measured at disparate, nonnested scales, including spatially varying covariates, latent spatially varying risk factors, and casespecific individual attributes
Bayesian Modelling of Inseparable SpaceTime Variation in Disease Risk
, 1998
"... This paper proposes a unified framework for the analysis of incidence or mortality data in space and time. The problem with such analysis is that the number of cases and the corresponding population at risk in any single unit of space \Theta time are too small to produce a reliable estimate of the u ..."
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Cited by 53 (2 self)
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This paper proposes a unified framework for the analysis of incidence or mortality data in space and time. The problem with such analysis is that the number of cases and the corresponding population at risk in any single unit of space \Theta time are too small to produce a reliable estimate of the underlying disease risk without "borrowing strength" from neighbouring cells. The goal here could be described as one of smoothing, in which both spatial and nonspatial considerations may arise, and spatiotemporal interactions may become an important feature. Based on an extended version of the main effects model proposed in KnorrHeld and Besag (1998), four generic types of space \Theta time interactions are introduced. Each type implies a certain degree of prior (in)dependence for interaction parameters, and corresponds to the product of one of the two spatial main effects with one of the two temporal main effects. Data analysis is implemented via Markov chain Monte Carlo methods. The methodology is illustrated by an analysis of Ohio lung cancer data 196888. We compare the fit and the complexity of each model by the DIC criterion, recently proposed in Spiegelhalter et al. (1998).
Modelling Risk from a Disease in Time and Space
 Statistics in Medicine 17
, 1997
"... This paper combines existing models for longitudinal and spatial data in a hierarchical Bayesian framework, with particular emphasis on the role of time and space varying covariate effects. Data analysis is implemented via Markov chain Monte Carlo methods. The methodology is illustrated by a ten ..."
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Cited by 48 (8 self)
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This paper combines existing models for longitudinal and spatial data in a hierarchical Bayesian framework, with particular emphasis on the role of time and space varying covariate effects. Data analysis is implemented via Markov chain Monte Carlo methods. The methodology is illustrated by a tentative reanalysis of Ohio lung cancer data 196888. Two approaches that adjust for unmeasured spatial covariates, particularly tobacco consumption, are described. The first includes random effects in the model to account for unobserved heterogeneity; the second adds a simple urbanization measure as a surrogate for smoking behaviour. The Ohio dataset has been of particular interest because of the suggestion that a nuclear facility in the southwest of the state may have caused increased levels of lung cancer there. However, we contend here that the data are inadequate for a proper investigation of this issue. Email: leo@stat.unimuenchen.de 1 Introduction Data on disease incidence or mor...
Bayesian SpatioTemporal Inference in Functional Magnetic Resonance Imaging
, 2001
"... this article is to present hierarchical Bayesian approaches that allow to simultaneously incorporate temporal and spatial dependencies between pixels directly in the model formulation. For reasons of computational feasibility, models have to be comparatively parsimonious, without oversimplifying. We ..."
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Cited by 47 (5 self)
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this article is to present hierarchical Bayesian approaches that allow to simultaneously incorporate temporal and spatial dependencies between pixels directly in the model formulation. For reasons of computational feasibility, models have to be comparatively parsimonious, without oversimplifying. We introduce parametric and semiparametric spatial and spatiotemporal models that proved appropriate and illustrate their performance by application to fMRI data from a visual stimulation experiment.
Penalized structured additive regression for spacetime data: a Bayesian perspective
 Statistica Sinica
, 2004
"... We propose extensions of penalized spline generalized additive models for analysing spacetime regression data and study them from a Bayesian perspective. Nonlinear effects of continuous covariates and time trends are modelled through Bayesian versions of penalized splines, while correlated spatia ..."
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Cited by 47 (21 self)
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We propose extensions of penalized spline generalized additive models for analysing spacetime regression data and study them from a Bayesian perspective. Nonlinear effects of continuous covariates and time trends are modelled through Bayesian versions of penalized splines, while correlated spatial effects follow a Markov random field prior. This allows to treat all functions and effects within a unified general framework by assigning appropriate priors with different forms and degrees of smoothness. Inference can be performed either with full (FB) or empirical Bayes (EB) posterior analysis. FB inference using MCMC techniques is a slight extension of own previous work. For EB inference, a computationally efficient solution is developed on the basis of a generalized linear mixed model representation. The second approach can be viewed as posterior mode estimation and is closely related to penalized likelihood estimation in a frequentist setting. Variance components, corresponding to smoothing parameters, are then estimated by using marginal likelihood. We carefully compare both inferential procedures in simulation studies and illustrate them through real data applications. The methodology is available in the open domain statistical package BayesX and as an Splus/R function.