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178
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 47 (12 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 42 (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...
Rates of Convergence for Gibbs Sampling for Variance Component Models
 Ann. Stat
, 1991
"... This paper analyzes the Gibbs sampler applied to a standard variance component model, and considers the question of how many iterations are required for convergence. It is proved that for K location parameters, with J observations each, the number of iterations required for convergence (for large K ..."
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Cited by 37 (10 self)
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This paper analyzes the Gibbs sampler applied to a standard variance component model, and considers the question of how many iterations are required for convergence. It is proved that for K location parameters, with J observations each, the number of iterations required for convergence (for large K and J) is a constant times
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 37 (9 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
Conditional prior proposals in dynamic models
 SCANDINAVIAN JOURNAL OF STATISTICS
, 1999
"... Dynamic models extend state space models to nonnormal observations. This paper suggests a specific hybrid MetropolisHastings algorithm as a simple device for Bayesian inference via Markov chain Monte Carlo in dynamic models. Hastings proposals from the (conditional) prior distribution of the unk ..."
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Cited by 33 (3 self)
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Dynamic models extend state space models to nonnormal observations. This paper suggests a specific hybrid MetropolisHastings algorithm as a simple device for Bayesian inference via Markov chain Monte Carlo in dynamic models. Hastings proposals from the (conditional) prior distribution of the unknown, timevarying parameters are used to update the corresponding full conditional distributions. It is shown through simulated examples that the methodology has optimal performance in situations where the prior is relatively strong compared to the likelihood. Typical examples include smoothing priors for categorical data. A specific blocking strategy is proposed to ensure good mixing and convergence properties of the simulated Markov chain. It is also shown that the methodology is easily extended to robust transition models using mixtures of normals. The applicability is illustrated with an analysis of a binomial and a binary time series, known in the literature.
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 31 (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...
Modelling spatially correlated data via mixtures: a Bayesian approach
 Journal of the Royal Statistical Society, Series B
, 2002
"... This paper develops mixture models for spatially indexed data. We confine attention to the case of finite, typically irregular, patterns of points or regions with prescribed spatial relationships, and to problems where it is only the weights in the mixture that vary from one location to another. Our ..."
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Cited by 31 (2 self)
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This paper develops mixture models for spatially indexed data. We confine attention to the case of finite, typically irregular, patterns of points or regions with prescribed spatial relationships, and to problems where it is only the weights in the mixture that vary from one location to another. Our specific focus is on Poisson distributed data, and applications in disease mapping. We work in a Bayesian framework, with the Poisson parameters drawn from gamma priors, and an unknown number of components. We propose two alternative models for spatiallydependent weights, based on transformations of autoregressive gaussian processes: in one (the Logistic normal model), the mixture component labels are exchangeable, in the other (the Grouped continuous model), they are ordered. Reversible jump Markov chain Monte Carlo algorithms for posterior inference are developed. Finally, the performance of both of these formulations is examined on synthetic data and real data on mortality from rare disease.
Bayesian Semiparametric Regression Analysis of Multicategorical TimeSpace Data
 Annals of the Institute of Statistical Mathematics
, 2000
"... this paper, we consider multicategorical timespace data (Y it ; x it ; s i ); i = 1; : : : ; n; t = 1; : : : ; T; where the spatial location or site s i of individual i is given as an additional information. A typical example are monthly register data from the German Employment Office 1 for the ..."
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Cited by 30 (18 self)
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this paper, we consider multicategorical timespace data (Y it ; x it ; s i ); i = 1; : : : ; n; t = 1; : : : ; T; where the spatial location or site s i of individual i is given as an additional information. A typical example are monthly register data from the German Employment Office 1 for the years 19801995, where Y it is the employment status (e.g. unemployed, part time job, full time job, others) of individual i during month t and s i is the district in Germany where i has its domicile. Data from surveys on forest damage are a further example: Damage state Y it of tree i in year t, indicated by the defoliation degree, is measured in ordered categories (none to severe) and s i is the site of the tree on a lattice map. In both examples, covariates can be categorical or continuous, and possibly timevarying
Chain Graphs for Learning
 In Uncertainty in Artificial Intelligence
, 1995
"... Chain graphs combine directed and undirected graphs and their underlying mathematics combines properties of the two. This paper gives a simplified definition of chain graphs based on a hierarchical combination of Bayesian (directed) and Markov (undirected) networks. Examples of a chain graph are mul ..."
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Cited by 27 (1 self)
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Chain graphs combine directed and undirected graphs and their underlying mathematics combines properties of the two. This paper gives a simplified definition of chain graphs based on a hierarchical combination of Bayesian (directed) and Markov (undirected) networks. Examples of a chain graph are multivariate feedforward networks, clustering with conditional interaction between variables, and forms of Bayes classifiers. Chain graphs are then extended using the notation of plates so that samples and data analysis problems can be represented in a graphical model as well. Implications for learning are discussed in the conclusion. 1 Introduction Probabilistic networks are a notational device that allow one to abstract forms of probabilistic reasoning without getting lost in the mathematical detail of the underlying equations. They offer a framework whereby many forms of probabilistic reasoning can be combined and performed on probabilistic models without careful hand programming. Efforts ...
Lang S: Generalized structured additive regression based on Bayesian P splines
 Computational Statistics & Data Analysis
"... Generalized additive models (GAM) for modelling nonlinear effects of continuous covariates are now well established tools for the applied statistician. In this paper we develop Bayesian GAM’s and extensions to generalized structured additive regression based on one or two dimensional Psplines as th ..."
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Cited by 26 (7 self)
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Generalized additive models (GAM) for modelling nonlinear effects of continuous covariates are now well established tools for the applied statistician. In this paper we develop Bayesian GAM’s and extensions to generalized structured additive regression based on one or two dimensional Psplines as the main building block. The approach extends previous work by Lang and Brezger (2003) for Gaussian responses. Inference relies on Markov chain Monte Carlo (MCMC) simulation techniques, and is either based on iteratively weighted least squares (IWLS) proposals or on latent utility representations of (multi)categorical regression models. Our approach covers the most common univariate response distributions, e.g. the Binomial, Poisson or Gamma distribution, as well as multicategorical responses. As we will demonstrate through two applications on the forest health status of trees and a spacetime analysis of health insurance data, the approach allows realistic modelling of complex problems. We consider the enormous flexibility and extendability of our approach as a main advantage of Bayesian inference based on MCMC techniques compared to more traditional approaches. Software for the methodology presented in the paper is provided within the public domain package BayesX. Key words: geoadditive models, IWLS proposals, multicategorical response, structured additive