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53
On Block Updating in Markov Random Field Models For . . .
 SCANDINAVIAN JOURNAL OF STATISTICS
, 2002
"... Gaussian Markov random field (GMRF) models are commonlyufz to model spatial correlation in disease mapping applications. For Bayesian inference by MCMC, so far mainly singlesiteuinglealgorithms have been considered. However, convergence and mixing properties ofsuD algorithms can be extremely ..."
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Cited by 85 (8 self)
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Gaussian Markov random field (GMRF) models are commonlyufz to model spatial correlation in disease mapping applications. For Bayesian inference by MCMC, so far mainly singlesiteuinglealgorithms have been considered. However, convergence and mixing properties ofsuD algorithms can be extremely poordu to strong dependencies ofparameters in the posteriordistribuQ84K In this paper, we propose variou block sampling algorithms in order to improve the MCMC performance. The methodology is rather general, allows for nonstandardfu6 conditionals, and can be applied in amoduzK fashion in a large nugef of di#erent scenarios. For illu##Kzf0 n we consider three di#erent applications: twoformu8Df0z3 for spatial modelling of a single disease (with andwithou additionaluditionalfL parameters respectively), and one formu## ion for the joint analysis of two diseases. TheresuKK indicate that the largest benefits are obtained ifparameters and the corresponding hyperparameter areuefz#L jointly in one large block. Implementation ofsuQ block algorithms is relatively easy usyf methods for fast sampling ofGaungf3 Markov random fields (Rus 2001). By comparison, Monte Carlo estimates based on singlesiteungles can be rather misleading, even for very long rugfOu resuL6 may have wider relevance for efficient MCMCsimu6z8#f in hierarchical models with Markov random field components.
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.
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 45 (23 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
Approximating Hidden Gaussian Markov Random Fields
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B
, 2003
"... This paper discusses how to construct approximations to a unimodal hidden Gaussian Markov random field on a graph of dimension n when the likelihood consists of mutually independent data. We demonstrate that a class of nonGaussian approximations can be constructed for a wide range of likelihood ..."
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Cited by 26 (4 self)
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This paper discusses how to construct approximations to a unimodal hidden Gaussian Markov random field on a graph of dimension n when the likelihood consists of mutually independent data. We demonstrate that a class of nonGaussian approximations can be constructed for a wide range of likelihood models. They have the appealing properties that exact samples can be drawn from them, the normalisation constant is computable, and the computational complexity is only O(n 2 ) in the spatial case. The nonGaussian approximations are refined versions of a Gaussian approximation. The latter serves well if the likelihood is nearGaussian, but it is not sufficiently accurate when the likelihood is not nearGaussian or if n is large. The accuracy of our approximations can be tuned by intuitive parameters to near any precision. We apply
Markov random field models for highdimensional parameters in simulations of fluid flow in porous media
 Technometrics
, 2002
"... We give an approach for using flow information from a system of wells to characterize hydrologic properties of an aquifer. In particular, we consider experiments where an impulse of tracer fluid is injected along with the water at the input wells and its concentration is recorded over time at the up ..."
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Cited by 24 (8 self)
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We give an approach for using flow information from a system of wells to characterize hydrologic properties of an aquifer. In particular, we consider experiments where an impulse of tracer fluid is injected along with the water at the input wells and its concentration is recorded over time at the uptake wells. We focus on characterizing the spatially varying permeability field which is a key attribute of the aquifer for determining flow paths and rates for a given flow experiment. As is standard for estimation from such flow data, we make use of complicated subsurface flow code which simulates the fluid flow through the aquifer for a particular well configuration and aquifer specification, which includes the permeability field over a grid. This illposed problem requires that some regularity be imposed on the permeability field. Typically this is accomplished by specifying a stationary Gaussian process model for the permeability field. Here we use an intrinsically stationary Markov random field which compares favorably and offers some additional flexibility and computational advantages. Our interest in quantifying uncertainty leads us to take a Bayesian approach, using Markov chain Monte Carlo for exploring the highdimensional posterior distribution. We demonstrate our approach with several examples.
Statistical methods for the prospective detection of infectious disease outbreaks: a review
"... Unusual clusters of disease must be detected rapidly for effective public health interventions to be introduced. Over the past decade there has been a surge in interest in statistical methods for the early detection of infectious disease outbreaks. This growth in interest has given rise to much new ..."
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Cited by 19 (2 self)
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Unusual clusters of disease must be detected rapidly for effective public health interventions to be introduced. Over the past decade there has been a surge in interest in statistical methods for the early detection of infectious disease outbreaks. This growth in interest has given rise to much new methodological work, ranging across the spectrum of statistical methods. This paper presents a comprehensive review of the statistical approaches that have been proposed. Applications to both laboratory and syndromic surveillance data are provided to illustrate the various methods.
Methodologic issues and approaches to spatial epidemiology. Environ Health Perspect 116
, 2008
"... Spatial epidemiology is increasingly being used to assess health risks associated with environmental hazards. Risk patterns tend to have both a temporal and a spatial component; thus, spatial epidemiology must combine methods from epidemiology, statistics, and geographic information science. Recent ..."
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Cited by 12 (1 self)
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Spatial epidemiology is increasingly being used to assess health risks associated with environmental hazards. Risk patterns tend to have both a temporal and a spatial component; thus, spatial epidemiology must combine methods from epidemiology, statistics, and geographic information science. Recent statistical advances in spatial epidemiology include the use of smoothing in risk maps to create an interpretable risk surface, the extension of spatial models to incorporate the time dimension, and the combination of individual and arealevel information. Advances in geographic information systems and the growing availability of modeling packages have led to an improvement in exposure assessment. Techniques drawn from geographic information science are being developed to enable the visualization of uncertainty and ensure more meaningful inferences are made from data. When public health concerns related to the environment arise, it is essential to address such anxieties appropriately and in a timely manner. Tools designed to facilitate the investigation process are being developed, although the availability of complete and clean health data, and appropriate exposure data often remain limiting factors. Key words: disease mapping, environmental epidemiology, geographic information systems (GIS), risk analysis, spatial epidemiology, uncertainty. Environ Health Perspect 116:1105–1110 (2008). doi:10.1289/ehp.10816 available via
Modeling Disease Incidence Data with Spatial and SpatioTemporal Dirichlet Process Mixtures
, 2007
"... Disease incidence or mortality data are typically available as rates or counts for specified regions, collected over time. We propose Bayesian nonparametric spatial modeling approaches to analyze such data. We develop a hierarchical specification using spatial random effects modeled with a Dirichlet ..."
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Cited by 9 (1 self)
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Disease incidence or mortality data are typically available as rates or counts for specified regions, collected over time. We propose Bayesian nonparametric spatial modeling approaches to analyze such data. We develop a hierarchical specification using spatial random effects modeled with a Dirichlet process prior. The Dirichlet process is centered around a multivariate normal distribution. This latter distribution arises from a logGaussian process model that provides a latent incidence rate surface, followed by block averaging to the areal units determined by the regions in the study. With regard to the resulting posterior predictive inference, the modeling approach is shown to be equivalent to an approach based on block averaging of a spatial Dirichlet process to obtain a prior probability model for the finite dimensional distribution of the spatial random effects. We introduce a dynamic formulation for the spatial random effects to extend the model to spatiotemporal settings. Posterior inference is implemented through Gibbs sampling. We illustrate the methodology with simulated data as well as with a data set on lung cancer incidences for all 88 counties in the state of Ohio over an observation period of 21 years.
BAYESIAN MODEL COMPARISON AND MODEL AVERAGING FOR SMALLAREA ESTIMATION 1
, 2008
"... This paper considers smallarea estimation with lung cancer mortality data, and discusses the choice of upperlevel model for the variation over areas. Inference about the random effects for the areas may depend strongly on the choice of this model, but this choice is not a straightforward matter. W ..."
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Cited by 5 (0 self)
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This paper considers smallarea estimation with lung cancer mortality data, and discusses the choice of upperlevel model for the variation over areas. Inference about the random effects for the areas may depend strongly on the choice of this model, but this choice is not a straightforward matter. We give a general methodology for both evaluating the data evidence for different models and averaging over plausible models to give robust area effect distributions. We reanalyze the data of Tsutakawa [Biometrics 41 (1985) 69–79] on lung cancer mortality rates in Missouri cities, and show the differences in conclusions about the city rates from this methodology. 1. The lung cancer data. The data are male lung cancer mortality frequencies and population sizes for the period 1972–1981 in N = 84 Missouri cities (see Table 1). The variables, given in Tsutakawa and reproduced below, are the number r of men aged 45–54 dying from lung cancer in each city over the period 1972–1981 and the city size n. Most of the “cities ” are small, though three are large. The mortality rates are poorly defined in small cities; four cities with populations less than 200 have no deaths at all, so the observed rate is zero. Our aim is to estimate the mortality rates in each city, using the information from other cities in the most appropriate way. 2. Smallarea estimation. Variance component models are widely used in smallarea estimation; the term borrowing strength is commonly used to
Conditionally specified spacetime models for multivariate processes
 Journal of Computational and Graphical Statistics
, 2006
"... This article proposes a class of conditionally specified models for the analysis of multivariate spacetime processes. Such models are useful in situations where there is sparse spatial coverage of one of the processes and much more dense coverage of the other process(es). The dependence structure a ..."
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Cited by 4 (0 self)
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This article proposes a class of conditionally specified models for the analysis of multivariate spacetime processes. Such models are useful in situations where there is sparse spatial coverage of one of the processes and much more dense coverage of the other process(es). The dependence structure across processes and over space, and time is completely specified through a neighborhood structure. These models are applicable to both point and block sources; for example, multiple pollutant monitors (point sources) or several countylevel exposures (block sources). We introduce several computational tricks that are integral for model fitting, give some simple sufficient and necessary conditions for the spacetime covariance matrix to be positive definite, and implement a Gibbs sampler, using Hybrid MC steps, to sample from the posterior distribution of the parameters. Model fit is assessed via the DIC. Predictive accuracy, over both time and space, is assessed both relatively and absolutely via mean squared prediction error and coverage probabilities. As an illustration of these models, we fit them to particulate matter and ozone data collected in the Los Angeles, CA, area in 1995 over a threemonth period. In these data, the spatial coverage of particulate matter was sparse relative to that of ozone.