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Simulating Normalized Constants: From Importance Sampling to Bridge Sampling to Path Sampling
 Statistical Science, 13, 163–185. COMPARISON OF METHODS FOR COMPUTING BAYES FACTORS 435
, 1998
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Cited by 145 (4 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Auxiliary Variable Methods for Markov Chain Monte Carlo with Applications
 Journal of the American Statistical Association
, 1997
"... Suppose one wishes to sample from the density ß(x) using Markov chain Monte Carlo (MCMC). An auxiliary variable u and its conditional distribution ß(ujx) can be defined, giving the joint distribution ß(x; u) = ß(x)ß(ujx). A MCMC scheme which samples over this joint distribution can lead to substanti ..."
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Cited by 63 (1 self)
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Suppose one wishes to sample from the density ß(x) using Markov chain Monte Carlo (MCMC). An auxiliary variable u and its conditional distribution ß(ujx) can be defined, giving the joint distribution ß(x; u) = ß(x)ß(ujx). A MCMC scheme which samples over this joint distribution can lead to substantial gains in efficiency compared to standard approaches. The revolutionary algorithm of Swendsen and Wang (1987) is one such example. In addition to reviewing the SwendsenWang algorithm and its generalizations, this paper introduces a new auxiliary variable method called partial decoupling. Two applications in Bayesian image analysis are considered. The first is a binary classification problem in which partial decoupling out performs SW and single site Metropolis. The second is a PET reconstruction which uses the gray level prior of Geman and McClure (1987). A generalized SwendsenWang algorithm is developed for this problem, which reduces the computing time to the point that MCMC is a viabl...
Hidden Markov models and disease mapping
 Journal of the American Statistical Association
, 2001
"... We present new methodology to extend Hidden Markov models to the spatial domain, and use this class of models to analyse spatial heterogeneity of count data on a rare phenomenon. This situation occurs commonly in many domains of application, particularly in disease mapping. We assume that the counts ..."
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Cited by 56 (4 self)
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We present new methodology to extend Hidden Markov models to the spatial domain, and use this class of models to analyse spatial heterogeneity of count data on a rare phenomenon. This situation occurs commonly in many domains of application, particularly in disease mapping. We assume that the counts follow a Poisson model at the lowest level of the hierarchy, and introduce a finite mixture model for the Poisson rates at the next level. The novelty lies in the model for allocation to the mixture components, which follows a spatially correlated process, the Potts model, and in treating the number of components of the spatial mixture as unknown. Inference is performed in a Bayesian framework using reversible jump MCMC. The model introduced can be viewed as a Bayesian semiparametric approach to specifying exible spatial distribution in hierarchical models. Performance of the model and comparison with an alternative wellknown Markov random field specification for the Poisson rates are demonstrated on synthetic data sets. We show that our allocation model avoids the problem of oversmoothing in cases where the underlying rates exhibit discontinuities, while giving equally good results in cases of smooth gradientlike or highly autocorrelated rates. The methodology is illustrated on an epidemiological application to data on a rare cancer in France.
ML parameter estimation for Markov random fields, with applications to Bayesian tomography
 IEEE Trans. on Image Processing
, 1998
"... Abstract 1 Markov random fields (MRF) have been widely used to model images in Bayesian frameworks for image reconstruction and restoration. Typically, these MRF models have parameters that allow the prior model to be adjusted for best performance. However, optimal estimation of these parameters (so ..."
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Cited by 48 (18 self)
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Abstract 1 Markov random fields (MRF) have been widely used to model images in Bayesian frameworks for image reconstruction and restoration. Typically, these MRF models have parameters that allow the prior model to be adjusted for best performance. However, optimal estimation of these parameters (sometimes referred to as hyperparameters) is difficult in practice for two reasons: 1) Direct parameter estimation for MRF’s is known to be mathematically and numerically challenging. 2) Parameters can not be directly estimated because the true image crosssection is unavailable. In this paper, we propose a computationally efficient scheme to address both these difficulties for a general class of MRF models, and we derive specific methods of parameter estimation for the MRF model known as a generalized Gaussian MRF (GGMRF). The first section of the paper derives methods of direct estimation of scale and shape parameters for a general continuously valued MRF. For the GGMRF case, we show that the ML estimate of the scale parameter, σ, has a simple closed form solution, and we present an efficient scheme for computing the ML estimate of the shape parameter, p, by an offline numerical computation of the dependence of the partition function on p.
Practical maximum pseudolikelihood for spatial point patterns
 Australian and New Zealand Journal of Statistics
, 2000
"... This paper describes a technique for computing approximate maximum pseudolikelihood estimates of the parameters of a spatial point process. The method is an extension of Berman & Turner’s (1992) device for maximizing the likelihoods of inhomogeneous spatial Poisson processes. For a very wide class o ..."
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Cited by 45 (7 self)
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This paper describes a technique for computing approximate maximum pseudolikelihood estimates of the parameters of a spatial point process. The method is an extension of Berman & Turner’s (1992) device for maximizing the likelihoods of inhomogeneous spatial Poisson processes. For a very wide class of spatial point process models the likelihood is intractable, while the pseudolikelihood is known explicitly, except for the computation of an integral over the sampling region. Approximation of this integral by a finite sum in a special way yields an approximate pseudolikelihood which is formally equivalent to the (weighted) likelihood of a loglinear model with Poisson responses. This can be maximized using standard statistical software for generalized linear or additive models, provided the conditional intensity of the process takes an ‘exponential family ’ form. Using this approach a wide variety of spatial point process models of Gibbs type can be fitted rapidly, incorporating spatial trends, interaction between points, dependence on spatial covariates, and mark information. Key words: areainteraction process; Berman–Turner device; Dirichlet tessellation; edge effects; generalized additive models; generalized linear models; Gibbs point processes; GLIM; hard core process; inhomogeneous point process; marked point processes; Markov spatial point processes; Ord’s process; pairwise interaction; profile pseudolikelihood; spatial clustering; soft core process; spatial trend; SPLUS; Strauss process; Widom–Rowlinson model. 1.
Spatstat: An R package for analyzing spatial point patterns
 Journal of Statistical Software
, 2005
"... spatstat is a package for analyzing spatial point pattern data. Its functionality includes exploratory data analysis, modelfitting, and simulation. It is designed to handle realistic datasets, including inhomogeneous point patterns, spatial sampling regions of arbitrary shape, extra covariate data, ..."
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Cited by 39 (2 self)
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spatstat is a package for analyzing spatial point pattern data. Its functionality includes exploratory data analysis, modelfitting, and simulation. It is designed to handle realistic datasets, including inhomogeneous point patterns, spatial sampling regions of arbitrary shape, extra covariate data, and ‘marks ’ attached to the points of the point pattern. A unique feature of spatstat is its generic algorithm for fitting point process models to point pattern data. The interface to this algorithm is a function ppm that is strongly analogous to lm and glm. This paper is a general description of spatstat and an introduction for new users.
Markov Chain Monte Carlo and Spatial Point Processes
, 1999
"... this paper) reversibility holds, that is f P(x, A)(,x) = f PC, B A for all A, B , whereby r is clearly invariant ..."
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Cited by 15 (5 self)
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this paper) reversibility holds, that is f P(x, A)(,x) = f PC, B A for all A, B , whereby r is clearly invariant
Bayesian smoothing in the estimation of the pair potential function of Gibbs point processes
, 1999
"... This paper introduces a method which can be viewed as the first step towards a truly nonparametric Bayesian estimation of Gibbs processes with pairwise interactions. The pair potential is approximated by a step function having a large number of fixed jump points. The induced high dimension of the pa ..."
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Cited by 14 (4 self)
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This paper introduces a method which can be viewed as the first step towards a truly nonparametric Bayesian estimation of Gibbs processes with pairwise interactions. The pair potential is approximated by a step function having a large number of fixed jump points. The induced high dimension of the parameter space causes two kinds of problems. First, each component of the sufficient statistic is typically a function of a small number of point locations, which causes instability in the estimation. Secondly, the computational complexity increases rapidly with the dimension. To combat the first problem we apply Bayesian smoothing by choosing a Markov chain prior which penalises large differences between nearby values of the pair potential function. This idea originates in Bayesian image analysis; see Besag (1986). As regards the computational complexity, we have found the full posterior analysis to be too demanding with the currently available machinery. Consequently, we have concentrated on the task of locating the posterior mode, which is computationally equivalent to that of ønding the maximum likelihood estimate (MLE). Starting from the Monte Carlo NewtonRaphson algorithm of Penttinen (1984) and the Monte Carlo likelihood approach of Geyer and Thompson (1992), we arrived at an efficient algorithm by modifying the former into an MCMC approximation of the Marquardt algorithm (Marquardt 1963) and then combining the two: The first approximation to the posterior mode is obtained using the Monte Carlo Marquardt algorithm, where the first two differentials of the logposterior are approximated by MCMC as in Penttinen (1984), and the final estimate is calculated using the Monte Carlo likelihood approximation. (The naming conventions applied here were introduced by Geyer 1998). Our appr...
A stochastic geometry model for fMRI data
, 1999
"... Functional magnetic resonance imaging (fMRI) is a principal method for mapping the human brain. fMRI data consist of a sequence of MR scans of the brain acquired during stimulation of specic cortical areas, and the purpose of analysing the data is to detect activated areas, i.e. areas where the i ..."
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Cited by 13 (3 self)
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Functional magnetic resonance imaging (fMRI) is a principal method for mapping the human brain. fMRI data consist of a sequence of MR scans of the brain acquired during stimulation of specic cortical areas, and the purpose of analysing the data is to detect activated areas, i.e. areas where the intensity changes according to the stimulation paradigm. A common analysis procedure is to estimate the activity pattern nonparametricly by smoothing the data spatially. The focus is then on assessing signicance of peaks or clusters in the smoothed activation surface by means of multiple hypothesis testing, rather than assessing the uncertainty of the estimated pattern itself. In this paper we formulate a more structured model for the spatial activation pattern. We achieve this by considering a stochastic geometry model where the activation surface is given by a sum of Gaussian functions, which to some extent can be thought of as individual centres of activation in the brain. The m...
Modelling spatial point patterns in R
 Case Studies in Spatial Point Pattern Modelling. Lecture Notes in Statistics 185, 23–74
, 2006
"... Summary. We describe practical techniques for fitting stochastic models to spatial point pattern data in the statistical package R. The techniques have been implemented in our package spatstat in R. They are demonstrated on two example datasets. 1 ..."
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Cited by 10 (3 self)
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Summary. We describe practical techniques for fitting stochastic models to spatial point pattern data in the statistical package R. The techniques have been implemented in our package spatstat in R. They are demonstrated on two example datasets. 1