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109
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
 Biometrika
, 1995
"... Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determi ..."
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Cited by 1330 (24 self)
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Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determination, where the dimensionality of the parameter vector is typically not xed. This article proposes a new framework for the construction of reversible Markov chain samplers that jump between parameter subspaces of di ering dimensionality, which is exible and entirely constructive. It should therefore have wide applicability in model determination problems. The methodology is illustrated with applications to multiple changepoint analysis in one and two dimensions, and toaBayesian comparison of binomial experiments.
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 203 (4 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.
Non and SemiParametric Estimation of Interaction in Inhomogeneous Point Patterns
, 2000
"... We develop methods for analysing the `interaction' or dependence between points in a spatial point pattern, when the pattern is spatially inhomogeneous. Completely nonparametric study of interactions is possible using an analogue of the Kfunction. Alternatively one may assume a semiparametr ..."
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Cited by 96 (19 self)
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We develop methods for analysing the `interaction' or dependence between points in a spatial point pattern, when the pattern is spatially inhomogeneous. Completely nonparametric study of interactions is possible using an analogue of the Kfunction. Alternatively one may assume a semiparametric model in which a (parametrically specified) homogeneous Markov point process is subjected to (nonparametric) inhomogeneous independent thinning. The effectiveness of these approaches is tested on datasets representing the positions of trees in forests.
Transdimensional Markov chain Monte Carlo
 in Highly Structured Stochastic Systems
, 2003
"... In the context of samplebased computation of Bayesian posterior distributions in complex stochastic systems, this chapter discusses some of the uses for a Markov chain with a prescribed invariant distribution whose support is a union of euclidean spaces of differing dimensions. This leads into a re ..."
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Cited by 91 (0 self)
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In the context of samplebased computation of Bayesian posterior distributions in complex stochastic systems, this chapter discusses some of the uses for a Markov chain with a prescribed invariant distribution whose support is a union of euclidean spaces of differing dimensions. This leads into a reformulation of the reversible jump MCMC framework for constructing such ‘transdimensional ’ Markov chains. This framework is compared to alternative approaches for the same task, including methods that involve separate sampling within different fixeddimension models. We consider some of the difficulties researchers have encountered with obtaining adequate performance with some of these methods, attributing some of these to misunderstandings, and offer tentative recommendations about algorithm choice for various classes of problem. The chapter concludes with a look towards desirable future developments.
Characterisation results and Markov chain Monte Carlo algorithms including exact simulation for some spatial point processes
, 1996
"... The areainteraction process and the continuum randomcluster model are characterised in terms of certain functional forms of their respective conditional intensities. In certain cases, these two point process models can be derived from a bivariate point process model which in many respects is simpl ..."
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Cited by 78 (6 self)
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The areainteraction process and the continuum randomcluster model are characterised in terms of certain functional forms of their respective conditional intensities. In certain cases, these two point process models can be derived from a bivariate point process model which in many respects is simpler to analyse and simulate. Using this correspondence we devise a twocomponent Gibbs sampler, which can be used for fast and exact simulation by extending the recent ideas of Propp and Wilson. We further introduce a SwendsenWang type algorithm. The relevance of the results within spatial statistics as well as statistical physics is discussed.
Efficient construction of reversible jump markov chain monte carlo proposal distributions
 Journal of the Royal Statistical Society: Series B (Statistical Methodology
"... Summary. The major implementational problem for reversible jump Markov chain Monte Carlo methods is that there is commonly no natural way to choose jump proposals since there is no Euclidean structure in the parameter space to guide our choice. We consider mechanisms for guiding the choice of propos ..."
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Cited by 63 (2 self)
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Summary. The major implementational problem for reversible jump Markov chain Monte Carlo methods is that there is commonly no natural way to choose jump proposals since there is no Euclidean structure in the parameter space to guide our choice. We consider mechanisms for guiding the choice of proposal. The first group of methods is based on an analysis of acceptance probabilities for jumps. Essentially, these methods involve a Taylor series expansion of the acceptance probability around certain canonical jumps and turn out to have close connections to Langevin algorithms.The second group of methods generalizes the reversible jump algorithm by using the socalled saturated space approach. These allow the chain to retain some degree of memory so that, when proposing to move from a smaller to a larger model, information is borrowed from the last time that the reverse move was performed. The main motivation for this paper is that, in complex problems, the probability that the Markov chain moves between such spaces may be prohibitively small, as the probability mass can be very thinly spread across the space. Therefore, finding reasonable jump proposals becomes extremely important. We illustrate the procedure by using several examples of reversible jump Markov chain Monte Carlo applications including the analysis of autoregressive time series, graphical Gaussian modelling and mixture modelling.
Residual analysis for spatial point processes (with discussion
 Journal of the Royal Statistical Society (series B
, 2005
"... [Read before The Royal Statistical Society at a meeting organized by the Research Section on ..."
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Cited by 48 (8 self)
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[Read before The Royal Statistical Society at a meeting organized by the Research Section on
Generalised Shot noise Cox processes
 ADVANCES IN APPLIED PROBABILITY 35
, 2003
"... We introduce a new class of Cox cluster processes called generalised shotnoise Cox processes (GSNCPs), which extends the definition of shot noise Cox processes (SNCPs) in two directions: the point process which drives the shot noise is not necessarily Poisson, and the kernel of the shot noise can b ..."
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Cited by 39 (8 self)
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We introduce a new class of Cox cluster processes called generalised shotnoise Cox processes (GSNCPs), which extends the definition of shot noise Cox processes (SNCPs) in two directions: the point process which drives the shot noise is not necessarily Poisson, and the kernel of the shot noise can be random. Thereby a very large class of models for aggregated or clustered point patterns is obtained. Due to the structure of GSNCPs, a number of useful results can be established. We focus first on deriving summary statistics for GSNCPs and next on how to make simulation for GSNCPs. Particularly, results for first and second order moment measures, reduced Palm distributions, the Jfunction, simulation with or without edge effects, and conditional simulation of the intensity function driving a GSNCP are given. Our results are exemplified for special important cases of GSNCPs, and we discuss the relation to corresponding results for SNCPs.
Transdimensional Markov Chains: A Decade of Progress and Future Perspectives
, 2005
"... The last 10 years have witnessed the development of sampling frameworks that permit the construction of Markov chains that simultaneously traverse both parameter and model space. Substantial methodological progress has been made during this period. In this article we present a survey of the current ..."
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Cited by 31 (3 self)
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The last 10 years have witnessed the development of sampling frameworks that permit the construction of Markov chains that simultaneously traverse both parameter and model space. Substantial methodological progress has been made during this period. In this article we present a survey of the current state of the art and evaluate some of the most recent advances in this field. We also discuss future research perspectives in the context of the drive to develop sampling mechanisms with high degrees of both efficiency and automation.
A tutorial on Reversible Jump MCMC with a view toward applications in QTLmapping
 ON QTL MAPPING. INTERNATIONAL STATISTICAL REVIEW
, 2006
"... A tutorial derivation of the reversible jump Markov chain Monte Carlo (MCMC) algorithm is given. Various examples illustrate how reversible jump MCMC is a general framework for MetropolisHastings algorithms where the proposal and the target distribution may have densities on spaces of varying dimen ..."
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Cited by 31 (2 self)
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A tutorial derivation of the reversible jump Markov chain Monte Carlo (MCMC) algorithm is given. Various examples illustrate how reversible jump MCMC is a general framework for MetropolisHastings algorithms where the proposal and the target distribution may have densities on spaces of varying dimension. It is nally discussed how reversible jump MCMC can be applied in genetics to compute the posterior distribution of the number, locations, eects, and genotypes of putative quantitative trait loci.