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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 827 (19 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.
On Bayesian analysis of mixtures with an unknown number of components
 INSTITUTE OF INTERNATIONAL ECONOMICS PROJECT ON INTERNATIONAL COMPETITION POLICY," COM/DAFFE/CLP/TD(94)42
, 1997
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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 56 (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.
A Metropolis Sampler for Polygonal Image Reconstruction
, 1995
"... We show how a stochastic model of polygonal objects can provide a Bayesian framework for the interpretation of colouring data in the plane. We describe a particular model and give a Markov Chain Monte Carlo (MCMC) algorithm for simulating the posterior distribution of the polygonal pattern. Two impo ..."
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Cited by 16 (1 self)
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We show how a stochastic model of polygonal objects can provide a Bayesian framework for the interpretation of colouring data in the plane. We describe a particular model and give a Markov Chain Monte Carlo (MCMC) algorithm for simulating the posterior distribution of the polygonal pattern. Two important observations arise from our implementation of the algorithm. First, it is computationally feasible to use MCMC to simulate the posterior distribution of a polygonal process for moderately large problems (ie, 10000 data points, with polygonal patterns involving around 120 edges). Our implementation, which we would describe as careful, but unsophisticated, produces satisfactory approximations to the mode of the posterior in about 5 minutes on a SUN Sparc 2. Independent samples from the posterior take a few seconds to generate. The second observation is that the Arak process, a particular type of polygonal process, makes a wonderful debugging tool for testing shape simulation software. Th...
Markov chain Monte Carlo in image analysis
 Complex Stochastic Systems, chapter 1
, 1995
"... this article is to discuss general reasons for this prominence of MCMC, to give an overview of a variety of image models and the use made of MCMC methods in dealing with them, to describe two applications in more detail, To appear as a chapter in the book Practical Markov chain Monte Carlo, edited b ..."
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Cited by 8 (0 self)
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this article is to discuss general reasons for this prominence of MCMC, to give an overview of a variety of image models and the use made of MCMC methods in dealing with them, to describe two applications in more detail, To appear as a chapter in the book Practical Markov chain Monte Carlo, edited by W. Gilks, S. Richardson and D. Spiegelhalter, published by Chapman and Hall.
Comparison of BirthandDeath and MetropolisHastings Markov chain Monte Carlo for the Strauss process
, 1994
"... The MetropolisHastings sampler (MH) is a discrete time Markov chain with MetropolisHastings dynamics. The measure of interest occurs as the stationary measure of the chain. We show that a sampler with MH dynamics may be used when the dimension of the random variable is itself variable, as is the c ..."
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Cited by 8 (2 self)
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The MetropolisHastings sampler (MH) is a discrete time Markov chain with MetropolisHastings dynamics. The measure of interest occurs as the stationary measure of the chain. We show that a sampler with MH dynamics may be used when the dimension of the random variable is itself variable, as is the case in a spatial point process. The Birth and Death (BD) sampler is a continuous time spatial birth and death process used to sample spatial point processes in the past. We check that the two processes we have designed have the same equilibrium measure. In order to explore the relative strengths of the derived sampling algorithms, we consider the efficiency of MH and BD as samplers for the Strauss process. We give a new proof for the existence of a stationary measure in the continuous time case, in order to advertise a general tool (due to Kaspi and Mandelbaum) which may be useful in extending continuous time stochastic process to a wider range of sampling applications. The method emphasises...
Bridge Estimation of the Probability Density At a Point
 Statistica Sinica
, 2000
"... Bridge estimation, as described by Meng and Wong in 1996, is used to estimate the value taken by a probability density at a point in the state space. When the normalisation of the prior density is known, this value may be used to estimate a Bayes factor. It is shown that the multiblock MetropolisH ..."
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Cited by 7 (1 self)
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Bridge estimation, as described by Meng and Wong in 1996, is used to estimate the value taken by a probability density at a point in the state space. When the normalisation of the prior density is known, this value may be used to estimate a Bayes factor. It is shown that the multiblock MetropolisHastings estimators of Chib and Jeliazkov (2001) are bridge estimators. This identification leads to more efficient estimators for the quantity of interest.
Chapter 6 Directions for Future Work
, 41
"... the range 3580 GHz. Most pattern theoretic algorithms to date have attempted "passive vision" in the sense that they interpret a given set of data but are not allowed any say in how the data are collected. We intend to extend our framework to formulate "active 45 vision" algorithms [92] which not o ..."
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the range 3580 GHz. Most pattern theoretic algorithms to date have attempted "passive vision" in the sense that they interpret a given set of data but are not allowed any say in how the data are collected. We intend to extend our framework to formulate "active 45 vision" algorithms [92] which not only interpret available data but make choices on how new data should be gathered to best facilitate inference. In addition to the pointing mechanism, many FLIR sensors provide a variety of magnifications, allowing the choice between highresolution, narrow field of view images and images with a wider field of view but lower resolution. The algorithm must decide where to point the sensor and what magnification to use. These decisions must be driven by the current state of the inference. For instance, if the algorithm is attemping to recognize a several objects which cannot all fit in the sensor's field of field, with resolution sufficient to perform recognition, the algorithm must have a str
A Bayesian analysis of the multiple changepoint problem for a Poisson process
"... this paper, when it exists. Presented at the 9th International Workshop on Statistical Modelling, Exeter, July 1994. 1 time (days) ..."
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this paper, when it exists. Presented at the 9th International Workshop on Statistical Modelling, Exeter, July 1994. 1 time (days)