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Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions.

Brooks, S. P. and Giudici, P. and Roberts, G. O. (2003) Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65 (1). pp. 3-39. ISSN 1467-9868

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Abstract

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 so-called 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.

Item Type: Article
Journal or Publication Title: Journal of the Royal Statistical Society: Series B (Statistical Methodology)
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Lancaster Environment Centre
ID Code: 10010
Deposited By: Mrs Yaling Zhang
Deposited On: 25 Jun 2008 16:41
Refereed?: Yes
Published?: Published
Last Modified: 06 Sep 2013 17:11
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/10010

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