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Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions

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  • S. P. Brooks
  • P. Giudici
  • G. O. Roberts

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. Copyright 2003 Royal Statistical Society.

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Bibliographic Info

Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

Volume (Year): 65 (2003)
Issue (Month): 1 ()
Pages: 3-39

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Handle: RePEc:bla:jorssb:v:65:y:2003:i:1:p:3-39

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Cited by:
  1. Griffin, J.E. & Steel, M.F.J., 2010. "Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2594-2608, November.
  2. McVinish, R. & Mengersen, K., 2008. "Semiparametric Bayesian circular statistics," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4722-4730, June.
  3. Liqun Wang & James Fu, 2007. "A practical sampling approach for a Bayesian mixture model with unknown number of components," Statistical Papers, Springer, vol. 48(4), pages 631-653, October.
  4. Streftaris, George & Worton, Bruce J., 2008. "Efficient and accurate approximate Bayesian inference with an application to insurance data," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2604-2622, January.
  5. Helen Armstrong & Christopher K. Carter & Kevin K. F. Wong & Robert Kohn, 2007. "Bayesian Covariance Matrix Estimation using a Mixture of Decomposable Graphical Models," Discussion Papers 2007-13, School of Economics, The University of New South Wales.
  6. Tsung-I Lin & Hsiu Ho & Pao Shen, 2009. "Computationally efficient learning of multivariate t mixture models with missing information," Computational Statistics, Springer, vol. 24(3), pages 375-392, August.

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