Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions

被引:182
作者
Brooks, SP
Giudici, P
Roberts, GO
机构
[1] Univ Cambridge, Stat Lab, Cambridge CB3 0WB, England
[2] Univ Pavia, I-27100 Pavia, Italy
[3] Univ Lancaster, Lancaster, England
关键词
autoregressive time series; Bayesian model selection; graphical models; Langevin algorithms; mixture modelling; optimal scaling;
D O I
10.1111/1467-9868.03711
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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.
引用
收藏
页码:3 / 39
页数:37
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