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The Collapsed Gibbs Sampler in Bayesian Computations with Applications to a Gene Regulation Problem
Jun S. Liu
Journal of the American Statistical Association
Vol. 89, No. 427 (Sep., 1994), pp. 958-966
Stable URL: http://www.jstor.org/stable/2290921
Page Count: 9
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This article describes a method of "grouping" and "collapsing" in using the Gibbs sampler and proves from an operator theory viewpoint that the method is in general beneficial. The norms of the forward operators associated with the corresponding nonreversible Markov chains are used to discriminate among different simulation schemes. When applied to Bayesian missing data problems, the idea of collapsing suggests skipping the steps of sampling parameter(s) values in standard data augmentation. By doing this, we obtain a predictive update version of the Gibbs sampler. A procedure of calculating the posterior odds ratio via the collapsed Gibbs sampler when incomplete observations are involved is presented. As an illustration of possible applications, three examples, along with a Bayesian treatment for identifying common protein binding sites in unaligned DNA sequences, are provided.
Journal of the American Statistical Association © 1994 American Statistical Association