Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. (English) Zbl 0861.62023

Green, Peter J.

Biometrika 82, No. 4, 711-732 (1995).

Summary: 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 fixed 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 fixed.
This paper proposes a new framework for the construction of reversible Markov chain samplers that jump between parameter subspaces of differing dimensionality, which is flexible and entirely constructive. It should therefore have wide applicability in model determination problems. The methodology is illustrated with applications to multiple change point analysis in one and two dimensions, and to a Bayesian comparison of binomial experiments.

MSC:

62F15	Bayesian inference
62M99	Inference from stochastic processes
62B15	Theory of statistical experiments

Keywords:

Markov chain Monte Carlo methods; image segmentation; jump diffusion; multiple binomial experiments; multiple shrinkage; step function; Voronoi tesselation; reversible Markov chain samplers; model determination; multiple change point analysis; Bayesian comparison of binomial experiments