Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
Reversible jump Markov chain Monte Carlo computation and
Bayesian model determination, by Peter J. Green.
Biometrika, 82, 711-732 (1995).
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 article 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.
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