Abstract
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.
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