On the posterior distribution of the number of components
in a finite mixture
by Agostino Nobile
The posterior distribution of the number of components k in a finite
mixture satisfies a set of inequality constraints.
The result holds irrespective of the parametric form of the mixture
components
and under
assumptions on the prior distribution
weaker than those routinely made in the literature on Bayesian
analysis of finite mixtures.
The inequality constraints can be used to perform an "internal" consistency
check of MCMC estimates of the posterior distribution of k
and to provide improved estimates which are required
to satisfy the constraints.
Bounds on the posterior probability of k components are derived
using the constraints.
Implications on prior distribution specification
and on the adequacy of the posterior distribution of k as a tool for
selecting an adequate number of components in the mixture are also
explored.
Keywords:
Bayesian analysis, Constrained estimation, Finite mixture distribution,
Markov Chain Monte Carlo, Prior distribution.
Click here for a pdf file with the paper.
Some Fortran and S-PLUS programs used to perform the computations
in Section 4 are available here (tar file).