  In this paper we present an extension of population-based Markov chain Monte
Carlo (MCMC) to the trans-dimensional case. One of the main challenges in
MCMC-based inference is that of simulating from high and trans-dimensional
target measures. In such cases, MCMC methods may not adequately traverse the
support of the target; the simulation results will be unreliable. We develop
population methods to deal with such problems, and give a result proving the
uniform ergodicity of these population algorithms, under mild assumptions. This
result is used to demonstrate the superiority, in terms of convergence rate, of
a population transition kernel over a reversible jump sampler for a Bayesian
variable selection problem. We also give an example of a population algorithm
for a Bayesian multivariate mixture model with an unknown number of components.
This is applied to gene expression data of 1000 data points in six dimensions
and it is demonstrated that our algorithm out performs some competing Markov
chain samplers.
