Parallel Adaptive Markov chain Monte Carlo with applications

Adaptive Markov chain Monte Carlo methods have been applied successfully to many Bayesian statistical problems. These algorithms are specifically designed to automatically adjust the proposal parameters to match the shape of the posterior distribution during the simulation process. In this paper we first introduce a new adaptive Markov chain Monte Carlo algorithm where the posterior distribution is approximated by a mixture of multivariate t-distributions whose parameters are updated at each iteration. Then we extend the proposed sampler by allowing multiple interacting chains to run in parallel. We compare the prosed algorithms in a simulation experiment showing the superiority of the interacting scheme.