On the influence of the proposal distributions on a reversible jump MCMC algorithm applied to the detection of multiple change-points

In this paper we address some issues arising in the implementation of Markov chain Monte Carlo methods; in particular we analyse whether the choice of transition kernels depending on a specific problem speeds up the convergence of a Metropolis-Hastings-type algorithm. This approach is applied to the retrospective detection of multiple structural changes in the physical process generating earthquakes. As the number of changes is unknown, the adopted hierarchical Bayesian model has variable-dimension parameters. The sensitivity of the method and issues related to the estimation of both the parameters and the posterior model distributions are also dealt with.