Perfect simulation for birth-and-death processes with applications to RJMCMC

Abstract

Perfect simulation methods have been applied successfully to Markovian processes, such as the one-dimensional, continuous, unbounded loss network. The construction of he perfect simulation is granted if the loss network is dominated by a subcritical percolation process, which can be dominated by a branching process.It was proved that a second order construction of the branching process improves the estimate of the critical rate $\lambda_c$ that ensures the construcution. We will build greater order braching processes as approximations of an infinite order process to get the rate $\lambda_c$ at the limit.As an application, we will use these results to build a perfect simulation scheme for the RJMCMC, which is employed to simulate posteriori distributions of variable dimension models.