Adaptation for Self Regenerative MCMC

SUMMARY The self regenerative MCMC is a tool for constructing a Markov chain with a given stationary distribution by constructing an auxiliary chain with some other stationary distribution. Elements of the auxiliary chain are picked a suitable random number of times so that the resulting chain has the stationary distribution , In this article we provide a generic adaptation scheme for the above algorithm. The adaptive scheme is to use the knowledge of the stationary distribution gathered so far and then to update during the course of the simulation. This method is easy to implement and often leads to considerable improvement. We obtain theoretical results for the adaptive scheme. Our proposed methodology is illustrated with a number of realistic examples in Bayesian computation and its performance is compared with other available MCMC techniques. In one of our applications we develop a non-linear dynamics model for modeling predator-prey relationships in the wild.