Selection of a Metropolis-Hastings simulation strategy via an entropy convergence criterion
Résumé
Various convergence properties of the Metropolis-Hastings (MH) algorithm have been proved under conditions relative to the instrumental (proposal) distribution. To implement this algorithm, many different choices for the instrumental distribution can be made, associated in practice to unknown rates of convergence. In this paper we propose a simulation-based methodology to compare these rates of convergence, grounded on an entropy criterion computed from parallel (i.i.d.) simulated Markov chains coming from each candidate strategy. Theoretically, we give general conditions under which the successive densities of the MH algorithm satisfy adequate smoothness and tail properties, so that this entropy criterion can be estimated consistently using kernel density estimate and Monte Carlo integration. Examples are provided to illustrate this convergence criterion.