  In MCMC methods, such as the Metropolis-Hastings (MH) algorithm, the Gibbs
sampler, or recent adaptive methods, many different strategies can be proposed,
often 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. Our criterion determines on
the very first iterations the best strategy among the candidates.
Theoretically, we give for the MH algorithm general conditions under which its
successive densities satisfy adequate smoothness and tail properties, so that
this entropy criterion can be estimated consistently using kernel density
estimate and Monte Carlo integration. Simulated examples are provided to
illustrate this convergence criterion.
