Stochastic adaptive selection of weights in the simulated tempering algorithm

Simulated Tempering is a new MCMC scheme that has been recently introduced to speed up the convergence of slow Markov chains. The implementation of the procedure depends on the choice of a set of parameters, the weights, which affect the efficiency of the sampling algorithm. In this paper we prove the a.s. convergence of a stochastic algorithm driven by a non-homogeneous Markov chain which select the weights adaptively. The problem of estimating the normalizing constants of a family of unnormalized densities k = I, ... , M is also discussed and an example of application is reported.