Efficient simulated annealing algorithms for Bayesian parameter estimation
In this paper we present simple conditions related to geometric ergodicity of Markov chains which ensure the convergence in a given sense of the simulated annealing algorithm. We prove that convergence of the algorithm occurs for a proper sequence of temperatures when a local minorization condition of the transition kernels and a drift condition are satisfied. This result may be useful in a Bayesian framework, where it is possible to take advantage of the statistical structure of the problem in order to perform efficient optimization. This is illustrated on several examples.