An Adaptive Metropolis Algorithm

A proper choice of a proposal distribution for MCMC methods, e.g. for the Metropolis-Hastings algorithm, is well known to be a crucial factor for the convergence of the algorithm. In this paper we introduce an adaptive Metropolis Algorithm (AM), where the Gaussian proposal distribution is updated along the process using the full information cumulated so far. Due to the adaptive nature of the process, the AM algorithm is non-Markovian, but we establish here that it has the correct ergodic properties. We also include the results of our numerical tests, which indicate that the AM algorithm competes well with traditional MetropolisHastings algorithms, and demonstrate that AM provides an easy to use algorithm for practical computation. 1991 Mathematics Subject Classification: 65C05, 65U05. Keywords: adaptive MCMC, comparison, convergence, ergodicity, Markov Chain Monte Carlo, Metropolis-Hastings algorithm 1 Introduction It is generally acknowledged that the choice of an effective proposal...