Improving Convergence of the Hastings–Metropolis Algorithm with an Adaptive Proposal

Didier Chauveau and Pierre Vandekerkhove

Scandinavian Journal of Statistics, 2002, vol. 29, issue 1, 13-29

Abstract: The Hastings–Metropolis algorithm is a general MCMC method for sampling from a density known up to a constant. Geometric convergence of this algorithm has been proved under conditions relative to the instrumental (or proposal) distribution. We present an inhomogeneous Hastings–Metropolis algorithm for which the proposal density approximates the target density, as the number of iterations increases. The proposal density at the nth step is a non‐parametric estimate of the density of the algorithm, and uses an increasing number of i.i.d. copies of the Markov chain. The resulting algorithm converges (in n) geometrically faster than a Hastings–Metropolis algorithm with any fixed proposal distribution. The case of a strictly positive density with compact support is presented first, then an extension to more general densities is given. We conclude by proposing a practical way of implementation for the algorithm, and illustrate it over simulated examples.

Date: 2002
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