An adaptive Metropolis algorithm
Heikki Haario, Eero Saksman, and Johanna Tamminen
Source: Bernoulli Volume 7, Number 2
(2001), 223-242.
Abstract
A proper choice of a proposal distribution for Markov chain Monte Carlo methods, for example 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 (AM) algorithm, 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 Metropolis-Hastings algorithms, and demonstrate that the AM algorithm is easy to use in practical computation.
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Keywords: adaptive Markov chain Monte Carlo; comparison; convergence; ergodicity; Markov chain Monte Carlo; Metropolis-Hastings algorithm
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.bj/1080222083
Mathematical Reviews number (MathSciNet): MR1828504
Zentralblatt MATH identifier: 0989.65004
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