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April 2001 An adaptive Metropolis algorithm
Heikki Haario, Eero Saksman, Johanna Tamminen
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Bernoulli 7(2): 223-242 (April 2001).


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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Heikki Haario. Eero Saksman. Johanna Tamminen. "An adaptive Metropolis algorithm." Bernoulli 7 (2) 223 - 242, April 2001.


Published: April 2001
First available in Project Euclid: 25 March 2004

zbMATH: 0989.65004
MathSciNet: MR1828504

Keywords: Adaptive Markov chain Monte Carlo , Comparison , convergence , ergodicity , Markov chain Monte Carlo , Metropolis-Hastings algorithm

Rights: Copyright © 2001 Bernoulli Society for Mathematical Statistics and Probability

Vol.7 • No. 2 • April 2001
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