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On an Adaptive Version of the Metropolis-Hastings Algorithm with Independent Proposal Distribution
Scandinavian Journal of Statistics
Vol. 30, No. 1 (Mar., 2003), pp. 159-173
Published by: Wiley on behalf of Board of the Foundation of the Scandinavian Journal of Statistics
Stable URL: http://www.jstor.org/stable/4616755
Page Count: 15
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In this paper, we present a general formulation of an algorithm, the adaptive independent chain (AIC), that was introduced in a special context in Gåsemyr et al. [Methodol. Comput. Appl. Probab. 3 (2001)]. The algorithm aims at producing samples from a specific target distribution Π, and is an adaptive, non-Markovian version of the Metropolis-Hastings independent chain. A certain parametric class of possible proposal distributions is fixed, and the parameters of the proposal distribution are updated periodically on the basis of the recent history of the chain, thereby obtaining proposals that get ever closer to Π. We show that under certain conditions, the algorithm produces an exact sample from Π in a finite number of iterations, and hence that it converges to Π. We also present another adaptive algorithm, the componentwise adaptive independent chain (CAIC), which may be an alternative in particular in high dimensions. The CAIC may be regarded as an adaptive approximation to the Gibbs sampler updating parametric approximations to the conditionals of Π.
Scandinavian Journal of Statistics © 2003 Board of the Foundation of the Scandinavian Journal of Statistics