On the ergodicity of the adaptive Metropolis algorithm on unbounded domains

Details On the ergodicity of the adaptive Metropolis algorithm on unbounded domains On the ergodicity of the adaptive Metropolis algorithm on unbounded domains

2008-06-18

arxiv.org/abs/0806.2933v5

Annals of Applied Probability 2010, Vol. 20, No. 6, 2178-2203

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AAP682 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/10-AAP682

This paper describes sufficient conditions to ensure the correct ergodicity of the Adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen [Bernoulli 7 (2001) 223--242] for target distributions with a noncompact support. The conditions ensuring a strong law of large numbers require that the tails of the target density decay super-exponentially and have regular contours. The result is based on the ergodicity of an auxiliary process that is sequentially constrained to feasible adaptation sets, independent estimates of the growth rate of the AM chain and the corresponding geometric drift constants. The ergodicity result of the constrained process is obtained through a modification of the approach due to Andrieu and Moulines [Ann. Appl. Probab. 16 (2006) 1462--1505].

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