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On the ergodicity of the adaptive Metropolis algorithm on unbounded domains

Abstract:

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 adaptat...

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Publisher copy:
10.1214/10-AAP682

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Journal:
Annals of Applied Probability
Volume:
20
Issue:
6
Pages:
2178-2203
Publication date:
2010-12-05
DOI:
EISSN:
1050-5164
ISSN:
1050-5164
URN:
uuid:5b533759-e558-4af8-b379-c8a94a3a0192
Source identifiers:
487898
Local pid:
pubs:487898

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