The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 20, Number 6 (2010), 2178-2203.
On the ergodicity of the adaptive Metropolis algorithm on unbounded domains
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].
Ann. Appl. Probab., Volume 20, Number 6 (2010), 2178-2203.
First available in Project Euclid: 19 October 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 65C05: Monte Carlo methods
Secondary: 65C40: Computational Markov chains 60J27: Continuous-time Markov processes on discrete state spaces 93E15: Stochastic stability 93E35: Stochastic learning and adaptive control
Saksman, Eero; Vihola, Matti. On the ergodicity of the adaptive Metropolis algorithm on unbounded domains. Ann. Appl. Probab. 20 (2010), no. 6, 2178--2203. doi:10.1214/10-AAP682. https://projecteuclid.org/euclid.aoap/1287494558