On the ergodicity of the adaptive Metropolis algorithm on unbounded domains

Saksman, Eero; Vihola, Matti

Ann. Appl. Probab., Tome 20 (2010) no. 1, p. 2178-2203 / Harvested from Project Euclid

Résumé

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].

Publié le : 2010-12-15
Classification: Adaptive Markov chain Monte Carlo, convergence, ergodicity, Metropolis algorithm, stochastic approximation, 65C05, 65C40, 60J27, 93E15, 93E35

@article{1287494558,
     author = {Saksman, Eero and Vihola, Matti},
     title = {On the ergodicity of the adaptive Metropolis algorithm on unbounded domains},
     journal = {Ann. Appl. Probab.},
     volume = {20},
     number = {1},
     year = {2010},
     pages = { 2178-2203},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1287494558}
}

Saksman, Eero; Vihola, Matti. On the ergodicity of the adaptive Metropolis algorithm on unbounded domains. Ann. Appl. Probab., Tome 20 (2010) no. 1, pp.  2178-2203. http://gdmltest.u-ga.fr/item/1287494558/