Can the adaptive Metropolis algorithm collapse without the covariance lower bound?

Electronic Journal of Probability

Volumn 16, Issue , 2011, Pages 45-75

  Vihola, Matti ^a  

^a UNIVERSITY OF JYVÄSKYLÄ   (Finland)

Author keywords

Adaptive Markov chain Monte Carlo; Metropolis algorithm; Stability; Stochastic approximation

Indexed keywords

EID: 79751503929     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v16-840     Document Type: Article

References (18)

1. C. Andrieu and É. Moulines. On the ergodicity properties of some adaptive MCMC algorithms. Ann. Appl. Probab., 16(3):1462-1505, 2006.
2. C. Andrieu and C. P Robert. Controlled MCMC for optimal sampling. Technical Report Ceremade 0125, Université Paris Dauphine, 2001.
3. C. Andrieu and J. Thoms. A tutorial on adaptive MCMC. Statist. Comput., 18(4):343-373, Dec. 2008.
4. Y. Atchadé and G. Fort. Limit theorems for some adaptive MCMC algorithms with subgeometric kernels. Bernoulli, 16(1):116-154, Feb. 2010.
5. Y. F. Atchade and J. S. Rosenthal. On adaptive Markov chain Monte Carlo algorithms. Bernoulli, 11 (5):815-828, 2005.
6. K. B. Athreya and P Ney. A new approach to the limit theory of recurrent Markov chains. Trans. Amer. Math. Soc., 245:493-501, 1978.
7. Y. Bai, G. O. Roberts, and J. S. Rosenthal. On the containment condition for adaptive Markov chain Monte Carlo algorithms. Preprint, July 2008. URL http://probability.ca/jeff/research.html.
8. C. G. Esseen. On the Kolmogorov-Rogozin inequality for the concentration function. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 5(3):210-216, Sept. 1966.
9. H. Haario, E. Saksman, and J. Tamminen. An adaptive Metropolis algorithm. Bernoulli, 7(2):223-242, 2001.
10. P. Hall and C. C. Heyde. Martingale Limit Theory and Its Application. Academic Press, New York, 1980. ISBN 0-12-319350-8.
11. S. F. Jarner and E. Hansen. Geometric ergodicity of Metropolis algorithms. Stochastic Process. Appl., 85:341-361, 2000.
12. E. Nummelin. A splitting technique for Harris recurrent Markov chains. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 43(3):309-318, Dec. 1978.
13. G. O. Roberts and J. S. Rosenthal. General state space Markov chains and MCMC algorithms. Probability Surveys, 1:20-71, 2004.
14. G. O. Roberts and J. S. Rosenthal. Coupling and ergodicity of adaptive Markov chain Monte Carlo algorithms. J. Appl. Probab., 44(2):458-475, 2007.
15. G. O. Roberts and J. S. Rosenthal. Examples of adaptive MCMC. J. Comput. Graph. Statist., 18(2): 349-367, 2009.
16. B. A. Rogozin. An estimate for concentration functions. Theory Probab. Appl., 6(1):94-97, Jan. 1961.
17. E. Saksman and M. Vihola. On the ergodicity of the adaptive Metropolis algorithm on unbounded domains. Ann. Appl. Probab., 20(6):2178-2203, Dec. 2010.
18. M. Vihola. On the stability and ergodicity of an adaptive scaling Metropolis algorithm. Preprint, arXiv:0903.4061v2, Mar. 2009.