On the stability and ergodicity of adaptive scaling Metropolis algorithms

Stochastic Processes and their Applications

Volumn 121, Issue 12, 2011, Pages 2839-2860

  Vihola, Matti ^a  

^a UNIVERSITY OF JYVÄSKYLÄ   (Finland)

Author keywords

Adaptive Markov chain Monte Carlo; Law of large numbers; Metropolis algorithm; Stability; Stochastic approximation

Indexed keywords

ADAPTIVE RANDOM WALKS; ADAPTIVE SCALING; COMPACT SUPPORT; ERGODICITY; ERGODICITY PROPERTY; LAW OF LARGE NUMBERS; MARKOV CHAIN MONTE CARLO; METROPOLIS ALGORITHMS; PROPOSAL DISTRIBUTION; SCALING PARAMETER; STOCHASTIC APPROXIMATIONS; STRONG LAW OF LARGE NUMBERS; TARGET DENSITY;

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; MARKOV PROCESSES; PROBABILITY DISTRIBUTIONS;

ADAPTIVE ALGORITHMS;

EID: 80053597715     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2011.08.006     Document Type: Article

References (24)

1. C. Andrieu, and Moulines On the ergodicity properties of some adaptive MCMC algorithms Ann. Appl. Probab. 16 2006 1462 1505 (Pubitemid 44662199)
2. C. Andrieu, Moulines, and P. Priouret Stability of stochastic approximation under verifiable conditions SIAM J. Control Optim. 44 2005 283 312
3. C. Andrieu, C.P. Robert, Controlled MCMC for Optimal Sampling, Technical Report Ceremade 0125, Université Paris Dauphine, 2001.
4. C. Andrieu, and J. Thoms A tutorial on adaptive MCMC Statist. Comput. 18 2008 343 373
5. Y. Atchadé, and G. Fort Limit theorems for some adaptive MCMC algorithms with subgeometric kernels Bernoulli 16 2010 116 154
6. Y.F. Atchadé, and J.S. Rosenthal On adaptive Markov chain Monte Carlo algorithms Bernoulli 11 2005 815 828 (Pubitemid 44966970)
7. M. Bédard Optimal acceptance rates for Metropolis algorithms: moving beyond 0.234 Stochastic Process. Appl. 118 2008 2198 2222
8. G. Fort, E. Moulines, P. Priouret, Convergence of adaptive MCMC algorithms: ergodicity and law of large numbers, Technical Report, 2010.
9. W.R. Gilks, S. Richardson, and D.J. Spiegelhalter Markov Chain Monte Carlo in Practice 1998 Chapman & Hall/CRC Boca Raton, Florida
10. W.R. Gilks, G.O. Roberts, and S.K. Sahu Adaptive Markov chain Monte Carlo through regeneration J. Amer. Statist. Assoc. 93 1998 1045 1054
11. H. Haario, E. Saksman, and J. Tamminen An adaptive Metropolis algorithm Bernoulli 7 2001 223 242 (Pubitemid 33793059)
12. P. Hall, and C.C. Heyde Martingale Limit Theory and its Application 1980 Academic Press New York
13. S.F. Jarner, and E. Hansen Geometric ergodicity of Metropolis algorithms Stochastic Process. Appl. 85 2000 341 361
14. E. Nummelin MC's for MCMC'ists Internat. Statist. Rev. 70 2002 215 240
15. C.P. Robert, and G. Casella Monte Carlo Statistical Methods 1999 Springer-Verlag New York
16. G.O. Roberts, A. Gelman, and W.R. Gilks Weak convergence and optimal scaling of random walk Metropolis algorithms Ann. Appl. Probab. 7 1997 110 120
17. G.O. Roberts, and J.S. Rosenthal Optimal scaling for various MetropolisHastings algorithms Statist. Sci. 16 2001 351 367 (Pubitemid 33636356)
18. G.O. Roberts, and J.S. Rosenthal General state space Markov chains and MCMC algorithms Probab. Surv. 1 2004 20 71
19. G.O. Roberts, and J.S. Rosenthal Coupling and ergodicity of adaptive Markov chain Monte Carlo algorithms J. Appl. Probab. 44 2007 458 475
20. G.O. Roberts, and J.S. Rosenthal Examples of adaptive MCMC J. Comput. Graph. Statist. 18 2009 349 367
21. E. Saksman, and M. Vihola On the ergodicity of the adaptive Metropolis algorithm on unbounded domains Ann. Appl. Probab. 20 2010 2178 2203
22. C. Sherlock, and G. Roberts Optimal scaling of the random walk Metropolis on elliptically symmetric unimodal targets Bernoulli 15 2009 774 798
23. M. Vihola Can the adaptive Metropolis algorithm collapse without the covariance lower bound? Electron. J. Probab. 16 2011 45 75
24. S.D. Wang, T.S. Kuo, and C.F. Hsu Trace bounds on the solution of the algebraic matrix Riccati and Lyapunov equation IEEE Trans. Automat. Control 31 1986 654 656