Convergence of heavy-tailed Monte Carlo Markov chain algorithms

Scandinavian Journal of Statistics

Volumn 34, Issue 4, 2007, Pages 781-815

  Jarner, Søren F ^a   Roberts, Gareth O ^a,b  

^a LANCASTER UNIVERSITY   (United Kingdom)

^b LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Heavy tailed proposals; Monte Carlo Markov Chain; Polynomial ergodicity

Indexed keywords

EID: 36749103743     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2007.00557.x     Document Type: Article

References (27)

1. Bailey, R. W. (1994). Polar generation of random variates with the t distribution. Math. Comp. 62, 779 781.
2. Besag, J. (1994). Comments on 'Representations of knowledge in complex systems' by U. Grenander and M. Miller. J. R. Stat. Soc. Ser. B Stat. Methodol. 56, 591 592.
3. Bingham, N. H., Goldie, C. M. Teugels, J. L. (1987). Regular variation. Cambridge University Press, Cambridge.
4. Chan, K. S. (1993a). Asymptotic behaviour of the Gibbs sampler. J. Amer. Statist Assoc. 88, 320 326.
5. Chan, K. S. (1993b). On the central limit theorem for an ergodic Markov chain. Stochastic Process. Appl. 47, 113 117.
6. Fort, G. Moulines, E. (2000). V-subgeometric ergodicity for a Hastings-Metropolis algorithm. Statist. Probab. Lett. 49, 401 410.
7. Fort, G. Moulines, E. (2003). Stochastic Process. Appl. 103, 57 99.
8. Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97 109.
9. Jarner, S. F. Hansen, E. (2000). Geometric ergodicity of Metropolis algorithms. Stochastic Process. Appl. 85, 341 361.
10. Jarner, S. F. Roberts, G. O. (2002). Polynomial convergence rates of Markov chains. Ann. Appl. Probab. 12, 224 247.
11. Jarner, S. F. Tweedie, R. L. (2003). Necessary conditions for geometric and polynomial ergodicity of random walk-type Markov chains. Bernoulli 9, 559 578.
12. Kipnis, C. Varadhan, S. R. S. (1986). Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Comm. Math. Phys. 104, 1 19.
13. Mengersen, K. L. Tweedie, R. L. (1996). Rates of convergence of the Hastings and Metropolis algorithms. Ann. Statist. 24, 101 121.
14. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. Teller, E. (1953). Equation of state calculations by fast computing machines. J. Chem. Phys. 21, 1087 1091.
15. Meyn, S. P. Tweedie, R. L. (1993). Markov chains and stochastic stability. Springer-Verlag, London.
16. Neal, R. M. (2003). Slice sampling (with discussion). Ann. Statist. 31, 705 767.
17. Nummelin, E. (1984). General irreducible Markov chains and non-negative operators. Cambridge University Press, Cambridge.
18. Roberts, G. O. (2003). Linking theory and practice of MCMC (with discussion by C. Robert and A. Frigessi). In Highly Structured Stochastic Systems eds P. J. Green, N. L. Hjort and S. Richardson) 145 178. Oxford University Press, Oxford.
19. Roberts, G. O. Rosenthal, J. S. (1997). Geometric ergodicity and hybrid Markov chains. Elect. Comm. Probab. 2, 13 25.
20. Roberts, G. O. Rosenthal, J. S. (1998a). Markov chain Monte Carlo: some practical implications of theoretical results. Canad. J. Statist. 26, 4 31.
21. Roberts, G. O. Rosenthal, J. S. (1998b). On convergence rates of Gibbs samplers for uniform distributions. Ann. Appl. Probab. 8, 1291 1302.
22. Roberts, G. O. Rosenthal, J. S. (1999). Convergence of slice sampler Markov chains. J. R. Stat. Soc. Ser. B Stat. Methodol. 61, 643 660.
23. Roberts, G. O. Tweedie, R. L. (1996a). Exponential convergence of Langevin diffusions and their discrete approximations. Bernoulli 2, 341 364.
24. Roberts, G. O. Tweedie, R. L. (1996b). Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms. Biometrika 83, 95 110.
25. Stramer, O. Tweedie, R. L. (1999a). Langevin-type models I: Diffusions with given stationary distributions and their discretizations. Methodol. Comput. Appl. Probab. 1, 283 306.
26. Stramer, O. Tweedie, R. L. (1999b). Langevin-type models II: self-targeting candidates for MCMC algorithms. Methodol. Comput. Appl. Probab. 1, 307 328.
27. Tuominen, P. Tweedie, R. L. (1994). Subgeometric rates of convergence of f-ergodic Markov chains. Adv. in Appl. Probab. 26, 775 798.