Convergence properties of the Gibbs sampler for perturbations of Gaussians

Annals of Statistics

Volumn 24, Issue 1, 1996, Pages 122-140

  Amit, Yali ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

Integral operators; Markov chains; Second eigenvalue

Indexed keywords

EID: 0030540047     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1033066202     Document Type: Article

References (19)

1. AMIT, Y. (1991). On rates of convergence of stochastic relaxation for Gaussian and non-Gaussian distributions. J. Multivariate Anal. 38 82-100.
2. AMIT, Y. and GRENANDER, U. (1991). Comparing sweep strategies for stochastic relaxation. J. Multivariate Anal. 37 197-222.
3. AMIT, Y., GRENANDER, U. and PICCIONI, M. (1991). Structural image restoration through deformable templates. J. Amer. Statist. Assoc. 86 376-387.
4. BARONE, P. and FRIGESSI, A. (1990). Improving stochastic relaxation for Gaussian random fields. Probab. Eng. Inform. Sci. 4 369-389.
5. BESAG, J. and GREEN, P. J. (1993). Spatial statistics and Bayesian computation. J. Roy. Statist. Soc. Ser. B 55 25-37.
6. CRAMÉR, H. (1946). Mathematical Methods of Statistics. Princeton Univ. Press.
7. DIACONIS, P. and SALOFF-COSTE, L. (1993). Comparison techniques for random walk on finite groups. Ann. Probab. 21 2131-2156.
8. FRIEZE, A., KANNAN, R. and POLSON, N. G. (1994). Sampling from log-concave distributions. Ann. Appl. Probab. 4 812-837. [Correction note (1994) 4 1255.]
9. GEMAN, D. (1991). Random Fields and Inverse Problems in Imaging. Lecture Notes in Math. 1427. Springer, Berlin.
10. GEMAN, S. and GEMAN, D. (1984). Stochastic relaxation. Gibbs distributions and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6 721-741.
11. GOODMAN, J. and SOKAL, A. D. (1989). Multigrid Monte-Carlo method. Conceptual foundations. Phys. Rev. D 40 2035-2071.
12. GRENANDER, U., CHOW, Y. and KEENAN, D. (1991). HANDS: A Pattern Theoretic Study of Biological Shapes. Springer, New York.
13. IBRAGIMOV, I. A. and ROZANOV, Y. A. (1978). Gaussian Processes. Springer, New York.
14. KATO, T. (1976). Perturbation Theory for Linear Operators, 2nd ed. Springer, New York.
15. KNOERR, A. P. (1988). Global models of natural boundaries: Theory and applications. Ph.D. Thesis, Div. of Applied Mathematics, Brown Univ.
16. McCULLAGH, P. (1987). Tensor Methods in Statistics. Chapman and Hall, London.
17. MENGERSEN, K. L. and TWEEDIE, R. L. (1996). Rates of convergence of the Hastings and Metropolis algorithms. Ann. Statist. 24 101-121.
18. ROSENTHAL, J. S. (1995). Minorization conditions and convergence rates for Markov chain Monte Carlo. J. Amer. Statist. Assoc. 90 558-566.
19. SMITH, A. F. M. and ROBERTS, G. O. (1993). Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods (with discussion). J. Roy. Statist. Soc. Ser. B 55 3-23.