Examples comparing importance sampling and the metropolis algorithm

Illinois Journal of Mathematics

Volumn 50, Issue 1, 2006, Pages 67-91

  Bassetti, Federico ^a   Diaconis, Persi ^b  

^a UNIVERSITY OF PAVIA   (Italy)

^b STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846268814     PISSN: 00192082     EISSN: None     Source Type: Journal    
DOI: 10.1215/ijm/1258059470     Document Type: Article

References (24)

1. Y. Chen, P. Diaconis, S. P. Holmes, and J. S. Liu, Sequential Monte Carlo methods for statistical analysis of tables, J. Amer. Statist. Assoc. 100 (2005), 109-120. MR 2156822 (2006f:62062)
2. P. Diaconis and L. Saloff-Coste, Comparison techniques for random walk on finite groups, Ann. Probab. 21 (1993), 2131-2156. MR 1245303 (95a:60009)
3. P. Diaconis and L. Saloff-Coste, What do we know about the Metropolis algorithm?, J. Comput. System Sci. 57 (1998), 20-36. MR 1649805 (2000b:68094)
4. P. Diaconis and D. Stroock, Geometric bounds for eigenvalues of Markov chains, Ann. Appl. Probab. 1 (1991), 36-61. MR 1097463 (92h:60103)
5. Sequential Monte Carlo methods in practice, Statistics for Engineering and Information Science, Springer-Verlag, New York, 2001. MR 1847783 (2003h:65007)
6. W. Feller, An introduction to probability theory and its applications. Vol. I, Third edition, John Wiley & Sons Inc., New York, 1968. MR 0228020 (37 #3604)
7. J. M. Hammersley and D. C. Handscomb, Monte Carlo methods, Methuen & Co. Ltd., London, 1965. MR 0223065 (36 #6114)
8. W. K. Hastings, Monte Carlo sampling methods using Markov chains and their application, Biometrika 57 (1970), 97-109.
9. H. Kahn, Modification of the Monte Carlo method, Proceedings, Seminar on Scientific Computation, November, 1949, International Business Machines Corp., New York, N. Y., 1950, pp. 20-27. MR 0044896 (13,495c)
10. _, Use of different Monte Carlo sampling techniques, Symposium on Monte Carlo methods, University of Florida, 1954, John Wiley and Sons, Inc., New York, 1956, pp. 146-190. MR 0079819 (18,151c)
11. D. E. Knuth, Estimating the efficiency of backtrack programs, Math. Comp. 29 (1975), 122-136. MR 0373371 (51 #9571)
12. _, Mathematics and computer science: coping with finiteness, Science 194 (1976), 1235-1242. MR 534161 (84i:68002a)
13. J. Liu, Metropolized independent sampling with comparisons to rejection sampling and importance sampling, Statistics and Computing 6 (1996), 113-119.
14. _, Monte Carlo strategies in scientific computing, Springer Series in Statistics, Springer-Verlag, New York, 2001. MR 1842342 (2002i:65006)
15. N. Madras and M. Piccioni, Importance sampling for families of distributions, Ann. Appl. Probab. 9 (1999), 1202-1225. MR 1728560 (2001e:60139)
16. N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys. 21 (1953), 1087-1092.
17. P. H. Peskun, Optimum Monte-Carlo sampling using Markov chains, Biometrika 60 (1973), 607-612. MR 0362823 (50 #15261)
18. _, Guidelines for choosing the transition matrix in Monte Carlo methods using Markov chains, J. Comput. Phys. 40 (1981), 327-344. MR 617102 (84c:65015)
19. C. P. Robert and G. Casella, Monte Carlo statistical methods, Springer Texts in Statistics, Springer-Verlag, New York, 2004. MR 2080278 (2005d:62006)
20. R. Y. Rubinstein, Simulation and the Monte Carlo method, John Wiley & Sons Inc., New York, 1981. MR 624270 (83k:68111)
21. L. Saloff-Coste, Lectures on finite Markov chains, Lectures on probability theory and statistics (Saint-Flour, 1996), Lecture Notes in Math., vol. 1665, Springer, Berlin, 1997, pp. 301-413. MR 1490046 (99b:60119)
22. D. Siegmund, Importance sampling in the Monte Carlo study of sequential tests, Ann. Statist. 4 (1976), 673-684. MR 0418369 (54 #6410)
23. N. J. A. Sloane, The online encyclopedia of integer sequences, http://www.research. att.com/~njas/sequences.
24. A. Sokal, Monte Carlo methods in statistical mechanics: foundations and new algorithms, Functional integration (Cargèse, 1996), NATO Adv. Sci. Inst. Ser. B Phys., vol. 361, Plenum, New York, 1997, pp. 131-192. MR 1477456 (98k:82101)