Extension of fill's perfect rejection sampling algorithm to general chains

Random Structures and Algorithms

Volumn 17, Issue 3-4, 2000, Pages 290-316

  Fill, James Allen ^a   Machida, Motoya ^a   Murdoch, Duncan J ^b   Rosenthal, Jeffrey S ^c  

^a JOHNS HOPKINS UNIVERSITY   (United States)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

Coupling from the past; Exact sampling; Fill's algorithm; Interruptibility; Markov chain monte carlo; Monotone transition rule; Perfect sampling; Read once coupling from the past; Realizable monotonicity; Rejection sampling; Stochastic monotonicity

Indexed keywords

EID: 0034360070     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/1098-2418(200010/12)17:3/4<290::AID-RSA6>3.0.CO;2-Q     Document Type: Article

References (45)

1. P. Bidigare, P. Hanlon, and D. Rockmore, A combinatorial description of the spectrum for the Tsetlin library and its generalization to hyperplane arrangements, Duke Math J 99 (1999), 135-174.
2. S.P. Brooks, P. Dellaportas, and G.O. Roberts, An approach to diagnosing total variation convergence of MCMC algorithms. J Comput Graph Statist 6 (1997), 251-265.
3. K. Brown and P. Diaconis, Random walk and hyperplane arrangements, Ann Probab 26 (1998), 1813-1854.
4. J. Corcoran and R.L. Tweedie, Perfect simulation of Harris recurrent Markov chains, (1999) Preprint, Colorado State University.
5. M.K. Cowles and B.P. Carlin, Markov chain Monte Carlo convergence diagnostics: a comparative review, J Amer Statist Assoc 91 (1996), 883-904.
6. L. Devroye, Nonuniform random variate generation, Springer, New York (1986).
7. P. Diaconis and J.A. Fill, Strong stationary times via a new form of duality, Ann Probab 18 (1990), 1483-1522.
8. P. Diaconis and D. Freedman, Iterated random functions, SIAM Rev 41 (1999), 45-76.
9. R.P. Dobrow and J.A. Fill, On the Markov chain for the move-to-root rule for binary search trees, Ann App Probab 5 (1995), 1-19.
10. R.P. Dobrow and J.A. Fill, Rates of convergence for the move-to-root Markov chains for binary search trees, Ann Appl Probab 5 (1995), 20-36.
11. J.A. Fill, An interruptible algorithm for perfect sampling via Markov chains, Ann Appl Probab 8 (1998a), 131-162.
12. J.A. Fill, The move-to-front rule: a case study for two perfect sampling algorithms. Probab Eng Inform Sci 12 (1998b), 283-302.
13. J.A. Fill and M. Machida, Stochastic and realizable monotonicity (1998), Preprint. Available from http://www.mts.jhu.edu/∼fill/.
14. J.A. Fill, M. Machida, D. Murdoch, and J. Rosenthal, Extension of Fill's perfect rejection sampling algorithm to general chains (Extended abstract) in Monte Carlo Methods, N. Madras (ed.) Fields Institute Comm 26 (2000), 37-52.
15. S.G. Foss and R.L. Tweedie, Perfect simulation and backward coupling, Stochastic Model 14 (1998), 187-203.
16. A.E. Gelfand and A.F.M. Smith, Sampling-based approaches to calculating marginal densities. J Amer Statist Assoc 85 (1990), 398-409.
17. W.R. Gilks, S. Richardson, and D.J. Spiegelhalter (eds.), Markov Chain Monte Carlo in Practice, Chapman and Hall, 1996.
18. P.J. Green and D.J. Murdoch, Exact sampling for Bayesian inference: Towards general purpose algorithms, Bayesian statistics 6 (Alcoceber, 1998), 301-321, Oxford Univ. Press, New York, 1998.
19. O. Häggström and K. Nelander, Exact sampling from anti-monotone systems. Statist Neerlandica 52 (1998), 360-380.
20. O. Häggström and K. Nelander, On exact simulation of Markov random fields using coupling from the past, Scand J Statist 26(3) (1999), 395-411.
21. J.P. Hobert, C.P. Robert, and D.M. Titterington, On perfect simulation for some mixtures of distributions, Statist Comput 9 (1999), 287-298.
22. M. Huber, Efficient exact sampling from the Ising model using Swendsen-Wang. A two-page version appears in Tenth Annual ACM-SIAM Symposium on Discrete Algorithms, 1998, Preprint.
23. M. Huber, Exact sampling and approximate counting techniques. In Proceedings of the 30th ACM Symposium on the Theory of Computing, 1998, pp. 31-40.
24. M. Huber, Interruptible exact sampling and construction of strong stationary times for Markov chains, 1998, Preprint.
25. T. Kamae, U. Krengel, and G.L. O'Brien, Stochastic inequalities on partially ordered state spaces, Ann Probab 5 (1977), 899-912.
26. W. Kendall, Perfect simulation for the area-interaction point process, in Probability Towards 2000, L. Accardi and C.C. Heyde (eds), Springer, New York, 1998, pp. 218-234.
27. W. Kendall and J. Møller, Perfect Metropolis-Hastings simulation of locally stable point processes, Advance Appl Prob (1999), to appear.
28. W. Kendall and E. Thönnes, Perfect simulation in stochastic geometry, J Pattern Recog, 32 (1999), 1569-1586. Special issue on random sets.
29. Y. Kifer, Ergodic Theory of Random Transformations, Birkhäuser, Boston, 1986.
30. M. Machida, Stochastic monotonicity and realizable monotonicity. Ph.D. dissertation, 1999, Department of Mathematical Sciences, The Johns Hopkins University. Available from http://www.mts.jhu.edu/∼machida/.
31. M. Machida, The FMMR algorithm for a stochastically monotone kernel in the absolutely continuous case. (2000), Draft available from http://www.mts.jhu.edu/∼machida/.
32. S.P. Meyn and R.L. Tweedie, Computable bounds for convergence rates of Markov chains, Ann Appl Probab 4 (1994), 981-1011.
33. J. Møller, Perfect simulation of conditionally specified models. J Roy Statist Soci, Seri B 61 (1999), 251-264.
34. J. Møller and K. Schladitz, Extensions of Fill's algorithm for perfect simulation, J Roy Statist Soc, Ser B 61 (1999), 955-969.
35. D.J. Murdoch and P.J. Green, Exact sampling from a continuous state space, Scand J Statist 25 (1998), 483-502.
36. D.J. Murdoch and J.S. Rosenthal, Efficient use of exact samples, Statistics and Computing, to appear.
37. J.G. Propp and D.B. Wilson. Exact sampling with coupled Markov chains and applications to statistical mechanics, Random Structures Algorithms 9 (1996), 223-252.
38. J.G. Propp and D.B. Wilson, Coupling from the past: a user's guide. In D. Aldous, and J.G. Propp (eds), Microsurveys in Discrete Probability, DIMACS Seri Discrete Math Theoret Comput Sci (1998), 181-192.
39. J.G. Propp and D.B. Wilson, How to get a perfectly random sample from a generic Markov chain and generate a random spanning tree of a directed graph, J Algorithms 27 (1998), 170-217.
40. J.S. Rosenthal, Minorization conditions and convergence rates for Markov chain Monte Carlo, J Amer Statist Assoc 90 558-566.
41. A.F.M. Smith and G.O. Roberts, Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods (with discussion), J Roy Statist Soc Ser B 55 (1993), 3-23.
42. E. Thönnes, Perfect simulation of some point processes for the impatient user, Adv App Probab 31 (1999), 69-87.
43. L. Tierney, Markov chains for exploring posterior distributions (with discussion), Ann Statist 22 (1994), 1701-1762.
44. D.B. Wilson, Annotated bibliography of perfectly random sampling with Markov chains, in D. Aldous, and J. Propp (eds), Microsurveys in Discrete Probability, DIMACS Ser Discrete Math Theoret Comput Sci (1998), 209-220. Latest updated version is posted at http://di.macs.rutgers.edu/∼dbwilson/exact/.
45. D.B. Wilson, How to couple from the past using a read-once source of randomness, Random Structures Algorithms 16 (2000), 85-113.