Sampling contingency tables

Random Structures and Algorithms

Volumn 10, Issue 4, 1997, Pages 487-506

  Dyer, Martin ^a   Kannan, Ravi ^b   Mount, John ^b  

^a UNIVERSITY OF LEEDS   (United Kingdom)

^b Carnegie Mellon University   (United States)

Author keywords

Contingency tables; Markov chain; Random sampling

Indexed keywords

EID: 0031476676     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2418(199707)10:4<487::AID-RSA4>3.0.CO;2-Q     Document Type: Article

References (27)

1. D. Aldous, Some inequalities for reversible Markov chains, J. Lond. Math. Soc. (2), 25, 564-576 (1982).
2. D. Applegate and R. Kannan, Sampling and integration of near log-concave functions, 23rd ACM Symp. Theory of Computing, 1991, pp. 156-163.
3. A. I. Barvinok, A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed, Proc. Symp. Foundation of Computer Science, 1993, pp. 566-572.
4. F. R. K. Chung, R. L. Graham, and S. T. Yau, On sampling with Markov chains, Random Struct. Alg., 9 (1/2), 55-77 (1996).
5. P. Diaconis and B. Efron, Testing for independence in a two-way table, Ann. Stat., 13, 845-913 (1985).
6. P. Diaconis and A. Gangolli, Rectangular arrays with fixed margins, Proc. Workship on Markov Chains, Institute of Mathematics and Its Applications, University of Minnesota, 1994, to appear.
7. P. Diaconis and D. Strook, Geometric bound for eigenvalues of Markov chains, Ann. Appl. Probab. 1, 36-61 (1991).
8. P. Diaconis and B. Sturmfels, Algebraic algorithms for sampling from conditional distributions, Technical Report, Department of Statistics, Stanford University, 1993.
9. M. E. Dyer and A. M. Frieze, Computing the volume of convex bodies: A case where randomness provably helps, Proc. Symp. Appl. Math., 1991, Vol. 44, pp. 123-170.
10. M. E. Dyer and A. M. Frieze, On the complexity of computing the volume of a polyhedron, SIAM J. Comput., 17, 27-37 (1988).
11. M. E. Dyer, A. M. Frieze, and R. Kannan, A random polynomial-time algorithm for approximating the volume of convex bodies, J. Assoc. Comput. Mach., 38(1), 1-17 (1991).
12. M. E. Dyer, A. Frieze, R. Kannan, A. Kapoor, L. Perkovic, and U. Vazirani, A mildly exponential time algorithm for approximating the number of solutions to a multidimensional knapsack problem, Combinat. Probab. Comput., to appear
13. J. A. Fill, Eigenvalue bounds on the convergence to stationarity for nonreversible Markov chains, with an application to the exclusion pocess, Ann. Appl. Probab., 1 62-87 (1991).
14. A. Frieze, R. Kannan and N. Polson, Sampling from log-concave distributions, Ann. Appl. Probab., 4(3), 812-837 (1994).
15. A. R. Gangolli, Convergence bounds for markov chains and applications to sampling, Ph.D. thesis, Stanford University, Palo Alto, CA, STAN-CS-91-1361, 1991.
16. D. Gillman, A Chernoff bound for random walks on expander graphs, Proc. 34th Annu. IEEE Conf. Found. Comput. Sci., 1993, pp. 680-691.
17. W. Hoeffding, Probability inequalities for sums of bounded random variables, Am. Stat. Assoc. J., March 1963, pp. 13-30.
18. N. Kahale, Large deviation bounds on Markov chains, DIMACS Technical Report 94-39, Rutgers University, New Brunswick, NJ, 1994.
19. 5) volume algorithm for convex bodies, preprint, 1996.
20. R. Kannan, P. Tetali, and S. Vempala, Simple Markov chain algorithms for generating bipartite graphs and tournaments, Eighth Annu. ACM-SlAM Symp. Discrete Alg., 1997, 193-200.
21. L. Lovász and M. Simonovits, Random walks in a convex body and an improved volume algorithm, revised version, preprint, March 1993.
22. C. R. Metha and N. R. Patel, A network algorithm for performing Fisher's exact test in r X c contingency tables, J. Am. Stat. Assoc., 78, 427-434 (1983).
23. A. Schrijver, Theory of Linear and Integer Programming, Wiley, Chichester, 1986.
24. E. Seneta, Non-Negative Matrices and Markov Chains, Springer-Verlag, New York, 1973.
25. R. P. Stanley, Enumerative Combinatorics, Wadsworth and Brooks/Cole, Monterey CA, 1986, Vol. I.
26. B. Sturmfels, How to count integer matrices, preprint, December, 1993.
27. L. B. Valiant, The complexity of computing the permanent, Theor. Comput. Sci., 8, 189-201 (1979).