Sampling large tables with constraints

Statistica Sinica

Volumn 21, Issue 4, 2011, Pages 1591-1609

  Dinwoodie, Ian H ^a   Chen, Yuguo ^b  

^a PORTLAND STATE UNIVERSITY   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Conditional inference; Contingency table; Exact test; Hypergeometric distribution; Importance sampling; Multivariate normal distribution; Sequential sampling

Indexed keywords

EID: 84863338133     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: 10.5705/ss.2008.078     Document Type: Article

References (29)

1. 4ti2 team (2006). 4ti2 - A software package for algebraic, geometric and combinatorial problems on linear spaces. Available at www.4ti2.de.
2. Agresti, A. and Coull, B. A. (1998). Approximate is better than "exact" for interval estimation of binomial proportions. Amer. Statist. 52, 119-126.
3. Berkelaar, M., Eikland, K. and Notebaert, P. (2004). lpsolve: Open Source (Mixed-Integer) Linear Programming System. GNU LGPL (Lesser General Public Licence).
4. Besag, J. and Clifford, P. (1989). Generalized Monte Carlo significance tests. Biometrika 76, 633-642.
5. Booth, J. G. and Butler, J. W. (1999). An importance sampling algorithm for exact conditional tests in loglinear models. Biometrika 86, 321-332. (Pubitemid 129767152)
6. Brown, L. D., Cai, T. T. and DasGupta, A. (2001). Interval estimation for a binomial proportion. Statist. Sci. 16, 101-133. (Pubitemid 33636344)
7. Caffo, B. S. (2006). The exactLoglinTest Package. Available at cran.r-project.org.
8. Chen, Y., Diaconis, P., Holmes, S. P. and Liu, J. S. (2005). Sequential Monte Carlo methods for statistical analysis of tables. J. Amer. Statist. Assoc. 100, 109-120. (Pubitemid 40366822)
9. Chen, Y., Dinwoodie, I. H. and Sullivant, S. (2006). Sequential importance sampling for multiway tables. Ann. Statist. 34, 523-545. (Pubitemid 43836811)
10. Chen, Y., Lin, C. H. and Sabatti, C. (2006). Volume measures for linkage disequilibrium. BMC Genetics 7, 54.
11. Chung, L. and Marden, J. I. (1993). Extensions of Mallows' ω model. In Probability Models and Statistical Analyses for Ranking Data (edited by Fligner and Verducci), 108-139. Springer- Verlag, New York.
12. Cover, T. M. and Thomas, J. A. (1991). Elements of Information Theory. Wiley, New York.
13. DeLoera, J. and Onn, S. (2006). Markov bases of three-way tables are arbitrarily complicated. J. Symbolic Comput. 41, 173-181. (Pubitemid 43024902)
14. Deresiewicz, R. L., Thaler, S. J., Hsu, L. and Zamani, A. A. (1997). Clinical and neuroradiographic manifestations of Eastern equine encephalitis. New England J. Medicine 336, 1867-1874. (Pubitemid 27263974)
15. Diaconis, P. (1989). A generalization of spectral analysis with application to ranked data. Ann. Statist. 17, 949-979.
16. Diaconis, P. and Efron, B. (1985). Testing for independence in a two-way table: new interpretations of the chi-square statistic. Ann. Statist. 13, 845-874.
17. Diaconis, P. and Sturmfels, B. (1998). Algebraic algorithms for sampling from conditional distributions. Ann. Statist. 26, 363-397.
18. Dobra, A. (2002). Statistical tools for disclosure limitation in multi-way contingency tables. Ph.D. Thesis, Department of Statistics, Carnegie Mellon University.
19. Eriksson, N., and Diaconis, P. (2005). Markov bases for noncommutative Fourier analysis of ranked data. arXiv:math.AC/0405060 v2.
20. Guo, S. W. and Thompson, E. A. (1992). Performing the exact test of Hardy-Weinberg proportion for multiple alleles. Biometrics 48, 361-372.
21. Hall, S. J. G. and Ruane, J. (1993). Livestock breeds and their conservation: a global overview. Conservation Biology 7, 815-825.
22. Harter, R., Hornik, K. and Theussl, S. (2008). Rsymphony: An R interface to the SYMPHONY MILP solver. GNU GPL (General Public License).
23. Holland, P. W. and Leinhardt, S. (1981). An exponential family of probability distributions for directed graphs. J. Amer. Statist. Assoc. 76, 33-50.
24. Lehmann, E. L. (1986). Testing Statistical Hypotheses. 2nd Edition. Springer, New York.
25. Liu, J. S. (2001). Monte Carlo Strategies in Scientific Computing. Springer, New York.
26. Marsaglia, G. (1964). Conditional means and covariances of normal variables with singular covariance matrix. J. Amer. Statist. Assoc. 59, 1203-1204.
27. R Development Core Team (2006). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org.
28. StatXact (2004). www.cytel.com.
29. Whittaker, J. (1990). Graphical Models in Applied Mathematical Statistics. Wiley, New York.