Algebraic algorithms for sampling from conditional distributions
- 1 February 1998
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 26 (1), 363-397
- https://doi.org/10.1214/aos/1030563990
Abstract
We construct Markov chain algorithms for sampling from discrete exponential familiesconditional on a sufficient statistic. Examples include generating tables with fixed row andcolumn sums and higher dimensional analogs. The algorithms involve finding bases forassociated polynomial ideals and so an excursion into computational algebraic geometry.Keywords
This publication has 66 references indexed in Scilit:
- Tests of odds ratio homogeneity with improved power in sparse fourfold tablesCommunications in Statistics - Theory and Methods, 1992
- On the Finding of Final PolynomialsEuropean Journal of Combinatorics, 1990
- The Conditional Distribution of Goodness-of-Fit Statistics for Discrete DataJournal of the American Statistical Association, 1986
- The complexity of the word problems for commutative semigroups and polynomial idealsAdvances in Mathematics, 1982
- Small-Sample Comparisons of Exact Levels for Chi-Squared Goodness-of-Fit StatisticsJournal of the American Statistical Association, 1978
- On Rereading R. A. FisherThe Annals of Statistics, 1976
- The necessity that a conditional decision procedure be almost everywhere admissibleProbability Theory and Related Fields, 1971
- A Comparison of Minimum Logit Chi-Square Estimation and Maximum Likelihood Estimation in 2×2×2 and 3×2×2 Contingency Tables: Tests for InteractionJournal of the American Statistical Association, 1970
- The Multivariate Analysis of Qualitative Data: Interactions among Multiple ClassificationsJournal of the American Statistical Association, 1970
- Some Problems Connected with Statistical InferenceThe Annals of Mathematical Statistics, 1958