Australian & New Zealand Journal of Statistics

Minimal Basis for a Connected Markov Chain over 3 × 3 × K Contingency Tables with Fixed Two‐Dimensional Marginals

Journal Article

Abstract

This paper considers a connected Markov chain for sampling 3 × 3 ×K contingency tables having fixed two‐dimensional marginal totals. Such sampling arises in performing various tests of the hypothesis of no three‐factor interactions. A Markov chain algorithm is a valuable tool for evaluating P‐values, especially for sparse datasets where large‐sample theory does not work well. To construct a connected Markov chain over high‐dimensional contingency tables with fixed marginals, algebraic algorithms have been proposed. These algorithms involve computations in polynomial rings using Gröbner bases. However, algorithms based on Gröbner bases do not incorporate symmetry among variables and are very time‐consuming when the contingency tables are large. We construct a minimal basis for a connected Markov chain over 3 × 3 ×K contingency tables. The minimal basis is unique. Some numerical examples illustrate the practicality of our algorithms.

Related Topics

Related Publications

Related Content

Site Footer

Address:

This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on StatisticsViews.com are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and StatisticsViews.com express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.