Markov chain Monte Carlo tests for designed experiments

2006/11/15 by Satoshi Aoki, Akimichi Takemura
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Computational Drug Discovery Methods #Statistical Methods in Clinical Trials #math.ST #msc:62K15 #stat.TH

paper · pdf · doi:10.1016/j.jspi.2009.09.010

published as Journal of Statistical Planning and Inference, 140 (2010), 817-830

arxiv created 2006/11/15 · openalex publication_date 2009/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider conditional exact tests of factor effects in designed experiments for discrete response variables. Similarly to the analysis of contingency tables, a Markov chain Monte Carlo method can be used for performing exact tests, when large-sample approximations are poor and the enumeration of the conditional sample space is infeasible. For designed experiments with a single observation for each run, we formulate log-linear or logistic models and consider a connected Markov chain over an appropriate sample space. In particular, we investigate fractional factorial designs with 2^p-q runs, noting correspondences to the models for 2^p-q contingency tables.

Citations

• Algebraic algorithms for sampling from conditional distributions
• NOTE ON AN EXACT TREATMENT OF CONTINGENCY, GOODNESS OF FIT AND OTHER PROBLEMS OF SIGNIFICANCE
• Monte Carlo sampling methods using Markov chains and their applications