Markov chain Monte Carlo tests for designed experiments |
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Authors: | Satoshi Aoki Akimichi Takemura |
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Affiliation: | 1. Faculty of Science, Graduate School of Science and Engineering (Science course), Kagoshima University, Japan;2. JST, CREST, Japan;3. Graduate School of Information Science and Technology, University of Tokyo, Japan |
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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 2p-q runs, noting correspondences to the models for 2p-q contingency tables. |
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Keywords: | Two-level designs Regular fractional factorial designs Markov chain Monte Carlo Contingency tables Markov basis |
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