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Article overview
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Running Markov chain without Markov basis | Hisayuki Hara
; Satoshi Aoki
; Akimichi Takemura
; | Date: |
1 Sep 2011 | Abstract: | The methodology of Markov basis initiated by Diaconis and Sturmfels(1998)
stimulated active research on Markov bases for more than ten years. It also
motivated improvements of algorithms for Grobner basis computation for toric
ideals, such as those implemented in 4ti2. However at present explicit forms of
Markov bases are known only for some relatively simple models, such as the
decomposable models of contingency tables. Furthermore general algorithms for
Markov bases computation often fail to produce Markov bases even for
moderate-sized models in a practical amount of time. Hence so far we could not
perform exact tests based on Markov basis methodology for many important
practical problems.
In this article we propose to use lattice bases for performing exact tests,
in the case where Markov bases are not known. Computation of lattice bases is
much easier than that of Markov bases. With many examples we show that the
approach with lattice bases is practical. We also check that its performance is
comparable to Markov bases for the problems where Markov bases are known. | Source: | arXiv, 1109.0078 | Services: | Forum | Review | PDF | Favorites |
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