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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENT SEMINAR}
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\centerline{4:15 p.m., Thursday, July 25, 2002}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Akimichi Takemura}
\centerline{\sl University of Tokyo}
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\centerline{\bf On minimal Markov basis for sampling from discrete conditional
distributions}
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Following Diaconis and Sturmfels (1998) we consider constructing
connected Markov chain over finite discrete sample space for
performing exact tests.  Our new viewpoint to the problem is explicit
consideration of minimality of Markov basis.  Even the reduced
Groebner basis is often not minimal.  We derive minimal Markov bases
for various relatively easy problems concerning two-way contingency
tables.  We also give many partial results on the surprisingly hard
problem of three-way contingency tables with fixed two-dimensional
marginals.  Our argument does not use Groebner basis technique and
is totally elementary. 

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