Department of Mathematics,
Graduate School of Science, Kobe University
Division : Applied Mathematics
|Building B, Room 318|
|Research Field :
Mathematical statistics and Computational algebraic statistics
|Research Summary :
My latest research field is computational algebraic statistics.
In this field, we consider applications of Groebner basis theory
in various statistical problems. One example is sampling method
based on Groebner basis theory in the analysis of contingency tables.
Another example is algebraic method in statistical design of experiments
for several multi-level factors.
|Primary Publications :|
S. Aoki, T. Hibi and H. Ohsugi (2013).
"Markov chain Monte Carlo methods for the regular two-level fractional
factorial designs and cut ideals".
Journal of Statistical Planning and Inference, 143, 1791--1806.
S. Aoki, H. Hara and A. Takemura (2012).
"Markov Bases in Algebraic Statistics".
Springer Series in Statistics.
H. Hara, S. Aoki and A. Takemura (2010).
"Minimal and minimal invariant Markov bases of decomposable models for
Bernoulli, 16, 208--233.
S. Aoki, and A. Takemura (2010).
"Markov chain Monte Carlo tests for designed experiments".
Journal of Statistical Planning and Inference, 140, 817--830.
S. Aoki, and A. Takemura (2009).
"Some characterizations of affinely full-dimensional factorial designs".
Journal of Statistical Planning and Inference, 139, 3525-3532.
S. Aoki, A. Takemura and R. Yoshida (2008).
``Indispensable monomials of toric ideals and Markov bases''.
Journal of Symbolic Computation, 43, 490--507.
S. Aoki and A. Takemura (2008).
``Minimal invariant Markov basis for sampling contingency tables with
Annals of the Institute of Statistical Mathematics, 60, 229--256.
A. Takemura and S. Aoki (2004).
``Some characterizations of minimal Markov basis for sampling from
discrete conditional distributions''.
Annals of the Institute of Statistical Mathematics, 56, 1--17.
S. Aoki and A. Takemura (2003).
``Minimal basis for connected Markov chain over 3x3xK contingency tables
with fixed two-dimensional marginals''.
Australian and New Zealand Journal of Statistics, 45, 229--249.