Satoshi AOKI

Satoshi AOKI

Department of Mathematics,
Graduate School of Science, Kobe University
Division : Applied Mathematics
Professor		 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 :
  1. 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.
  2. S. Aoki, H. Hara and A. Takemura (2012). "Markov Bases in Algebraic Statistics". Springer Series in Statistics.
  3. H. Hara, S. Aoki and A. Takemura (2010). "Minimal and minimal invariant Markov bases of decomposable models for contingency tables". Bernoulli, 16, 208--233.
  4. S. Aoki, and A. Takemura (2010). "Markov chain Monte Carlo tests for designed experiments". Journal of Statistical Planning and Inference, 140, 817--830.
  5. S. Aoki, and A. Takemura (2009). "Some characterizations of affinely full-dimensional factorial designs". Journal of Statistical Planning and Inference, 139, 3525-3532.
  6. S. Aoki, A. Takemura and R. Yoshida (2008). ``Indispensable monomials of toric ideals and Markov bases''. Journal of Symbolic Computation, 43, 490--507.
  7. S. Aoki and A. Takemura (2008). ``Minimal invariant Markov basis for sampling contingency tables with fixed marginals''. Annals of the Institute of Statistical Mathematics, 60, 229--256.
  8. 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.
  9. 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.