39 citations · 99 across the 18 of their papers we have counts for
9 papers · 1 filter
Characterizations of indicator functions and contrast representations of fractional factorial designs with multi-level factors
Satoshi Aoki
A polynomial indicator function of designs is first introduced by Fontana, Pistone and Rogantin (2000) for two-level designs. They give the structure of the indicator function of t…
An introduction to computational algebraic statistics
Satoshi Aoki
In this paper, we introduce the fundamental notion of a Markov basis, which is one of the first connections between commutative algebra and statistics. The notion of a Markov basis…
Markov chain Monte Carlo methods for the Box-Behnken designs and centrally symmetric configurations
Satoshi Aoki, Takayuki Hibi, Hidefumi Ohsugi
We consider Markov chain Monte Carlo methods for calculating conditional p values of statistical models for count data arising in Box-Behnken designs. The statistical model we cons…
Markov chain Monte Carlo methods for the regular two-level fractional factorial designs and cut ideals
Satoshi Aoki, Takayuki Hibi, Hidefumi Ohsugi
It is known that a Markov basis of the binary graph model of a graph corresponds to a set of binomial generators of cut ideals of the suspension …
Minimal Markov basis for tests of main effect models for fractional factorial designs of resolution
Satoshi Aoki
We consider conditional exact tests of factor effects in designed experiments for discrete response variables. Similarly to the analysis of contingency tables, Markov chain Monte C…
Running Markov chain without Markov basis
Hisayuki Hara, Satoshi Aoki, Akimichi Takemura
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 algo…