39 citations · 99 across the 18 of their papers we have counts for
18 papers
Algebraic Signatures for Structural Learning in Probability Tensors
Akihiro Maeda, Shohei Hidaka, Satoshi Aoki
Algebraic statistics characterizes statistical models through polynomial constraints, but it has mainly been used for analytically specified model classes. This paper studies the i…
Use of indicator functions to enumerate cross-array designs without direct product structure
Satoshi Aoki, Masayuki Noro
Use of polynomial indicator functions to enumerate fractional factorial designs with given properties is first introduced by Fontana, Pistone and Rogantin (2000) for two-level fact…
Use of primary decomposition of polynomial ideals arising from indicator functions to enumerate orthogonal fractions
Satoshi Aoki, Masayuki Noro
A polynomial indicator function of designs is first introduced by Fontana {\it et al}. (2000) for two-level cases. They give the structure of the indicator functions, especially th…
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…
Markov bases for two-way change-point models of ladder determinantal tables
Satoshi Aoki, Takayuki Hibi
To evaluate a fitting of a statistical model to given data, calculating a conditional value by a Markov chain Monte Carlo method is one of the effective approaches. For this pu…
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…