Yulia Alexandr, Miles Bakenhus, Maize Curiel, Sameer K.
Deshpande, Elizabeth Gross, Yuqi Gu, Max Hill, Joseph
Johnson, Bryson Kagy, Vishesh Karwa, Jiayi Li, Hanbaek Lyu,
Sonja Petrović and Jose Israel Rodriguez
In the last quarter of a century, algebraic statistics has established itself as an
expanding field which uses multilinear algebra, commutative algebra, computational
algebra, geometry, and combinatorics to tackle problems in mathematical and
computational statistics. These developments have found applications in a
growing number of areas, including biology, neuroscience, economics, and social
sciences.
Naturally, new connections continue to be made with other areas of mathematics
and statistics. We outline three such connections: to statistical models used in
educational testing, to a classification problem for a family of nonparametric
regression models, and to phase transition phenomena under uniform sampling of
contingency tables. We illustrate the motivating problems, each of which is for
algebraic statistics a new direction, and demonstrate an enhancement of related
methodologies.