Algebraic Study of Discrete Imsetal Models
Amira Alkeswani · 2020
Probabilistic conditional independence is an important concept in statistics and many other scientific fields.Given a collection of conditional independence state-ments over a set of random variables, the primary decomposition of the conditional independence ideal allows understanding inferences and implications.Following Mi-lan Studeny's work, in describing conditional independence relations we associate a -1, 0, 1 vector, called an imset, to sets of disjoint subsets of the random variables.The set of elementary imsets generates a rational polyhedral cone.Each face of this cone induces a unique independence model called an imsetal model.Considering these models as probabilistic models, we first partition the cone's faces into equiva-lence classes to reduce the amount of computation for dealing with a large number of models, and then we study the primary decomposition of the corresponding ideals in relation to the geometric and combinatorial structure of the cone in the case of three and four binary random variables.