Algorithm for direct sampling from conditional distributions of toric models

Abstract

We show that contiguity relations of hypergeometric functions of several variables give a direct sampling algorithm from the conditional distribution of toric models in statistics. The algorithm is based on a Markov chain on a lattice generated by a matrix $A$. A correspondence between decomposable graphical models and $A$-hypergeometric systems is discussed. We give a sum formula of special values of $A$-hypergeometric polynomials. Some examples with implementations are presented.

40 pages, 2 figures

References in corpus (4)

• Macaulay Matrix for Feynman Integrals: Linear Relations and Intersection Numbers
• Partition structure and the A-hypergeometric distribution associated with the rational normal curve
• Pfaffian Systems of A-Hypergeometric Systems II --- Holonomic Gradient Method
• Holonomic Gradient Method for Two Way Contingency Tables