Algorithm for direct sampling from conditional distributions of toric models

TL;DR

This paper introduces a direct sampling algorithm for conditional distributions of toric models using hypergeometric functions, Markov chains, and lattice structures, with practical examples and implementation details.

Contribution

It presents a novel sampling algorithm based on hypergeometric functions and Markov chains for toric models, linking graphical models and hypergeometric systems.

Findings

Algorithm enables efficient sampling from toric model distributions.

Provides sum formulas for hypergeometric polynomial values.

Includes practical examples and implementation insights.

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.