We show that the 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
. Some
examples with implementations are presented. In addition, known special
properties of decomposable graphical models are revisited in terms of the
-hypergeometric
systems.
Keywords
$A$-hypergeometric system, discrete exponential family,
GKZ-hypergeometric system, graphical model, Markov chain
Monte Carlo