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Algorithm for
direct sampling from conditional distributions of toric
models
Shuhei Mano and Nobuki Takayama |
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Vol. 17 (2026), No. 1, 151–181
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Abstract |
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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. |
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Keywords
$A$-hypergeometric system, discrete exponential family,
GKZ-hypergeometric system, graphical model, Markov chain
Monte Carlo
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Mathematical Subject Classification
Primary: 62R01
Secondary: 33C65, 33C90, 33F99, 62H17, 65C05
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Milestones
Received: 28 December 2025
Revised: 12 May 2026
Accepted: 19 May 2026
Published: 21 June 2026
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Authors |
| Shuhei Mano | |
| The Institute of Statistical
Mathematics Tachikawa Japan |
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| Nobuki Takayama | |
| Department of Mathematics Kobe University Kobe Japan |
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| © 2026 MSP (Mathematical Sciences Publishers). |
