Algebraic algorithm for direct sampling from toric models
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We show that Pfaffians or contiguity relations of hypergeometric functions of several variables give a direct sampling algorithm from toric models in statistics, which is a Markov chain on a lattice generated by a matrix A. A correspondence among graphical toric models and A-hypergeometric system is discussed and we give a sum formula of special values of A-hypergeometric polynomials. Some hypergeometric series which are interesting in view of statistics are presented.
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