Gröbner bases and factorisation in discrete probability and Bayes

Authors:
G. Pistone;E. Riccomagno;Henry P. Wynn
Affiliations:
Department of Mathematics, Polytechnic in Turin, Corso Duce Degli Abruzzi, 10129 Turin, Italy. pistone@calvino.polito.it;Department of Statistics, University of Warwick, CV4 7AL Coventry, United Kingdom. Riccomagno@eurandm.tue.nl;Department of Statistics, University of Warwick, CV4 7AL Coventry, United Kingdom. H.P.Wynn@warwick.ac.uk
Venue:
Statistics and Computing
Year:
2001

Citing 3
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Abstract

Gröbner bases, elimination theory and factorization may be used to perform calculations in elementary discrete probability and more complex areas such as Bayesian networks (influence diagrams). The paper covers the application of computational algebraic geometry to probability theory. The application to the Boolean algebra of events is straightforward (and essentially known). The extension into the probability superstructure is via the polynomial interpolation of densities and log densities and this is used naturally in the Bayesian application.