Relations among conditional probabilities

Jason Morton

doi:10.1016/j.jsc.2012.02.005

Relations among conditional probabilities

Jason Morton

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We describe a universal Gröbner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and other special cases. We also investigate the connection to generalized permutohedra and describe a "conditional probability simplex" which is the image of a multigraded moment map.

Original language	English (US)
Pages (from-to)	478-492
Number of pages	15
Journal	Journal of Symbolic Computation
Volume	50
DOIs	https://doi.org/10.1016/j.jsc.2012.02.005
State	Published - Mar 2013

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Computational Mathematics

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10.1016/j.jsc.2012.02.005

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title = "Relations among conditional probabilities",

abstract = "We describe a universal Gr{\"o}bner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and other special cases. We also investigate the connection to generalized permutohedra and describe a {"}conditional probability simplex{"} which is the image of a multigraded moment map.",

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doi = "10.1016/j.jsc.2012.02.005",

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journal = "Journal of Symbolic Computation",

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N2 - We describe a universal Gröbner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and other special cases. We also investigate the connection to generalized permutohedra and describe a "conditional probability simplex" which is the image of a multigraded moment map.

AB - We describe a universal Gröbner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and other special cases. We also investigate the connection to generalized permutohedra and describe a "conditional probability simplex" which is the image of a multigraded moment map.

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U2 - 10.1016/j.jsc.2012.02.005

DO - 10.1016/j.jsc.2012.02.005

M3 - Article

AN - SCOPUS:84870236076

SN - 0747-7171

VL - 50

SP - 478

EP - 492

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

ER -

Relations among conditional probabilities

Abstract

All Science Journal Classification (ASJC) codes

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