## Parameter priors for directed acyclic graphical models and the characterization of several probability distributions (1999)

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Venue: | MICROSOFT RESEARCH, ADVANCED TECHNOLOGY DIVISION |

Citations: | 26 - 1 self |

### BibTeX

@TECHREPORT{Geiger99parameterpriors,

author = {Dan Geiger and David Heckerman},

title = {Parameter priors for directed acyclic graphical models and the characterization of several probability distributions},

institution = {MICROSOFT RESEARCH, ADVANCED TECHNOLOGY DIVISION},

year = {1999}

}

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### Abstract

We show that the only parameter prior for complete Gaussian DAG models that satisfies global parameter independence, complete model equivalence, and some weak regularity assumptions, is the normal-Wishart distribution. Our analysis is based on the following new characterization of the Wishart distribution: let W be an n × n, n ≥ 3, positive-definite symmetric matrix of random variables and f(W) be a pdf of W. Then, f(W) is a Wishart distribution if and only if W11 − W12W −1 is independent 22 W ′ 12 of {W12, W22} for every block partitioning