Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions
Dan Geiger, David Heckerman
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 normalWishart distribution. Our analysis is based on the following new characterization of the Wishart distribution: let W be an n x n, n >= 3, positivedefinite symmetric matrix of random variables and f(W) be a pdf of W. Then, f(W) is a Wishart distribution if and only if W_{11}W_{12}W_{22}^{1}W_{12}' is independent of {W_{12}, W_{22}} for every block partitioning W_{11}, W_{12}, W_{12}', W_{22} of W. Similar characterizations of the normal and normalWishart distributions are provided as well. We also show how to construct a prior for every DAG model over X from the prior of a single regression model.
Keywords:
Pages: 216225
PS Link:
PDF Link: /papers/99/p216geiger.pdf
BibTex:
@INPROCEEDINGS{Geiger99,
AUTHOR = "Dan Geiger
and David Heckerman",
TITLE = "Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions",
BOOKTITLE = "Proceedings of the Fifteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI99)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1999",
PAGES = "216225"
}

