Irrelevance and Independence Relations in Quasi-Bayesian Networks

Author:

Fabio Cozman
Escola Politecnica, Universidade de Sao Paulo, Brazil
e-mail: fgcozman@usp.br

Abstract:

This paper analyzes irrelevance and independence relations in graphical models associated with convex sets of probability distributions (called Quasi-Bayesian networks). The basic question in Quasi-Bayesian networks is, How can irrelevance/independence relations in Quasi-Bayesian networks be detected, enforced and exploited? This paper addresses these questions through Walley's definitions of irrelevance and independence. Novel algorithms and results are presented for inferences with the so-called natural extensions using fractional linear programming, and the properties of the so-called type-1 extensions are clarified through a new generalization of d-separation.

Keywords:

Convex sets of probability, robust statistics, graphical models, Bayesian networks, d-separation relations, linear and nonlinear programming.

Availability:

This paper is also available in HTML and compressed Postscript formats.

Other information:

An introduction to the concepts behind convex sets of probabilities and pointers to other papers of interest are available.