Irrelevance and Independence Relations in Quasi-Bayesian Networks


Fabio Cozman
Escola Politecnica, Universidade de Sao Paulo, Brazil


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.


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


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