Irrelevance and Independence Relations in Quasi-Bayesian Networks
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
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.
This paper is also available in
to the concepts behind convex sets of probabilities and pointers
to other papers of interest are available.