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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:

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### Other information:

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