A finitely generated credal set is the convex hull of a finite number of probability distributions.

Consider the situation where a single variable x_{1} is associated with
a credal set, and the credal set for x_{1} is the convex hull of
m different distributions: (_{j=1}^{m} p_{1,j}

( C_{j=1}^{m} p_{1,j} )
prod_{i>1} p_{i}.

r_{j}(x) = p_{1,j} prod_{i>1} p_{i}.

Consider a Quasi-Bayesian network with two credal sets associated with
variables x_{1} and x_{2}.
To produce a convex set of joint distributions, we use the convex hull:

C_{j,k} ( p_{1,j} p_{2,k} ) prod_{i>2} p_{i}.

This ``convexification'' technique is assumed in the remainder of the paper. When a network with several credal sets is used, we take the convex hull of the combined credal sets.

© Fabio Cozman[Send Mail?]

Tue Jan 21 15:59:56 EST 1997