Robustness Analysis of Bayesian Networks with Local Convex Sets of
  Distributions
  Robust Bayesian inference is the calculation of posterior probability bounds
given perturbations in a probabilistic model. This paper focuses on
perturbations that can be expressed locally in Bayesian networks through convex
sets of distributions. Two approaches for combination of local models are
considered. The first approach takes the largest set of joint distributions
that is compatible with the local sets of distributions; we show how to reduce
this type of robust inference to a linear programming problem. The second
approach takes the convex hull of joint distributions generated from the local
sets of distributions; we demonstrate how to apply interior-point optimization
methods to generate posterior bounds and how to generate approximations that
are guaranteed to converge to correct posterior bounds. We also discuss
calculation of bounds for expected utilities and variances, and global
perturbation models.
