Robustness Analysis of Bayesian Networks with Finitely Generated Convex Sets of Distributions

Fabio Cozman
tech. report CMU-RI-TR-96-41, Robotics Institute, Carnegie Mellon University, January, 1997


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Abstract
This paper presents exact solutions and convergent approximations for inferences in Bayesian networks associated with finitely generated convex sets of distributions. Robust Bayesian inference is the calculation of bounds on posterior values given perturbations in a probabilistic model. The paper presents exact inference algorithms and analyzes the circumstances where exact inference becomes intractable. Two classes of algorithms for numeric approximations are developed through transformations on the original model. The first transformation reduces the robust inference problem to the estimation of probabilistic parameters in a Bayesian network. The second transformation uses Lavine's bracketing algorithm to generate a sequence of maximization problems in a Bayesian network. The analysis is extended to the \\epsilon-contaminated, the lower density bounded, the belief function, the sub-sigma, the density bounded, the total variation and the density ratio classes of distributions.

Notes
Sponsor: NASA
Grant ID: NAGW-1175
Number of pages: 20

Text Reference
Fabio Cozman, "Robustness Analysis of Bayesian Networks with Finitely Generated Convex Sets of Distributions," tech. report CMU-RI-TR-96-41, Robotics Institute, Carnegie Mellon University, January, 1997

BibTeX Reference
@techreport{Cozman_1997_433,
   author = "Fabio Cozman",
   title = "Robustness Analysis of Bayesian Networks with Finitely Generated Convex Sets of Distributions",
   booktitle = "",
   institution = "Robotics Institute",
   month = "January",
   year = "1997",
   number= "CMU-RI-TR-96-41",
   address= "Pittsburgh, PA",
}