Bayesian network implementation of Levi's epistemic utility decision theory

Darryl Morrell, Eric Driver

Research output: Contribution to journalArticle

Abstract

Isaac Levi has proposed an epistemic decision rule that requires two convex sets of probability distributions: a set of credal probability distributions that represent a decision agent's state of knowledge, and a set of information-determining distributions that represent the decision agent's assessment of the informational value of various hypotheses. In this paper, we investigate the feasibility of using Bayesian network structures, in which conditional probability distributions are computed using local computations and conditional independence relationships, to implement Levi's decision rule. We find that Bayesian network update algorithms do not in general result in convex sets of distributions; however, Bayesian networks can compute sets of a posteriori extremal distributions from sets of a priori and conditional extremal distributions. We also show that Levi's decision rule gives the same answer when applied to arbitrary sets of credal and information-determining distributions as it gives when applied to the convex closure of those sets of distributions. Thus, implementation of Levi's decision rule using Bayesian network structures is feasible.

Original languageEnglish (US)
Pages (from-to)127-149
Number of pages23
JournalInternational Journal of Approximate Reasoning
Volume13
Issue number2
DOIs
StatePublished - 1995

Fingerprint

Utility Theory
Decision Theory
Decision theory
Bayesian networks
Bayesian Networks
Decision Rules
Probability distributions
Probability Distribution
Network Structure
Convex Sets
Local Computation
Conditional Independence
Conditional probability
Conditional Distribution
Closure
Update
Arbitrary

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Applied Mathematics
  • Theoretical Computer Science

Cite this

Bayesian network implementation of Levi's epistemic utility decision theory. / Morrell, Darryl; Driver, Eric.

In: International Journal of Approximate Reasoning, Vol. 13, No. 2, 1995, p. 127-149.

Research output: Contribution to journalArticle

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