### 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 language | English (US) |
---|---|

Pages (from-to) | 127-149 |

Number of pages | 23 |

Journal | International Journal of Approximate Reasoning |

Volume | 13 |

Issue number | 2 |

DOIs | |

State | Published - 1995 |

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### 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.

Research output: Contribution to journal › Article

*International Journal of Approximate Reasoning*, vol. 13, no. 2, pp. 127-149. https://doi.org/10.1016/0888-613X(95)00037-H

}

TY - JOUR

T1 - Bayesian network implementation of Levi's epistemic utility decision theory

AU - Morrell, Darryl

AU - Driver, Eric

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=58149321628&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58149321628&partnerID=8YFLogxK

U2 - 10.1016/0888-613X(95)00037-H

DO - 10.1016/0888-613X(95)00037-H

M3 - Article

AN - SCOPUS:58149321628

VL - 13

SP - 127

EP - 149

JO - International Journal of Approximate Reasoning

JF - International Journal of Approximate Reasoning

SN - 0888-613X

IS - 2

ER -