# A Model of Evidential Reasoning In a Hierarchical Hypothesis Space

### John Yen

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-86-277

December 1985

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1986/CSD-86-277.pdf

The Dempster-Shafer (D-S) theory of evidence suggests a coherent approach to aggregate evidence bearing on hierarchically related hypotheses. However, the representation of uncertain implications between evidence and hypotheses has been a serious difficulty in applications of the theory. We propose a model of evidential reasoning based on a modified D-S theory where the implication strengths are measured by conditional probabilities. Combining belief updates instead of belief functions using Dempster's rule is justified with clear assumptions, and it is consistent with Bayes theorem under the conditional independence assumption. Like the D-S theory, our model expresses degree of ignorance when there is not enough evidence to determine a precise belief function. The model is most appropriate for the problem areas where prior probabilities of the hierarchically related hypotheses are available.

BibTeX citation:

@techreport{Yen:CSD-86-277, Author = {Yen, John}, Title = {A Model of Evidential Reasoning In a Hierarchical Hypothesis Space}, Institution = {EECS Department, University of California, Berkeley}, Year = {1985}, Month = {Dec}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1985/6119.html}, Number = {UCB/CSD-86-277}, Abstract = {The Dempster-Shafer (D-S) theory of evidence suggests a coherent approach to aggregate evidence bearing on hierarchically related hypotheses. However, the representation of uncertain implications between evidence and hypotheses has been a serious difficulty in applications of the theory. We propose a model of evidential reasoning based on a modified D-S theory where the implication strengths are measured by conditional probabilities. Combining belief updates instead of belief functions using Dempster's rule is justified with clear assumptions, and it is consistent with Bayes theorem under the conditional independence assumption. Like the D-S theory, our model expresses degree of ignorance when there is not enough evidence to determine a precise belief function. The model is most appropriate for the problem areas where prior probabilities of the hierarchically related hypotheses are available.} }

EndNote citation:

%0 Report %A Yen, John %T A Model of Evidential Reasoning In a Hierarchical Hypothesis Space %I EECS Department, University of California, Berkeley %D 1985 %@ UCB/CSD-86-277 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1985/6119.html %F Yen:CSD-86-277