A Bayesian Variant of Shafer's Commonalities For Modelling Unforeseen Events

TL;DR

This paper introduces a Bayesian approach to model unforeseen events by integrating Shafer's commonalities, aiming to reconcile Bayesian probability with Shafer's belief theory in decision-making under uncertainty.

Contribution

It develops a Bayesian variant of Shafer's commonalities, enabling the inclusion of unforeseen events in expected utility theory.

Findings

Bayesian variant of Shafer's commonalities models unforeseen events.

Unified framework for Bayesian probability and Shafer's belief theory.

Enhanced decision analysis incorporating unforeseen events.

Abstract

Shafer's theory of belief and the Bayesian theory of probability are two alternative and mutually inconsistent approaches toward modelling uncertainty in artificial intelligence. To help reduce the conflict between these two approaches, this paper reexamines expected utility theory-from which Bayesian probability theory is derived. Expected utility theory requires the decision maker to assign a utility to each decision conditioned on every possible event that might occur. But frequently the decision maker cannot foresee all the events that might occur, i.e., one of the possible events is the occurrence of an unforeseen event. So once we acknowledge the existence of unforeseen events, we need to develop some way of assigning utilities to decisions conditioned on unforeseen events. The commonsensical solution to this problem is to assign similar utilities to events which are similar. Implementing this commonsensical solution is equivalent to replacing Bayesian subjective probabilities over the space of foreseen and unforeseen events by random set theory probabilities over the space of foreseen events. This leads to an expected utility principle in which normalized variants of Shafer's commonalities play the role of subjective probabilities. Hence allowing for unforeseen events in decision analysis causes Bayesian probability theory to become much more similar to Shaferian theory.