Extended Relative Maximum Likelihood Updating of Choquet Beliefs

TL;DR

This paper introduces an Extended Relative Maximum Likelihood (RML) updating rule for convex capacity-based beliefs, unifying classical updating rules like Dempster-Shafer and Fagin-Halpern as special cases.

Contribution

It extends RML updating to convex capacities, providing a unified framework that encompasses classical belief updating rules.

Findings

Extended RML generalizes classical updating rules.

Dempster-Shafer and Fagin-Halpern are special cases of Extended RML.

The framework offers a new approach for belief updating under ambiguity.

Abstract

Cheng(2021) proposes and characterizes Relative Maximum Likelihood (RML) updating rule when the ambiguous beliefs are represented by a set of priors. Relatedly, this note proposes and characterizes Extended RML updating rule when the ambiguous beliefs are represented by a convex capacity. Two classical updating rules for convex capacities, Dempster-Shafer (Shafer, 1976) and Fagin-Halpern rules (Fagin and Halpern, 1990) are included as special cases of Extended RML.