Constructive Proofs of Generalized Boole--Frechet Bounds: A Dynamic Programming Approach

TL;DR

This paper introduces a dynamic programming method to constructively derive generalized Boole--Frechet bounds, providing sharp probability bounds for compound events based on atomic event probabilities.

Contribution

It presents a novel dynamic programming approach for constructing generalized Boole--Frechet bounds, enhancing the ability to compute sharp probability bounds.

Findings

Provides a constructive method for bounds calculation

Improves computational efficiency of bounds derivation

Applicable to complex probability scenarios

Abstract

Extensions of the Boole--Frechet inequalities give sharp bounds for the probabilities of compound events, particularly when only the probabilities of atomic events (that make up the compound events) are known. We present a constructive approach to obtaining generalized Boole--Frechet bounds using dynamic programming.