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

2025/12/09 by Kizito Salako, Salako, Kizito
Computer Science · #Algebra over a field #Bayesian Modeling and Causal Inference #Calculus (dental) #Complexity and Algorithms in Graphs #Computability, Logic, AI Algorithms #Constructive #Dynamic programming #FOS: Mathematics #Mathematical proof #Primary 60E15 #Probability (math.PR) #Secondary 60-08

paper · pdf · doi:10.48550/arxiv.2512.09161

openalex publication_date 2025/12/09 · openalex created_date 2025/12/12 · openalex updated_date 2026/08/05

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.

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