A Short Survey on Bounding the Union Probability using Partial Information
Jun Yang, Fady Alajaji, Glen Takahara
TL;DR
This survey reviews methods for bounding the union probability of multiple events using partial information, providing new proofs and insights into existing bounds like Gallot–Kounias.
Contribution
It offers a comprehensive overview of bounds on union probabilities, introduces new proofs, and provides novel observations on the Gallot–Kounias bound.
Findings
New proofs for existing bounds
Enhanced understanding of Gallot–Kounias bound
Comparison of bounds using partial information
Abstract
This is a short survey on existing upper and lower bounds on the probability of the union of a finite number of events using partial information given in terms of the individual or pairwise event probabilities (or their sums). New proofs for some of the existing bounds are provided and new observations regarding the existing Gallot--Kounias bound are given.
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Taxonomy
TopicsProbability and Risk Models · Bayesian Modeling and Causal Inference · Risk and Portfolio Optimization