Lower Bounds for the Probability of a Union via Chordal Graphs
Klaus Dohmen
TL;DR
This paper introduces new lower bounds for the probability of a union of events using chordal graph structures to determine intersections, advancing probabilistic inequalities in combinatorial settings.
Contribution
It develops Bonferroni-type bounds based on the clique complex of chordal graphs, providing a novel approach to probabilistic union bounds.
Findings
New lower bounds for union probabilities established
Bounds are based on chordal graph clique complexes
Method improves existing probabilistic inequalities
Abstract
We establish new Bonferroni-type lower bounds for the probability of a union of finitely many events where the selection of intersections in the estimates is determined by the clique complex of a chordal graph.
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Topological and Geometric Data Analysis · Bayesian Modeling and Causal Inference