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- W2953231316 abstract "In this paper, lower bounds on the probability of a finite union of events are considered, i.e. $Pleft(bigcup_{i=1}^N A_iright)$, in terms of the individual event probabilities ${P(A_i), i=1,ldots,N}$ and the sums of the pairwise event probabilities, i.e., ${sum_{j:jneq i} P(A_icap A_j), i=1,ldots,N}$. The contribution of this paper includes the following: (i) in the class of all lower bounds that are established in terms of only the $P(A_i)$'s and $sum_{j:jneq i} P(A_icap A_j)$'s, the optimal lower bound is given numerically by solving a linear programming (LP) problem with $N^2-N+1$ variables; (ii) a new analytical lower bound is proposed based on a relaxed LP problem, which is at least as good as the bound due to Kuai, et al.; (iii) numerical examples are provided to illustrate the performance of the bounds." @default.
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- W2953231316 date "2014-01-21" @default.
- W2953231316 modified "2023-09-27" @default.
- W2953231316 title "Lower Bounds on the Probability of a Finite Union of Events" @default.
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- W2953231316 doi "https://doi.org/10.48550/arxiv.1401.5543" @default.
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