# Unimodality, Independence Lead to NP-Hardness of Interval Probability Problems

Unimodality, Independence Lead to NP-Hardness of Interval Probability Problems In many real-life situations, we only have partial information about probabilities. This information is usually described by bounds on moments, on probabilities of certain events, etc. –i.e., by characteristics c(p) which are linear in terms of the unknown probabilities p j. If we know interval bounds on some such characteristics $$\underline{a}_i\leq c_i(p)\leq \bar{a}_i$$ , and we are interested in a characteristic c(p), then we can find the bounds on c(p) by solving a linear programming problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Unimodality, Independence Lead to NP-Hardness of Interval Probability Problems

, Volume 13 (3) – Dec 20, 2006
22 pages
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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2007 by Springer Science + Business Media B.V.
Subject
Mathematics; Numeric Computing; Mathematical Modeling and Industrial Mathematics; Approximations and Expansions; Computational Mathematics and Numerical Analysis
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1007/s11155-006-9031-4
Publisher site
See Article on Publisher Site

### Abstract

In many real-life situations, we only have partial information about probabilities. This information is usually described by bounds on moments, on probabilities of certain events, etc. –i.e., by characteristics c(p) which are linear in terms of the unknown probabilities p j. If we know interval bounds on some such characteristics $$\underline{a}_i\leq c_i(p)\leq \bar{a}_i$$ , and we are interested in a characteristic c(p), then we can find the bounds on c(p) by solving a linear programming problem.

### Journal

Reliable ComputingSpringer Journals

Published: Dec 20, 2006

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