Dirty Pages of Logarithm Tables, Lifetime of the Universe, and (Subjective) Probabilities on Finite and Infinite Intervals

Dirty Pages of Logarithm Tables, Lifetime of the Universe, and (Subjective) Probabilities on... In many engineering problems, we want a physical characteristic y to lie within given range Y; e.g., for all possible values of the load x from 0 to x 0, the resulting stress y of a mechanical structure should not exceed a given value y 0. If no such design is possible, then, from the purely mathematical viewpoint, all possible designs are equally bad. Intuitively, however, a design for which y ≤ y 0 for all values x ∈ [0,0.99 ⋅ x 0] is “more probable” to work well than a design for which y ≤ y 0 only for the values x ∈ [0,0.5 ⋅ x 0]. In this paper, we describe an interval computations-related formalization for this subjective notion of probability. We show that this description is in good accordance with the empirical distribution of numerical data and with the problems related to estimating the lifetime of the Universe. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Dirty Pages of Logarithm Tables, Lifetime of the Universe, and (Subjective) Probabilities on Finite and Infinite Intervals

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Publisher
Springer Journals
Copyright
Copyright © 2004 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/B:REOM.0000015848.19449.12
Publisher site
See Article on Publisher Site

Abstract

In many engineering problems, we want a physical characteristic y to lie within given range Y; e.g., for all possible values of the load x from 0 to x 0, the resulting stress y of a mechanical structure should not exceed a given value y 0. If no such design is possible, then, from the purely mathematical viewpoint, all possible designs are equally bad. Intuitively, however, a design for which y ≤ y 0 for all values x ∈ [0,0.99 ⋅ x 0] is “more probable” to work well than a design for which y ≤ y 0 only for the values x ∈ [0,0.5 ⋅ x 0]. In this paper, we describe an interval computations-related formalization for this subjective notion of probability. We show that this description is in good accordance with the empirical distribution of numerical data and with the problems related to estimating the lifetime of the Universe.

Journal

Reliable ComputingSpringer Journals

Published: Oct 18, 2004

References

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