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Interval approach challenges Monte Carlo simulation

Интервальный подход составляет конкуренцию моделированию методом Монте-Карло

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Reliable Computing

Abstract

Intervals are used to represent imprecise numerical values. Modelling uncertain values with precise bounds without considering their probability distribution is infeasible in many applications. As a solution, this paper proposes the use of probability density functions instead of intervals; we consider evaluation of an arithmetical function of random variables. Since the result density cannot in general be solved algebraically, an interval method for determining itsguaranteed bounds is developed. This possibility challenges traditional Monte Carlo methods in which only stochastic characterizations for the result distribution, such as confidence bounds for fractiles, can be determined.

Abstract

Интервалы используются для ¶rt;редставления неточных численных значений. однако моделирование неточных величин интервалами с точными грани¶rt;ами без учета рас¶rt;ределений вероятности этих величин во многих случаях неприемлемо. В качестве одного из ре¶rt;ений ¶rt;редложено ис¶rt;ользовать функ¶rt;ии плотности вероятности вместо интервалов. Рассматривается вычисление арифметической функ¶rt;ии случайных переменных. Поскольку ¶rt;лотность результата не может быть в об¶rt;ем случае получена алгебраическими методами, ¶rt;редлагается интервальный подход, даю¶rt;ий для этой величины грани¶rt;ы. Такой ¶rt;одход составляет конкурен¶rt;ию тради¶rt;ионным методам Монте-Карло, которые ¶rt;озволяют о¶rt;ределить только стохастические характеристики распределения результата, такие как доверительные грани¶rt;ы квантилей.

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Authors and Affiliations

  1. VTT Information Technology, P.O. Box 1201, 02044, Finland

    Janne Pesonen & Eero Hyvönen

Authors
  1. Janne Pesonen
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  2. Eero Hyvönen
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J. Pesonen, E. Hyvönen, 1996

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Pesonen, J., Hyvönen, E. Interval approach challenges Monte Carlo simulation. Reliable Comput 2, 155–160 (1996). https://doi.org/10.1007/BF02425918

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  • DOI: https://doi.org/10.1007/BF02425918

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