The Comparison of Approaches Used for Estimating Uncertain Probabilities

Oleg Uzhga-Rebrov,Galina Kuleshova,

doi:10.2478/itms-2013-0020

Oleg Uzhga-Rebrov, Galina Kuleshova,

Open Access

https://doi.org/10.2478/itms-2013-0020

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Abstract

Probabilistic estimates are numerical representations of chances of random event occurrence. The classical theory of probability is based on the assumption that probabilistic estimates are deterministic. If available initial data are sufficient, this kind of estimates can be really obtained. However, when such data are not available, probabilistic estimates become uncertain. This paper analyses and compares three widespread approaches to modelling uncertain estimates and provides practical recommendations on their use.

Highlights

The classical theory of probability postulates that the probabilities of random events have to be determined unambiguously
This postulate underlies all other operations on probabilities, e.g., calculation of probabilities for unions and intersections of the sets of random events, recalculation of the posterior probabilities according to Bayes’ theorem, probabilistic inference on the networks etc
One evident example could be estimating the safety of technical system operation

Summary

INTRODUCTION

The classical theory of probability postulates that the probabilities of random events have to be determined unambiguously This postulate underlies all other operations on probabilities, e.g., calculation of probabilities for unions and intersections of the sets of random events, recalculation of the posterior probabilities according to Bayes’ theorem, probabilistic inference on the networks etc. It is true that probabilities of relevant events can be determined unambiguously if sufficient initial information is available. One evident example could be estimating the safety of technical system operation. The probabilities of technical system component failures are evaluated on the basis of insufficient statistical information. The probability estimates of profit level earned through investing capital into securities, made on the basis of the available information, may become meaningless due to various fluctuations and upheavals in the financial market.

FUNDAMENTALS OF THE THEORY OF PROBABILITY EVALUATION

CONCEPTUAL PRINCIPLES OF UNCERTAIN PROBABILITIES

INTERVAL PROBABILITIES

A X the lower and the upper functions can be determined using these expressions:

A COMPARATIVE ANALYSIS OF THE APPROACHES