Towards Combining Probabilistic and Interval Uncertainty in Engineering Calculations: Algorithms for Computing Statistics under Interval Uncertainty, and Their Computational Complexity

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Gang Xiang
Scott A. Starks, The University of Texas at El PasoFollow
Luc Longpre, The University of Texas at El PasoFollow
Martine Ceberio, The University of Texas at El PasoFollow
Roberto Araiza, The University of Texas at El PasoFollow
J. Beck
R. Kandathi
A. Nayak
R. Torres
J. Hajagos

Publication Date

6-2005

Comments

UTEP-CS-04-20b.

Published in Reliable Computing, 2006, Vol. 12, No. 6, pp. 471-501.

Abstract

In many engineering applications, we have to combine probabilistic and interval uncertainty. For example, in environmental analysis, we observe a pollution level x(t) in a lake at different moments of time t, and we would like to estimate standard statistical characteristics such as mean, variance, autocorrelation, correlation with other measurements. In environmental measurements, we often only measure the values with interval uncertainty. We must therefore modify the existing statistical algorithms to process such interval data.

In this paper, we provide a survey of algorithms for computing various statistics under interval uncertainty and their computational complexity. The survey includes both known and new algorithms.