Martine Ceberio

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

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.

Computing Population Variance and Entropy under Interval Uncertainty: Linear-Time Algorithms

In statistical analysis of measurement results it is often necessary to compute the range

Interval-based robust statistical techniques for non-negative convex functions, with application to timing analysis of computer chips

[\underline V ,\,\overline V]

Determination of Human Gait Phase Using Fuzzy Inference

of the population variance

Speculative constraint processing with iterative revision for disjunctive answers

V = \frac{1}{n}\, \cdot \,\sum\limits_{i = 1}^n (x_i \, - \,E)^2 \,\left({\rm where}\,E = \frac{1}{n}\, \cdot \,\sum\limits_{i = 1}^n {x_i }\,\right)

Fast Multiplication of Interval Matrices (Interval Version of Strassen's Algorithm)

when we only know the intervals