Grid-Based Histogram Arithmetic for the Probabilistic Analysis of Functions

Abstract

The selection of predefined analytic grids (partitions of the numeric ranges) to represent input and output functions as histograms has been proposed as a mechanism of approximation in order to control the tradeoff between accuracy and computation times in several areas ranging from simulation to constraint solving. In particular, the applicati on of interval methods for probabilistic function characterization has been shown to have advantages over other methods based on the simulati on of random samples. However, standard interval arithmetic has always been used for the computation steps. In this paper, we introduce an alternative approximate arithmetic aimed at controlling the cost of the interval operations. Its distinctive feature is that grids are taken into account by the operators. We apply the technique in the context of probability density functions in order to improve the accuracy of the probability estimates. Results show that this approach has advantages over existing approaches in some particular situations, although computation times tend to increase significantly when analyzing large functions.

The authors would like to thank the anonymous reviewers for their comments on previous versions of this paper. This work was funded in part by projects CICYT TIC97-0928 and TIC99-1151.