Computer experimentation in applied probability

Abstract

This is a discussion of the place of empirical methods in the study of probability models. It is argued that, for models of great complexity, careful experimentation may be a legitimate source of factual information on the behavior of such models. The need for rigorous standards of empirical methodology and of appropriate reporting is stressed. A simple, but interesting question on the distribution of the maximal eigenvalue of positive matrices with random elements is used as an example of an experimental study. In the course of the discussion of that example, several operational rules of sound computer experimentation are stated.