Postscript

Abstract

The examples were collected haphazardly over the period 1983–1987. Current issues of the probability journals usually have one or two papers dealing with problems related to our heuristic, so it is hard to know when to stop adding examples. There are a few areas which, given unlimited time, I would have like to go into more deeply. My scattered examples on queueing are fairly trite; it would be interesting to study hard examples. The area of physics illustrated by Kramer’s problem (Example I14) seems a rich source of potential examples. There is a huge area of “data-snooping statistics” where you have a family of test statistics T(a) whose null distribution is known for fixed a, but where you use the test statistic T = T(a) for some a chosen using the data. Here one can hope to estimate the tail of the null distribution of T, similar to the Kolmogorov-Smirnov type statistics of Chapter J.