Statistical estimation of the number of minima in a function with a finite number of variables

Abstract

The statistical estimate of the number of local minima in an energy function obtained by a finite random sampling, due to Walker and Walstedt (W%), is clarified. In particular, it is found that an additional assumption, of the Bayesian type, seems to be needed, and the consequences are discussed in some detail. The relaxation of the explicit assumption of W%', that each minimum has equal a priori probability of being sampled, is discussed briefly.