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 (WW), 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 WW, that each minimum has equal a priori probability of being sampled, is discussed briefly.