On Uniform Covering, Adaptive Random Search and Raspberries

The problem of generating a random sample over a level set, called Uniform Covering, is considered. A variant is discussed of an algorithm known as Pure Adaptive Search which is a global optimisation ideal with a desirable complexity. The algorithm of Uniform Covering by Probabilistic Rejection is discussed as an approach to the practical realisation of PAS. Consequences for the complexity and practical performance in comparison to other algorithms are illustrate