Biased Samples from a Search and the Asymptotic Behaviour of Bayesian Models

Abstract

Consider a hidden population of N objects and a search in which different objects are discovered independently, with probabilities that depend on their values. This paper investigates the distribution of values in the population of discovered objects. It also studies the behaviour of a Bayesian model with a prior process, for the number N and the set of values in the hidden population, which consists of a mixture of Poisson processes. If N is large, the weights on different components in the mixture change in a coherent way during the search.