On Bernoulli experiments with imprecise prior probabilities

This paper deals with a situation where the prior distribution in a Bayesian treatment of a Bernoulli experiment is not known precisely. Imprecision for Bernoulli experiments is discussed for the case where the prior densities are defined in the form of intervals of measures, and a simple model with conjugate imprecise prior densities is used for ease of calculation in case of updating. Attention is focussed on imprecision with regard to predictive probabilities. The main aim of the paper is an analysis of imprecision, emphasizing the important relation between information and imprecision. This paper contributes to the theory advocated by Walley (1991). Imprecision within the chosen model is compared to intuition, and it is shown that complete lack of prior information can be reasonably well represented. Key Words: Bayesian analysis, Bernoulli experiments, conjugate prior densities, imprecision, information, intervals of measures, predictive probabilities.