Calculating the optimal sample size for binomial populations

This paper examines the problem of calculating the optimal sample size in the general case of a hypothesis test among many binomial proportions. The methodology follows the Bayesian point of view. Initially, an upper bound on the posterior risk is imposed. Since this is a pre-experimental process, a similar constraint is set on the probability of the unknown data not satisfying the previous condition. We examine the cases when the proportions are equal to a fixed or a random value and analyze the results for three binomial populations.