Optimal Stopping Regions with Islands and Peninsulas

Abstract

An urn contains a known number of balls, an unknown number $R$ of which are red. Sequential sampling with replacement is possible and cost is proportional to sample size. The objective is to estimate $R$ with 0-1 loss, given that a priori $R$ has a discrete uniform distribution. It is shown that optimal stopping regions may be disconnected and composed of islands and peninsulas.