Discounted Bayesian search problems with unknown detection probabilities

This paper considers three discrete-time discounted Bayesian search problems with an unknown number of objects and uncertainty about the distribution of the objects among the boxes. Moreover, it admits uncertainty about the detection probabilities. The goal is to determine a policy which finds (dependent on the search problem) at least one object or all objects with minimal expected total cost. The paper gives sufficient conditions for the optimality of the greedy policy which has been introduced in Liebig/Rieder. For some examples in which the greedy policy is not optimal it derives a bound for the error.