Bayesian solutions to graduate admissions and related selection problems

A graduate program has to decide how many offers of admission to make to achieve a targeted number of acceptances for its entering class given uncertainty about how many will accept such offers. We first structure and solve selection problems under the assumption that probabilities associated with uncertain outcomes have assumed values using symmetric and asymmetric loss functions and show sensitivity of solutions to errors in these assumed values. Then we show how these problems can be solved when these probabilities are heterogeneous and have to be estimated from sample data.