Bayesian models for limiting dilution assay and group test data

Bayesian models are presented for determining posterior densities for the unknown proportion of positive samples in a population. The probability densities are used here for calculating point estimates and exact 100(1-alpha)% central credible sets. The models apply to limiting dilution assays or group tests, and are useful with even small sets of data. Calculations and graphs using group test data for gene transfer experiments and limiting dilution assay data for immunocompetency studies illustrate the models and results.