Bayesian-Analysis of Prevalence from the Results of Small Screening Samples
Bayesian analysis is applied to the number of cases screened positive to estimate the disease prevalence and to predict the number of future cases with disease. The analysis makes use of additional experimental information about the test's sensitivity and specificity and of prior information on the prevalence of disease. Prior and posterior probability distributions of disease prevalence are conjugate mixtures of Beta densities and can be expressed in exact algebraic form
Viana, M. A. G., Ramakrishnan, V., & Levy, P. (1993). Bayesian-Analysis of Prevalence from the Results of Small Screening Samples. Communications in Statistics-Theory and Methods, 22(2), 575-585.