We discuss the application of Mixtures of Polya Trees to the semi-parametric estimation of mixture distributions in the context of assessing disease risk and of assessing the quality of a diagnostic procedure. Sampled individuals are either diseased or not and their status is unknown. Diagnostic procedures result in a score from a corresponding mixture distribution where the mixing parameter is the prevalence of the disease. Bayesian nonparametric and semi-parametric inferences are provided for Receiver Operating Characteristic curves and areas under them, as well as for prevalences. Covariates are modeled for the purpose of classification of individuals with unknown status as either "diseased" or "non-diseased" and are also incorporated as factors that might affect the quality of a diagnostic test. This work constitutes part of the dissertation of Adam Branscum, formerly at UC Davis and currently at the University of Kentucky.
Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.