The Generalized Polynomial Tails Comparison Theorem and its consequences in Clinical Trials,   Luis Pericchi ,   University of Puerto Rico,  Fri, 18 March, 2011,   1:30 p.m. C-356


This theorem establishes the analytical behavior of any likelihood function with tails bounded by a polynomial when used with priors in the general class of location-scale densities, such as Normal, Cauchy, Student’s t or Double Exponential. The GPTC theorem was developed to understand the interaction between likelihoods and priors in Bayesian Statistics and it extends the theory of Regularly Verying Distributions. The consequences are far reaching. Essentially it allows evaluation of the behavior of statistical procedures in the presence of conflict between data and prior knowledge. We developed the theorem motivated by an application of clinical trials: i) If we are analyzing a clinical trial now and here, what should be the influence of a previous clinical trial there? ii) Clinical trial are contentious between pharmaceutical companies and researchers (optimistic priors) and regulatory agencies like FDA (skeptical priors), so there is always conflict. Robust priors allows a faster convergence between conflicting partners.