Statistic Seminar – Monday, February 12, 2018
Department of Statistics and Biostatistics
Title: Confidence Distribution (CD) and Approximate Computing for Frequentist Inference
Abstract: A confidence distribution (CD) is a sample-dependent distribution function that can serve as a distribution estimate, contrasting with a point or interval estimate, of an unknown parameter. It can represent confidence intervals (regions) of all levels for the parameter. It is to provide “simple and interpretable summaries of what can reasonably be learned from data,” as well as meaningful answers for all questions in statistical inference. An emerging theme is “Any statistical approach, regardless of being frequentist, fiducial or Bayesian, can potentially be unified under the concept of confidence distributions, as long as it can be used to derive confidence intervals of all levels, exactly or asymptotically.”
In this talk, we articulate the logic behind the CD developments and also, to illustrate its utility for methodology development, present a likelihood-free approximate computing method, called Approximate CD computing (ACC). ACC is a frequentist analog of Approximate Bayesian computing (ABC), a Bayesian approximate computing method that has grown increasingly popular since early applications in population genetics. However, complications arise in the theoretical justification for Bayesian inference when using ABC with a non-sufficient summary statistic. We seek to re-frame ABC within a frequentist context and justify its performance by the frequency coverage rate. In doing so, we develop the ACC method and provide theoretical support for the use of non-sufficient summary statistics in likelihood-free methods. Furthermore, we demonstrate that ACC extends the scope of ABC to include data-dependent priors without damaging the inferential integrity but to increase computing efficiency. We will supplement the theory with both simulation and real data analysis to illustrate the benefits of the ACC method, namely the potential for broader applications than ABC and the increased computing speed compared to ABC.