An Integrated Mathematical Statistics Primer: Objective Bayesian Construction, Frequentist Evaluation

Bayesian Statistics is typically taught, if at all, separately from conventional frequentist methods. It is becoming clear, however, that the emergence of powerful objective Bayesian methods (where the result, as in frequentist statistics, only depends on the assumed model and the observed data) provides a new unifying perspective on most established methods, and may be used in situations (e.g. hierarchical structures) where frequentist methods cannot. On the other hand, frequentist procedures provide mechanisms to evaluate and calibrate any statistical method. Hence, it may be the right time to consider an integrated approach to mathematical statistics, where objective Bayesian methods provide the inferential construction elements, and frequentist methods the necessary evaluations. The emphasis of this presentation will be on undergraduate courses on mathematical statistics, but the main ideas may also be applied to more basic introductory and service courses.