Bayesian and Frequentist Regression Methods

Abstract

The past 25 years have seen great advances in both Bayesian and frequentist methods for data analysis. The most significant advance for the Bayesian approach has been the development of Markov chain Monte Carlo methods for estimating expectations with respect to the posterior, hence allowing flexible inference and routine implementation for a wide range of models. In particular, this development has led to the more widespread use of hierarchical models for dependent data. With respect to frequentist methods, estimating functions have emerged as a unifying approach for determining the properties of estimators. Generalized estimating equations provide a particularly important example of this methodology that allows inference for dependent data. The aim of this book is to provide a modern description of Bayesian and frequentist methods of regression analysis and to illustrate the use of these methods on real data. Many books describe one or the other of the Bayesian or frequentist approaches to regression modeling in different contexts, and many mathematical statistics texts describe the theory behind Bayesian and frequentist approaches without providing a detailed description of specific methods. References to such texts are given at the end of Chaps. 2 and 3. Bayesian and frequentist methods are not viewed here as competitive, but rather as complementary techniques, and in this respect this book has some uniqueness.