Bayesian and Frequentist Regression Methods Website

    Bayesian and Frequentist Regression Methods provides a modern account of both Bayesian and frequentist methods of regression analysis. Many texts cover one or the other of the approaches, but this is the most comprehensive combination of Bayesian and frequentist methods that exists in one place. The two philosophical approaches to regression methodology are featured here as complementary techniques, with theory and data analysis providing supplementary components of the discussion. In particular, methods are illustrated using a variety of data sets. The majority of the data sets are drawn from biostatistics but the techniques are generalizable to a wide range of other disciplines. While the philosophy behind each approach is discussed, the book is not ideological in nature and an emphasis is placed on practical application and it is shown that, in many situations, careful application of the respective approaches can lead to broadly similar conclusions. To use this text, the reader requires a basic understanding of calculus and liner algebra, and introductory courses in probability and statistical theory. The book is based on the author's experience teaching a graduate sequence in regression methods.

    An introductory chapter describes a number of motivating examples and discusses general issues that need consideration before a regression analysis is carried out. The book is then broken into four parts: I Inferential Approaches; II Independent Data; III Dependent Data; IV Nonparametric Modeling. Exercises reinforce the content of each chapter in the four parts of the book. The first two chapters of Part I provide general descriptions of the frequentist and Bayesian approaches to inference, with a particular emphasis on the rationale of each approach and a delineation of situations in which one or the other approach is preferable. The third chapter in Part I discusses model selection and hypothesis testing. Part II considers independent data and contains three chapters on linear models, general regression models (including generalized linear models) and binary data models. The two chapters of Part III consider dependent data with linear models and general regression models. Mixed models and generalized estimating equations are the approaches to inference that are emphasized. Part IV contains three chapters on nonparametric modeling with a concentration on spline and kernel methods. The examples and simulation studies of the text are almost exclusively carried out using the freely-available R software.

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    R Code for all Analyses and Figures

    Chapter 1: Introduction
    Part I: Inferential Approaches

    Chapter 2: Frequentist Inference
    Chapter 3: Bayesian Inference
    Chapter 4: Hypothesis Testing
    Part II: Independent Data

    Chapter 5: Linear Models
    Chapter 6: General Regression Models
    Chapter 7: Binary Data Models
    Part III: Dependent Data

    Chapter 8: Linear Models
    Chapter 9: General Regression Models

    Part IV: Nonparametric Modeling

    Chapter 10: Preliminaries for Nonparametric Modeling
    Chapter 11: Spline and Kernel Methods
    Chapter 12: Nonparametric Regression with Multiple Predictors