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A Balanced Treatment of Bayesian and Frequentist Inference

Statistical Inference: An Integrated Approach, Second Edition presents an account of the Bayesian and frequentist approaches to statistical inference. Now with an additional author, this second edition places a more balanced emphasis on both perspectives than the first edition.

New to the Second Edition


New material on empirical Bayes and penalized likelihoods and their impact on regression models
Expanded material on hypothesis testing, method of moments, bias correction, and hierarchical models
More examples and exercises
More comparison between the approaches, including their similarities and differences
Designed for advanced undergraduate and graduate courses, the text thoroughly covers statistical inference without delving too deep into technical details. It compares the Bayesian and frequentist schools of thought and explores procedures that lie on the border between the two. Many examples illustrate the methods and models, and exercises are included at the end of each chapter.



Introduction

Information

The concept of probability

Assessing subjective probabilities

An example

Linear algebra and probability

Notation

Outline of the book

Elements of Inference

Common statistical models

Likelihood-based functions

Bayes theorem

Exchangeability

Sufficiency and exponential family

Parameter elimination

Prior Distribution

Entirely subjective specification

Specification through functional forms

Conjugacy with the exponential family

Non-informative priors

Hierarchical priors

Estimation

Introduction to decision theory

Bayesian point estimation

Classical point estimation

Empirical Bayes estimation

Comparison of estimators

Interval estimation

Estimation in the Normal model

Approximating Methods

The general problem of inference

Optimization techniques

Asymptotic theory

Other analytical approximations

Numerical integration methods

Simulation methods

Hypothesis Testing

Introduction

Classical hypothesis testing

Bayesian hypothesis testing

Hypothesis testing and confidence intervals

Asymptotic tests

Prediction

Bayesian prediction

Classical prediction

Prediction in the Normal model

Linear prediction

Introduction to Linear Models

The linear model

Classical estimation of linear models

Bayesian estimation of linear models

Hierarchical linear models

Dynamic linear models

Linear models with constraints

Sketched Solutions to Selected Exercises

List of Distributions

References

Index

Exercises appear at the end of each chapter.