Statistical Inference: An Integrated Approach, Second Edition

Summary

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.

Table of Contents

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

Exercises appear at the end of each chapter.

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