Statistical Inference : An Integrated Approach, Second Edition book cover
2nd Edition

Statistical Inference
An Integrated Approach, Second Edition

ISBN 9781439878804
Published September 3, 2014 by Chapman and Hall/CRC
385 Pages 34 B/W Illustrations

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Book Description

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

    The concept of probability
    Assessing subjective probabilities
    An example
    Linear algebra and probability
    Outline of the book

    Elements of Inference
    Common statistical models
    Likelihood-based functions
    Bayes theorem
    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

    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
    Classical hypothesis testing
    Bayesian hypothesis testing
    Hypothesis testing and confidence intervals
    Asymptotic tests

    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



    Exercises appear at the end of each chapter.

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