2nd Edition

Statistical Inference An Integrated Approach, Second Edition

    386 Pages 34 B/W Illustrations
    by Chapman & Hall

    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.

      Biography

      Helio S. Migon (Universidade Federal do Rio de Janeiro, Brazil) (Author) , Dani Gamerman (Universidade Federal do Rio de Janeiro, Brazil) (Author) , Francisco Louzada (Universidade Federal de Sao Carlos, Brazil) (Author)