Table of Contents
Preface
1. Preliminaries
      1. Probability and Bayes' Theorem
      2. Examples on Bayes' Theorem
      3. Random variables
      4. Several random variables
      5. Means and variances
      6. Exercises on Chapter I
2. Bayesian Inference for the Normal Distribution
      1. Nature of Bayesian inference
      2. Normal prior and likelihood
      3. Several normal observations with a normal prior
      4. Dominant likelihoods
      5. Locally uniform priors
      6. Highest density regions (HDRs)
      7. Normal variance
      8. HDRs for the normal variance 
      9. The role of sufficiency
     10. Conjugate prior distributions
     11. The exponential family
     12. Normal mean and variance both unknown
     13. Conjugate joint prior for the normal
     14. Exercises on Chapter 2
3. Some Other Common Distributions
     1. The binomial distribution
     2. Reference prior for the binomial likelihood
     3. Jeffreys' rule
     4. The Poisson distribution
     5. The uniform distribution
     6. Reference prior for the uniform distribution
     7. The tramcar problem
     8. The first digit problem; invariant priors
     9. The circular normal distribution
    10. Approximations based on the likelihood
    11. Reference posterior distributions
    12. Exercises on Chapter 3
4. Hypothesis testing
     1. Hypothesis testing
     2. One-sided hypothesis tests
     3. Lindley's method
     4. Point null hypotheses with prior information
     5. Point null hypotheses (normal case)
     6. The Doogian philosophy
     7. Exercises on Chapter 4
5. Two-sample problems
    1. Two-sample problems-both variances unknown
    2. Variances unknown but equal
    3. Behrens-Fisher problem
    4. The Behrens-Fisher controversy
    5. Inferences concerning a variance ratio
    6. Comparison of two proportions; the 2x2 tabls
    7. Exercises on Chapter 5
6. Correlation, Regression and ANOVA 
     1. Theory of the correlation coefficient 
     2. Examples on correlation
     3. Regression and the bivariate normal model
     4. Conjugate prior for bivariate regression
     5. Comparison of several means-the one-way model
     6. The two way layout
     7. The general linear model
     8. Exercises on Chapter 6
7. Other Topics
     1. The likelihood principle
     2. The stopping rule principle 
     3. Informative stopping rules
     4. The likelihood principle and reference priors
     5. Bayesian decision theory
     6. Bayes linear methods
     7. Decsion theory and hypothesis testing
     8. Empirical Bayes methods
     9. Exercises on Chapter 7
8. Hierachical methods
     1. The idea of a hierachical method
     2. The hierachical normal model
     3. The baseball example
     4. The Stein estimator
     5. Bayesian analysis for an unknown overall mean
     6. The general linear model revisited
     7. Exercises on Chapter 8
9. The Gibbs Sampler
     1. Introduction to numerical methods 
     2. The EM algorithm
     3. Data augmentation by Monte Carlo
     4. The Gibbs sampler
     5. Rejection sampling
     6. The Metropolis-Hastings algorithm 
     7. Introduction to WinBUGS
     8. Generalized linear models
     9. Exercises on Chapter 9
A. Common Statistical Distributions
1. Normal distribution
2. Chi-squared distribution
3. Normal approximation to chi-squared
4. Gamma distribution
5. Inverse chi-squared distribution
6. Inverse chi distribution
7. Log chi-squared distribution
8. Student's t distribution
9. Normal/chi-squared distribution
10. Beta distribution
11. Binomial distribution
12. Poisson distribution
13. Negative binomial distribution
14. Hypergeometric distribution
15. Uniform distribution
16. Pareto distribution
17. Circular normal distribution
18. Behrens' distribution
19. Snedecor's F distribution
20. Fisher's z distribution
21. Cauchy distribution
22. Difference of beta variables
23. Bivariate normal distribution
24. Multivariate normal distribution
25. Distribution of the correlation coefficient
B. Tables
1. Percentage points of the Behrens-Fisher distribution
2. HDRs for the chi-squared distribution
3. HDRs for the inverse chi-squared distribution
4. Chi-squared forresponding to HDRs for log chi-squared
5. Values of F corresponding to HDRs for log F
C. R Programs
o Functions for HDRs and for Behrens' distribution
D. Further Reading
• References
• Index

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