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| Preface | |
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| Preface to the First Edition | |
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| Preliminaries | |
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| Probability and Bayes' Theorem | |
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| Examples on Bayes' Theorem | |
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| Random variables | |
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| Several random variables | |
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| Means and variances | |
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| Exercises on Chapter | |
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| Bayesian inference for the normal distribution | |
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| Nature of Bayesian inference | |
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| Several normal observations with a normal prior | |
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| Dominant likelihoods | |
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| Locally uniform priors | |
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| Highest density regions | |
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| Normal variance | |
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| HDRs for the normal variance | |
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| The role of sufficiency | |
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| Conjugate prior distributions | |
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| The exponential family | |
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| Normal mean and variance both unknown | |
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| Conjugate joint prior for the normal distribution | |
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| Exercises on Chapter | |
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| Some other common distributions | |
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| The binomial distribution | |
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| Reference prior for the binomial likelihood | |
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| Jeffreys' rule | |
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| The Poisson distribution | |
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| The uniform distribution | |
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| Reference prior for the uniform distribution | |
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| The tramcar problem | |
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| The first digit problem; invariant priors | |
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| The circular normal distribution | |
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| Approximations based on the likelihood | |
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| Reference posterior distributions | |
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| Exercises on Chapter | |
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| Hypothesis testing | |
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| Hypothesis testing | |
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| One-sided hypothesis tests | |
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| Lindley's method | |
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| Point (or sharp) null hypotheses with prior information | |
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| Point null hypotheses for the normal distribution | |
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| The Doogian philosophy | |
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| Exercises on Chapter | |
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| Two-sample problems | |
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| Two-sample problems - both variances unknown | |
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| Variances unknown but equal | |
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| Variances unknown and unequal (Behrens-Fisher problem) | |
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| The Behrens-Fisher controversy | |
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| Inferences concerning a variance ratio | |
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| Comparison of two proportions; the 2 � 2 table | |
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| Exercises on Chapter | |
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| Correlation, regression and the analysis of variance | |
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| Theory of the correlation coefficient | |
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| Examples on the use of the correlation coefficient | |
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| Regression and the bivariate normal model | |
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| Conjugate prior for the bivariate regression model | |
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| Comparison of several means - the one way model | |
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| The two way layout | |
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| The general linear model | |
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| Exercises on Chapter | |
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| Other topics | |
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| The likelihood principle | |
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| The stopping rule principle | |
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| Informative stopping rules | |
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| The likelihood principle and reference priors | |
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| Bayesian decision theory | |
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| Bayes linear methods | |
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| Decision theory and hypothesis testing | |
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| Empirical Bayes methods | |
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| Exercises on Chapter | |
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| Hierarchical models | |
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| The idea of a hierarchical model | |
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| The hierarchical normal model | |
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| The baseball example | |
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| The Stein estimator | |
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| Bayesian analysis for an unknown overall mean | |
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| The general linear model revisited | |
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| Exercises on Chapter | |
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| The Gibbs sampler and other numerical methods | |
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| Introduction to numerical methods | |
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| The EM algorithm | |
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| Data augmentation by Monte Carlo | |
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| The Gibbs sampler | |
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| Rejection sampling | |
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| The Metropolis-Hastings algorithm | |
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| Introduction to WinBUGS and OpenBUGS | |
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| Generalized linear models | |
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| Exercises on Chapter | |
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| Some approximate methods | |
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| Bayesian importance sampling | |
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| Variational Bayesian methods: simple case | |
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| Variational Bayesian methods: general case | |
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| ABC : Approximate Bayesian Computation | |
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| Reversible Jump Markov Chain Monte Carlo | |
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| Exercises on Chapter | |
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| common statistical distributions | |
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| Normal distribution | |
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| Chi-squared distribution | |
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| Normal approximation to chi-squared | |
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| Gamma distribution | |
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| Inverse chi-squared distribution | |
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| Inverse chi distribution | |
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| Log chi-squared distribution | |
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| Student's t distribution | |
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| Normal/chi-squared distribution | |
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| Beta distribution | |
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| Binomial distribution | |
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| Poisson distribution | |
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| Negative binomial distribution | |
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| Hypergeometric distribution | |
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| Uniform distribution | |
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| Pareto distribution | |
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| Circular normal distribution | |
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| Behrens' distribution | |
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| Snedecor's F distribution | |
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| Fisher's z distribution | |
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| Cauchy distribution | |
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| The probability that one beta variable is greater than another | |
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| Bivariate normal distribution | |
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| Multivariate normal distribution | |
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| Distribution of the correlation coefficient | |
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| tables | |
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| Percentage points of the Behrens-Fisher distribution | |
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| Highest density regions for the chi-squared distribution | |
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| HDRs for the inverse chi-squared distribution | |
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| Chi-squared corresponding to HDRs for log chi-squared | |
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| Values of F corresponding to HDRs for log F | |
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| R programs | |
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| further reading | |
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| Robustness | |
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| Nonparametric methods | |
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| Multivariate estimation | |
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| Time series and forecasting | |
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| Sequential methods | |
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| Numerical methods | |
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| Bayesian Networks | |
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| General reading | |
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| References | |
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| Index | |