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| Preface | |
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| Acknowledgments | |
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| List of abbreviations | |
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| List of symbols | |
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| List of figures | |
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| List of tables | |
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| Introduction | |
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| Motivating examples | |
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| Stochastic representation and the d operator | |
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| Definition of stochastic representation | |
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| More properties on the d operator | |
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| Beta and inverted beta distributions | |
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| Some useful identities and integral formulae | |
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| Partial-fraction expansion | |
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| Cambanis-Keener-Simons integral formulae | |
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| Hermite-Genocchi integral formula | |
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| The Newton-Raphson algorithm | |
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| Likelihood in missing-data problems | |
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| Missing-data mechanism | |
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| The expectation-maximization (EM) algorithm | |
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| The expectation/conditional maximization (ECM) algorithm | |
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| The EM gradient algorithm | |
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| Bayesian MDPs and inversion of Bayes' formula | |
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| The data augmentation (DA) algorithm | |
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| True nature of Bayesian MDP: inversion of Bayes' formula | |
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| Explicit solution to the DA integral equation | |
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| Sampling issues in Bayesian MDPs | |
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| Basic statistical distributions | |
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| Discrete distributions | |
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| Continuous distributions | |
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| Dirichlet distribution | |
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| Definition and basic properties | |
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| Density function and moments | |
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| Stochastic representations and mode | |
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| Marginal and conditional distributions | |
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| Survival function and cumulative distribution function | |
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| Survival function | |
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| Cumulative distribution function | |
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| Characteristic functions | |
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| The characteristic function of u ∼ U(T<sub>n</sub>) | |
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| The characteristic function of v ∼ U(V<sub>n</sub>) | |
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| The characteristic function of a Dirichlet random vector | |
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| Distribution for linear function of a Dirichlet random vector | |
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| Density for linear function of v ∼ U(V<sub>n</sub>) | |
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| Density for linear function of u ∼ U(T<sub>n</sub>) | |
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| A unified approach to linear functions of variables and order statistics | |
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| Cumulative distribution function for linear function of a Dirichlet random vector | |
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| Characterizations | |
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| Mosimann's characterization | |
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| Darroch and Ratcliff's characterization | |
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| Characterization through neutrality | |
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| Characterization through complete neutrality | |
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| Characterization through global and local parameter independence | |
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| MLEs of the Dirichlet parameters | |
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| MLE via the Newton-Raphson algorithm | |
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| MLE via the EM gradient algorithm | |
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| Analyzing serum-protein data of Pekin ducklings | |
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| Generalized method of moments estimation | |
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| Method of moments estimation | |
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| Generalized method of moments estimation | |
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| Estimation based on linear models | |
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| Preliminaries | |
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| Estimation based on individual linear models | |
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| Estimation based on the overall linear model | |
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| Application in estimating ROC area | |
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| The ROC curve | |
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| The ROC area | |
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| Computing the posterior density of the ROC area | |
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| Analyzing the mammogram data of breast cancer | |
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| Grouped Dirichlet distribution | |
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| Three motivating examples | |
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| Density function | |
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| Basic properties | |
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| Marginal distributions | |
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| Conditional distributions | |
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| Extension to multiple partitions | |
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| Density function | |
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| Some properties | |
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| Marginal distributions | |
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| Conditional distributions | |
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| Statistical inferences: likelihood function with GDD form | |
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| Large-sample likelihood inference | |
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| Small-sample Bayesian inference | |
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| Analyzing the cervical cancer data | |
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| Analyzing the leprosy survey data | |
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| Statistical inferences: likelihood function beyond GDD form | |
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| Incomplete 2�2 contingency tables: the neurological complication data | |
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| Incomplete r � c contingency tables | |
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| Wheeze study in six cities | |
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| Discussion | |
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| Applications under nonignorable missing data mechanism | |
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| Incomplete r � c tables: nonignorable missing mechanism | |
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| Analyzing the crime survey data | |
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| Nested Dirichlet distribution | |
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| Density function | |
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| Two motivating examples | |
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| Stochastic representation, mixed moments, and mode | |
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| Marginal distributions | |
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| Conditional distributions | |
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| Connection with exact null distribution for sphericity test | |
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| Large-sample likelihood inference | |
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| Likelihood with NDD form | |
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| Likelihood beyond NDD form | |
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| Comparison with existing likelihood strategies | |
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| Small-sample Bayesian inference | |
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| Likelihood with NDD form | |
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| Likelihood beyond NDD form | |
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| Comparison with the existing Bayesian strategy | |
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| Applications | |
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| Sample surveys with nonresponse: simulated data | |
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| Dental caries data | |
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| Competing-risks model: failure data for radio transmitter receivers | |
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| Sample surveys: two data sets for death penalty attitude | |
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| Bayesian analysis of the ultrasound rating data | |
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| A brief historical review | |
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| The neutrality principle | |
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| The short memory property | |
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| Inverted Dirichlet distribution | |
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| Definition through the density function | |
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| Density function | |
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| Several useful integral formulae | |
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| The mixed moment and the mode | |
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| Definition through stochastic representation | |
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| Marginal and conditional distributions | |
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| Cumulative distribution function and survival function | |
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| Cumulative distribution function | |
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| Survival function | |
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| Characteristic function | |
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| Univariate case | |
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| The confluent hypergeometric function of the second kind | |
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| General case | |
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| Distribution for linear function of inverted Dirichlet vector | |
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| Introduction | |
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| The distribution of the sum of independent gamma variates | |
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| The case of two dimensions | |
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| Connection with other multivariate distributions | |
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| Connection with the multivariate t distribution | |
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| Connection with the multivariate logistic distribution | |
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| Connection with the multivariate Pareto distribution | |
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| Connection with the multivariate Cook-Johnson distribution | |
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| Applications | |
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| Bayesian analysis of variance in a linear model | |
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| Confidence regions for variance ratios in a linear model with random effects | |
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| Dirichlet-multinomial distribution | |
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| Probability mass function | |
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| Motivation | |
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| Definition via a mixture representation | |
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| Beta-binomial distribution | |
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| Moments of the distribution | |
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| Marginal and conditional distributions | |
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| Marginal distributions | |
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| Conditional distributions | |
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| Multiple regression | |
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| Conditional sampling method | |
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| The method of moments estimation | |
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| Observations and notations | |
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| The traditional moments method | |
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| Mosimann's moments method | |
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| The method of maximum likelihood estimation | |
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| The Newton-Raphson algorithm | |
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| The Fisher scoring algorithm | |
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| The EM gradient algorithm | |
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| Applications | |
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| The forest pollen data | |
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| The teratogenesis data | |
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| Testing the multinomial assumption against the Dirichlet-multinomial alternative | |
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| The likelihood ratio statistic and its null distribution | |
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| The C(�) test | |
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| Two illustrative examples | |
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| Truncated Dirichlet distribution | |
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| Density function | |
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| Definition | |
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| Truncated beta distribution | |
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| Motivating examples | |
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| Case A: matrix � is known | |
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| Case B: matrix � is unknown | |
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| Case C: matrix � is partially known | |
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| Conditional sampling method | |
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| Consistent convex polyhedra | |
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| Marginal distributions | |
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| Conditional distributions | |
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| Generation of random vector from a truncated Dirichlet distribution | |
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| Gibbs sampling method | |
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| The constrained maximum likelihood estimates | |
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| Application to misclassification | |
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| Screening test with binary misclassifications | |
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| Case-control matched-pair data with polytomous misclassifications | |
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| Application to uniform design of experiment with mixtures | |
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| Other related distributions | |
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| The generalized Dirichlet distribution | |
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| Density function | |
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| Statistical inferences | |
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| Analyzing the crime survey data | |
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| Choice of an effective importance density | |
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| The hyper-Dirichlet distribution | |
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| Motivating examples | |
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| Density function | |
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| The scaled Dirichlet distribution | |
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| Two motivations | |
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| Stochastic representation and density function | |
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| Some properties | |
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| The mixed Dirichlet distribution | |
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| Density function | |
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| Stochastic representation | |
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| The moments | |
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| Marginal distributions | |
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| Conditional distributions | |
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| The Liouville distribution | |
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| The generalized Liouville distribution | |
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| Some useful S-plus Codes | |
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| References | |
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| Author index | |
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| Subject index | |