| Description |
1 online resource (442 pages) |
| Series |
Chapman and Hall/CRC Biostatistics Ser |
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Chapman and Hall/CRC Biostatistics Ser
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| Contents |
Cover; Half Title; Title Page; Copyright Page; Contents; I: General Overview; 1 Generalized Linear Models: A Bayesian View; 1. Introduction; 2. GLMs and Bayesian Models; 2.1 GLMs; 2.2 Bayesian Models; 3. Propriety of Posteriors; 4. Semiparametric GLMs; 5. Overdispersed Generalized Linear Models; 6. Model Determination Approaches; 2 Random Effects in Generalized Linear Mixed Models (GLMMs); 1. Introduction; 2. The Model; 3. Random Effects; 3.1 Independent Random Effects; 3.2 Correlated Random Effects; 3.3 Strongly Correlated Random Effects; 3.4 Some Examples of the AR(d) Model |
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4. Hierarchical GLMMs5. Bayesian Computation; 3 Prior Elicitation and Variable Selection for Generalized Linear Mixed Models; 1. Introduction; 2. Generalized Linear Mixed Models; 2.1 Models; 2.2 The Prior Distributions; 2.3 Propriety of the Prior Distribution; 2.4 Specifying the Hyperparameters; 2.5 The Posterior Distribution and its Computation; 3. Bayesian Variable Selection; 4. Pediatric Pain Data; 5. Discussion; II: Extending the GLMs; 4 Dynamic Generalized Linear Models; 1. Introduction; 2. Dynamic linear models; 3. Definition and first approaches to inference; 3.1 Linear Bayes Approach |
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3.2 Piecewise Linear Approximation3.3 Posterior Mode Estimation; 3.4 Other Approaches and Models; 4. MCMC-based Approaches; 4.1 Gibbs Sampling; 4.2 Metropolis-Hasting Algorithm; 5. Applications; 5.1 Application 1: Meningococcic Meningitis; 5.2 Application 2: Respiratory Diseases and Level of Pollutants; 6. Discussions and Extensions; 5 Bayesian Approaches for Overdispersion in Generalized Linear Models; 1. Introduction; 2. Classes of Overdispersed General Linear Models; 3. Fitting OGLM in the Parametric Bayesian Framework; 3.1 Model Fitting; 3.2 Example: Overdispersed Poisson Regression Model |
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3.3 Model Determination for Parametric OGLM's4. Modeling Overdispersion in the Nonparametric Bayesian Framework; 4.1 Fitting DP Mixed GLM and OGLM; 4.2 Example: Overdispersed Binomial Regression Model; 4.3 Model Determination for Dirichlet Process Mixed Models; 5. Overdispersion in Multistage GLM; 6 Bayesian Generalized Linear Models for Inference About Small Areas; 1. Introduction; 2. Logistic Regression Models; 3. Poisson Regression Models; 4. Computational Issues; 5. Models for the U.S. Mortality Data; 6. Challenges in Small Area Estimation; 7. Concluding Remarks |
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III: Categorical and Longitudinal Data7 Bayesian Methods for Correlated Binary Data; 1. Introduction; 2. The Multivariate Probit Model; 2.1 Dependence Structures; 2.2 Student-t Specification; 2.3 Estimation of the MVP Model; 2.4 Fitting of the Multivariate t-link Model; 3. Longitudinal Binary Data; 3.1 Probit (or logit) Normal Model; 3.2 Inference; 3.3 Computations for the Probit-Normal Model; 3.4 Binary Response Hierarchical Model; 3.5 Other Models; 4. Comparison of Alternative Models; 4.1 Likelihood Ordinate; 4.2 Posterior Ordinate; 5. Concluding Remarks; 6. Appendix; 6.1 Algorithm 1 |
| Notes |
6.2 Algorithm 2 |
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Print version record |
| Subject |
Linear models (Statistics)
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Bayesian statistical decision theory.
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Linear Models
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Bayes Theorem
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Bayesian statistical decision theory
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Linear models (Statistics)
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Lineares Modell
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Lineaire modellen.
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Methode van Bayes.
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Modèles linéaires (statistique)
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Statistique bayésienne.
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| Form |
Electronic book
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| Author |
Ghosh, Sujit K
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Mallick, Bani K
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| ISBN |
9781482293456 |
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1482293455 |
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