Bayesian data analysis - Gelman, Andrew (London ; New York : Chapman & Hall, 1995)
Bayesian Data Analysis is a comprehensive treatment of the statistical analysis of data from a Bayesian perspective. Modern computational tools are emphasized, and inferences are typically obtained using computer simulations.
The principles of Bayesian analysis are described with an emphasis on practical rather than theoretical issues, and illustrated using actual data. A variety of models are considered, including linear regression, hierarchical (random effects) models, robust models, generalized linear models and mixture models.
Two important and unique features of this text are thorough discussions of the methods for checking Bayesian models and the role of the design of data collection in influencing Bayesian statistical analysis. Issues of data collection, model formulation, computation, model checking and sensitivity analysis are all considered. The student or practising statistician will find that there is guidance on all aspects of Bayesian data analysis.
1. Background -- 2. Single-parameter models -- 3. Introduction to multiparameter models -- 4. Large-sample inference and connections to standard statistical methods -- 5. Hierarchical models -- 6. Model checking and sensitivity analysis -- 7. Study design in Bayesian analysis -- 8. Introduction to regression models -- 9. Approximations based on posterior modes -- 10. Posterior simulation and integration -- 11. Markov chain simulation -- 12. Models for robust inference and sensitivity analysis -- 13. Hierarchical linear models -- 14. Generalized linear models -- 15. Multivariate models -- 16. Mixture models -- 17. Models for missing data -- 18. Concluding advice -- A Standard probability distributions -- B Outline of proofs of asymptotic theorems.
Includes Index.
Keywords: Bayesian statistical decision theory; Mathematical statistics