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Doing Bayesian Data Analysis : a Tutorial Introduction with R and BUGS.
There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis obtainable to a wide audience. Doing Bayesian Data Analysis, A Tutorial Introduction with R and BUGS provides an accessible approach to Bayesian data...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Burlington :
Elsevier Science,
2010.
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| Temas: | |
| Acceso en línea: | Texto completo (Requiere registro previo con correo institucional) |
Tabla de Contenidos:
- Front Cover; Doing Bayesian Data Analysis; Copyright page; Dedication; Table of contents; Chapter 1. This Book's Organization: Read Me First!; 1.1 Real People Can Read This Book; 1.2 Prerequisites; 1.3 The Organization of This Book; 1.4 Gimme Feedback (Be Polite); 1.5 Acknowledgments; Part 1: The Basics: Parameters, Probability, Bayes' Rule, and R; Chapter 2. Introduction: Models We Believe In; 2.1 Models of Observations and Models of Beliefs; 2.2 Three Goals for Inference from Data; 2.3 The R Programming Language; 2.4 Exercises; Chapter 3. What Is This Stuff Called Probability?
- 3.1 The Set of All Possible Events3.2 Probability: Outside or Inside the Head; 3.3 Probability Distributions; 3.4 Two-Way Distributions; 3.5 R Code; 3.6 Exercises; Chapter 4. Bayes' Rule; 4.1 Bayes' Rule; 4.2 Applied to Models and Data; 4.3 The Three Goals of Inference; 4.4 R Code; 4.5 Exercises; Part 2: All the Fundamentals Applied to Inferring a Binomial Proportion; Chapter 5. Inferring a Binomial Proportion via Exact Mathematical Analysis; 5.1 The Likelihood Function: Bernoulli Distribution; 5.2 A Description of Beliefs: The Beta Distribution; 5.3 Three Inferential Goals.
- 5.4 Summary: How to Do Bayesian Inference5.5 R Code; 5.6 Exercises; Chapter 6. Inferring a Binomial Proportion via Grid Approximation; 6.1 Bayes' Rule for Discrete Values of?; 6.2 Discretizing a Continuous Prior Density; 6.3 Estimation; 6.4 Prediction of Subsequent Data; 6.5 Model Comparison; 6.6 Summary; 6.7 R Code; 6.8 Exercises; Chapter 7. Inferring a Binomial Proportion via the Metropolis Algorithm; 7.1 A Simple Case of the Metropolis Algorithm; 7.2 The Metropolis Algorithm More Generally; 7.3 From the Sampled Posterior to the Three Goals; 7.4 MCMC in BUGS; 7.5 Conclusion; 7.6 R Code.
- 7.7 ExercisesChapter 8. Inferring Two Binomial Proportions via Gibbs Sampling; 8.1 Prior, Likelihood, and Posterior for Two Proportions; 8.2 The Posterior via Exact Formal Analysis; 8.3 The Posterior via Grid Approximation; 8.4 The Posterior via Markov Chain Monte Carlo; 8.5 Doing It with BUGS; 8.6 How Different Are the Underlying Biases?; 8.7 Summary; 8.8 R Code; 8.9 Exercises; Chapter 9. Bernoulli Likelihood with Hierarchical Prior; 9.1 A Single Coin from a Single Mint; 9.2 Multiple Coins from a Single Mint; 9.3 Multiple Coins from Multiple Mints; 9.4 Summary; 9.5 R Code; 9.6 Exercises.
- Chapter 10. Hierarchical Modeling and Model Comparison10.1 Model Comparison as Hierarchical Modeling; 10.2 Model Comparison in BUGS; 10.3 Model Comparison and Nested Models; 10.4 Review of Hierarchical Framework for Model Comparison; 10.5 Exercises; Chapter 11. Null Hypothesis Significance Testing; 11.1 NHST for the Bias of a Coin; 11.2 Prior Knowledge about the Coin; 11.3 Confidence Interval and Highest Density Interval; 11.4 Multiple Comparisons; 11.5 What a Sampling Distribution Is Good For; 11.6 Exercises; Chapter 12. Bayesian Approaches to Testing a Point ("Null") Hypothesis.