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Bayesian statistics : an introduction /

"--Presents extensive examples throughout the book to complement the theory presented. Includes significant new material on recent techniques such as variational methods, importance sampling, approximate computation and reversible jump MCMC"--

Detalles Bibliográficos
Clasificación:	Libro Electrónico
Autor principal:	Lee, Peter M.
Formato:	Electrónico eBook
Idioma:	Inglés
Publicado:	Chichester, West Sussex ; Hoboken, N.J. : Wiley, 2012.
Edición:	4th ed.
Temas:	Bayesian statistical decision theory. Théorie de la décision bayésienne. MATHEMATICS > Probability & Statistics > Bayesian Analysis.
Acceso en línea:	Texto completo (Requiere registro previo con correo institucional)

Tabla de Contenidos:

Note continued: 7.3. Informative stopping rules
7.3.1. An example on capture and recapture of fish
7.3.2. Choice of prior and derivation of posterior
7.3.3. The maximum likelihood estimator
7.3.4. Numerical example
7.4. The likelihood principle and reference priors
7.4.1. The case of Bernoulli trials and its general implications
7.4.2. Conclusion
7.5. Bayesian decision theory
7.5.1. The elements of game theory
7.5.2. Point estimators resulting from quadratic loss
7.5.3. Particular cases of quadratic loss
7.5.4. Weighted quadratic loss
7.5.5. Absolute error loss
7.5.6. Zero-one loss
7.5.7. General discussion of point estimation
7.6. Bayes linear methods
7.6.1. Methodology
7.6.2. Some simple examples
7.6.3. Extensions
7.7. Decision theory and hypothesis testing
7.7.1. Relationship between decision theory and classical hypothesis testing
7.7.2.Composite hypotheses
7.8. Empirical Bayes methods
7.8.1. Von Mises' example
7.8.2. The Poisson case
7.9. Exercises on Chapter 7
8. Hierarchical models
8.1. The idea of a hierarchical model
8.1.1. Definition
8.1.2. Examples
8.1.3. Objectives of a hierarchical analysis
8.1.4. More on empirical Bayes methods
8.2. The hierarchical normal model
8.2.1. The model
8.2.2. The Bayesian analysis for known overall mean
8.2.3. The empirical Bayes approach
8.3. The baseball example
8.4. The Stein estimator
8.4.1. Evaluation of the risk of the James-Stein estimator
8.5. Bayesian analysis for an unknown overall mean
8.5.1. Derivation of the posterior
8.6. The general linear model revisited
8.6.1. An informative prior for the general linear model
8.6.2. Ridge regression
8.6.3.A further stage to the general linear model
8.6.4. The one way model
8.6.5. Posterior variances of the estimators
8.7. Exercises on Chapter 8
9. The Gibbs sampler and other numerical methods
9.1. Introduction to numerical methods
9.1.1. Monte Carlo methods
9.1.2. Markov chains
9.2. The EM algorithm
9.2.1. The idea of the EM algorithm
9.2.2. Why the EM algorithm works
9.2.3. Semi-conjugate prior with a normal likelihood
9.2.4. The EM algorithm for the hierarchical normal model
9.2.5.A particular case of the hierarchical normal model
9.3. Data augmentation by Monte Carlo
9.3.1. The genetic linkage example revisited
9.3.2. Use of R
9.3.3. The genetic linkage example in R
9.3.4. Other possible uses for data augmentation
9.4. The Gibbs sampler
9.4.1. Chained data augmentation
9.4.2. An example with observed data
9.4.3. More on the semi-conjugate prior with a normal likelihood
9.4.4. The Gibbs sampler as an extension of chained data augmentation
9.4.5. An application to change-point analysis
9.4.6. Other uses of the Gibbs sampler
9.4.7. More about convergence
9.5. Rejection sampling
9.5.1. Description
9.5.2. Example
9.5.3. Rejection sampling for log-concave distributions
9.5.4.A practical example
9.6. The Metropolis-Hastings algorithm
9.6.1. Finding an invariant distribution
9.6.2. The Metropolis-Hastings algorithm
9.6.3. Choice of a candidate density
9.6.4. Example
9.6.5. More realistic examples
9.6.6. Gibbs as a special case of Metropolis-Hastings
9.6.7. Metropolis within Gibbs
9.7. Introduction to WinBUGS and OpenBUGS
9.7.1. Information about WinBUGS and OpenBUGS
9.7.2. Distributions in WinBUGS and OpenBUGS
9.7.3.A simple example using WinBUGS
9.7.4. The pump failure example revisited
9.7.5. DoodleBUGS
9.7.6.coda
9.7.7.R2WinBUGS and R2OpenBUGS
9.8. Generalized linear models
9.8.1. Logistic regression
9.8.2.A general framework
9.9. Exercises on Chapter 9
10. Some approximate methods
10.1. Bayesian importance sampling
10.1.1. Importance sampling to find HDRs
10.1.2. Sampling importance re-sampling
10.1.3. Multidimensional applications
10.2. Variational Bayesian methods: simple case
10.2.1. Independent parameters
10.2.2. Application to the normal distribution
10.2.3. Updating the mean
10.2.4. Updating the variance
10.2.5. Iteration
10.2.6. Numerical example
10.3. Variational Bayesian methods: general case
10.3.1.A mixture of multivariate normals
10.4. ABC: Approximate Bayesian Computation
10.4.1. The ABC rejection algorithm
10.4.2. The genetic linkage example
10.4.3. The ABC Markov Chain Monte Carlo algorithm
10.4.4. The ABC Sequential Monte Carlo algorithm
10.4.5. The ABC local linear regression algorithm
10.4.6. Other variants of ABC
10.5. Reversible jump Markov chain Monte Carlo
10.5.1. RJMCMC algorithm
10.6. Exercises on Chapter 10
Appendix A Common statistical distributions
A.1. Normal distribution
A.2. Chi-squared distribution
A.3. Normal approximation to chi-squared
A.4. Gamma distribution
A.5. Inverse chi-squared distribution
A.6. Inverse chi distribution
A.7. Log chi-squared distribution
A.8. Student's t distribution
A.9. Normal/chi-squared distribution
A.10. Beta distribution
A.11. Binomial distribution
A.12. Poisson distribution
A.13. Negative binomial distribution
A.14. Hypergeometric distribution
A.15. Uniform distribution
A.16. Pareto distribution
A.17. Circular normal distribution
A.18. Behrens' distribution
A.19. Snedecor's F distribution
A.20. Fisher's z distribution
A.21. Cauchy distribution
A.22. The probability that one beta variable is greater than another
A.23. Bivariate normal distribution
A.24. Multivariate normal distribution
A.25. Distribution of the correlation coefficient
Appendix B Tables
B.1. Percentage points of the Behrens-Fisher distribution
B.2. Highest density regions for the chi-squared distribution
B.3. HDRs for the inverse chi-squared distribution
B.4. Chi-squared corresponding to HDRs for log chi-squared
B.5. Values of F corresponding to HDRs for log F
Appendix C R programs
Appendix D Further reading
D.1. Robustness
D.2. Nonparametric methods
D.3. Multivariate estimation
D.4. Time series and forecasting
D.5. Sequential methods
D.6. Numerical methods
D.7. Bayesian networks
D.8. General reading.

Bayesian statistics : an introduction /

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