Coverart for item
The Resource Bayesian statistics : an introduction, Peter M. Lee

Bayesian statistics : an introduction, Peter M. Lee

Label
Bayesian statistics : an introduction
Title
Bayesian statistics
Title remainder
an introduction
Statement of responsibility
Peter M. Lee
Creator
Subject
Language
eng
Summary
"--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"--
Assigning source
Provided by publisher
Cataloging source
DLC
http://library.link/vocab/creatorName
Lee, Peter M
Dewey number
519.5/42
Index
index present
LC call number
QA279.5
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/subjectName
  • Bayesian statistical decision theory
  • MATHEMATICS
  • Bayesian statistical decision theory
Label
Bayesian statistics : an introduction, Peter M. Lee
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
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
Control code
778857701
Dimensions
unknown
Edition
4th ed.
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9781118359754
Lccn
2012008714
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
c
http://library.link/vocab/ext/overdrive/overdriveId
cl0500000223
Quality assurance targets
unknown
Reformatting quality
unknown
Specific material designation
remote
System control number
(OCoLC)778857701
Label
Bayesian statistics : an introduction, Peter M. Lee
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
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
Control code
778857701
Dimensions
unknown
Edition
4th ed.
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9781118359754
Lccn
2012008714
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
c
http://library.link/vocab/ext/overdrive/overdriveId
cl0500000223
Quality assurance targets
unknown
Reformatting quality
unknown
Specific material designation
remote
System control number
(OCoLC)778857701

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