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BL
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| Record Number
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640411
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dltt
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| Main Entry
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Lee, Peter M.
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| Title & Author
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Bayesian statistics : : an introduction /\ Peter M. Lee
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| Edition Statement
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4th ed
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4th ed
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| Page. NO
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1 online resource (xxiii, 462 pages)
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| ISBN
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9781118359754
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: 1118359755
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1118359755
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9781118359761
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1118359763
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9781118359778
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1118359771
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9781118332573
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9781118166406
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: 1118332571
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: 9781118332573
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: 9781280775765
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: 1280775769
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| Bibliographies/Indexes
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Includes bibliographical references and index
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| Contents
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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
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| Abstract
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"--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"--
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| Subject
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Bayesian statistical decision theory.
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| LC Classification
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QA279.5.L44 2012
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