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    Cover
    Series
    Contents
    Preface
    Part I: Fundamentals of Bayesian Inference
    Chapter 1: Probability and Inference
    Chapter 2: Single-parameter Models
    Chapter 3: Introduction to Multiparameter Models
    Chapter 4: Asymptotics and Connections to non-Bayesian Approaches
    Chapter 5: Hierarchical Models
    Part II: Fundamentals of Bayesian Data Analysis
    Chapter 6: Model Checking
    Chapter 7: Evaluating, Comparing, and Expanding Models
    Chapter 8: Modeling Accounting for Data Collection
    Chapter 9: Decision Analysis
    Part III: Advanced Computation
    Chapter 10: Introduction to Bayesian Computation
    Chapter 11: Basics of Markov Chain Simulation
    Chapter 12: Computationally Efficient Markov Chain Simulation
    Chapter 13: Modal and Distributional Approximations
    Part IV: Regression Models
    Chapter 14: Introduction to Regression Models
    Chapter 15: Hierarchical Linear Models
    Chapter 16: Generalized Linear Models
    Chapter 17: Models for Robust Inference
    Chapter 18: Models for Missing Data
    Part V: Nonlinear and Nonparametric Models
    Chapter 19: Parametric Nonlinear Models
    Chapter 20: Basis Function Models
    Chapter 21: Gaussian Process Models
    Chapter 22: Finite Mixture Models
    Chapter 23: Dirichlet Process Models
    Appendix A: Standard Probability Distributions
    Appendix B: Outline of Proofs of Limit Theorems
    Appendix C: Computation in R and Stan
    References
    Back Cover
    Bayesian Data Analysis Third Edition K11900_FM.indd 1 10/1/13 4:18 PM
    CHAPMAN & HALL/CRC Texts in Statistical Science Series Series Editors Francesca Dominici, Harvard School of Public Health, USA Julian J. Faraway, University of Bath, UK Martin Tanner, Northwestern University, USA Jim Zidek, University of British Columbia, Canada Analysis of Failure and Survival Data P. J. Smith The Analysis of Time Series: An Introduction, Sixth Edition C. Chatfield Applied Bayesian Forecasting and Time Series Analysis A. Pole, M. West, and J. Harrison Applied Categorical and Count Data Analysis W. Tang, H. He, and X.M. Tu Applied Nonparametric Statistical Methods, Fourth Edition P. Sprent and N.C. Smeeton Applied Statistics: Handbook of GENSTAT Analyses E.J. Snell and H. Simpson Applied Statistics: Principles and Examples D.R. Cox and E.J. Snell Applied Stochastic Modelling, Second Edition B.J.T. Morgan Bayesian Data Analysis, Third Edition A. Gelman, J.B. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari, and D.B. Rubin Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians R. Christensen, W. Johnson, A. Branscum, and T.E. Hanson Bayesian Methods for Data Analysis, Third Edition B.P. Carlin and T.A. Louis Beyond ANOVA: Basics of Applied Statistics R.G. Miller, Jr. The BUGS Book: A Practical Introduction to Bayesian Analysis D. Lunn, C. Jackson, N. Best, A. Thomas, and D. Spiegelhalter A Course in Categorical Data Analysis T. Leonard A Course in Large Sample Theory T.S. Ferguson Data Driven Statistical Methods P. Sprent Decision Analysis: A Bayesian Approach J.Q. Smith Design and Analysis of Experiments with SAS J. Lawson Elementary Applications of Probability Theory, Second Edition H.C. Tuckwell Elements of Simulation B.J.T. Morgan Epidemiology: Study Design and Data Analysis, Third Edition M. Woodward Essential Statistics, Fourth Edition D.A.G. Rees Exercises and Solutions in Statistical Theory L.L. Kupper, B.H. Neelon, and S.M. O’Brien Exercises and Solutions in Biostatistical Theory L.L. Kupper, B.H. Neelon, and S.M. O’Brien Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models J.J. Faraway A First Course in Linear Model Theory N. Ravishanker and D.K. Dey Generalized Additive Models: An Introduction with R S. Wood Generalized Linear Mixed Models: Modern Concepts, Methods and Applications W. W. Stroup Graphics for Statistics and Data Analysis with R K.J. Keen Interpreting Data: A First Course in Statistics A.J.B. Anderson Introduction to General and Generalized Linear Models H. Madsen and P. Thyregod K11900_FM.indd 2 10/1/13 4:18 PM
    An Introduction to Generalized Linear Models, Third Edition A.J. Dobson and A.G. Barnett Introduction to Multivariate Analysis C. Chatfield and A.J. Collins Introduction to Optimization Methods and Their Applications in Statistics B.S. Everitt Introduction to Probability with R K. Baclawski Introduction to Randomized Controlled Clinical Trials, Second Edition J.N.S. Matthews Introduction to Statistical Inference and Its Applications with R M.W. Trosset Introduction to Statistical Limit Theory A.M. Polansky Introduction to Statistical Methods for Clinical Trials T.D. Cook and D.L. DeMets Introduction to Statistical Process Control P. Qiu Introduction to the Theory of Statistical Inference H. Liero and S. Zwanzig Large Sample Methods in Statistics P.K. Sen and J. da Motta Singer Linear Algebra and Matrix Analysis for Statistics S. Banerjee and A. Roy Logistic Regression Models J.M. Hilbe Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition D. Gamerman and H.F. Lopes Mathematical Statistics K. Knight Modeling and Analysis of Stochastic Systems, Second Edition V.G. Kulkarni Modelling Binary Data, Second Edition D. Collett Modelling Survival Data in Medical Research, Second Edition D. Collett Multivariate Analysis of Variance and Repeated Measures: A Practical Approach for Behavioural Scientists D.J. Hand and C.C. Taylor Multivariate Statistics: A Practical Approach B. Flury and H. Riedwyl Multivariate Survival Analysis and Competing Risks M. Crowder Nonparametric Methods in Statistics with SAS Applications O. Korosteleva Pólya Urn Models H. Mahmoud Practical Data Analysis for Designed Experiments B.S. Yandell Practical Longitudinal Data Analysis D.J. Hand and M. Crowder Practical Multivariate Analysis, Fifth Edition A. Afifi, S. May, and V.A. Clark Practical Statistics for Medical Research D.G. Altman A Primer on Linear Models J.F. Monahan Principles of Uncertainty J.B. Kadane Probability: Methods and Measurement A. O’Hagan Problem Solving: A Statistician’s Guide, Second Edition C. Chatfield Randomization, Bootstrap and Monte Carlo Methods in Biology, Third Edition B.F.J. Manly Readings in Decision Analysis S. French Sampling Methodologies with Applications P.S.R.S. Rao Stationary Stochastic Processes: Theory and Applications G. Lindgren Statistical Analysis of Reliability Data M.J. Crowder, A.C. Kimber, T.J. Sweeting, and R.L. Smith Statistical Methods for Spatial Data Analysis O. Schabenberger and C.A. Gotway K11900_FM.indd 3 10/1/13 4:18 PM
    Statistical Methods for SPC and TQM D. Bissell Statistical Methods in Agriculture and Experimental Biology, Second Edition R. Mead, R.N. Curnow, and A.M. Hasted Statistical Process Control: Theory and Practice, Third Edition G.B. Wetherill and D.W. Brown Statistical Theory: A Concise Introduction F. Abramovich and Y. Ritov Statistical Theory, Fourth Edition B.W. Lindgren Statistics for Accountants S. Letchford Statistics for Epidemiology N.P. Jewell Statistics for Technology: A Course in Applied Statistics, Third Edition C. Chatfield Statistics in Engineering: A Practical Approach A.V. Metcalfe Statistics in Research and Development, Second Edition R. Caulcutt Stochastic Processes: An Introduction, Second Edition P.W. Jones and P. Smith Survival Analysis Using S: Analysis of Time-to-Event Data M. Tableman and J.S. Kim The Theory of Linear Models B. Jørgensen Time Series Analysis H. Madsen Time Series: Modeling, Computation, and Inference R. Prado and M. West Understanding Advanced Statistical Methods P.H. Westfall and K.S.S. Henning K11900_FM.indd 4 10/1/13 4:18 PM
    Texts in Statistical Science Bayesian Data Analysis Third Edition Andrew Gelman John B. Carlin Hal S. Stern David B. Dunson Aki Vehtari Donald B. Rubin K11900_FM.indd 5 10/1/13 4:18 PM
    CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2014 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20131003 International Standard Book Number-13: 978-1-4398-9820-8 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid- ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or uti- lized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopy- ing, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
    Contents Preface Part I: Fundamentals of Bayesian Inference 1 Probability and inference 1.1 The three steps of Bayesian data analysis 1.2 General notation for statistical inference 1.3 Bayesian inference 1.4 Discrete probability examples: genetics and spell checking 1.5 Probability as a measure of uncertainty 1.6 Example of probability assignment: football point spreads 1.7 Example: estimating the accuracy of record linkage 1.8 1.9 Computation and software 1.10 Bayesian inference in applied statistics 1.11 Bibliographic note 1.12 Exercises Some useful results from probability theory 2 Single-parameter models Summarizing posterior inference Informative prior distributions 2.1 Estimating a probability from binomial data 2.2 Posterior as compromise between data and prior information 2.3 2.4 2.5 Estimating a normal mean with known variance 2.6 Other standard single-parameter models 2.7 Example: informative prior distribution for cancer rates 2.8 Noninformative prior distributions 2.9 Weakly informative prior distributions 2.10 Bibliographic note 2.11 Exercises 3 Introduction to multiparameter models 3.1 Averaging over ‘nuisance parameters’ 3.2 Normal data with a noninformative prior distribution 3.3 Normal data with a conjugate prior distribution 3.4 Multinomial model for categorical data 3.5 Multivariate normal model with known variance 3.6 Multivariate normal with unknown mean and variance 3.7 Example: analysis of a bioassay experiment 3.8 3.9 Bibliographic note 3.10 Exercises Summary of elementary modeling and computation vii xiii 1 3 3 4 6 8 11 13 16 19 22 24 25 27 29 29 32 32 34 39 42 47 51 55 56 57 63 63 64 67 69 70 72 74 78 78 79
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