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Front Cover
Contents
Preface
Chapter 1 - The Golem of Prague
Chapter 2 - Small Worlds and Large Worlds
Chapter 3 - Sampling the Imaginary
Chapter 4 - Linear Models
Chapter 5 - Multivariate Linear Models
Chapter 6 - Overfitting, Regularization, and Information Criteria
Chapter 7 - Interactions
Chapter 8 - Markov Chain Monte Carlo
Chapter 9 - Big Entropy and the Generalized Linear Model
Chapter 10 - Counting and Classification
Chapter 11 - Monsters and Mixtures
Chapter 12 - Multilevel Models
Chapter 13 - Adventures in Covariance
Chapter 14 - Missing Data and Other Opportunities
Chapter 15 - Horoscopes
Endnotes
Bibliography
Back Cover
Statistics “Statistical Rethinking is a fun and inspiring look at the hows, whats, and whys of statistical modeling. This is a rare and valuable book that combines readable explanations, computer code, and active learning.” —Andrew Gelman, Columbia University Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds your knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today’s model-based statistics, the book pushes you to perform step-by-step calculations that are usually automated. This unique computational approach ensures that you understand enough of the details to make reasonable choices and interpretations in your own modeling work. The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation. Features • Integrates code fully into the main text, allowing you to implement the code and compare results Illustrates many concepts through worked data analysis examples • • Presents full explanations of the code, enabling you to diagnose and fix problems • Explains important and unusual programming tricks • Shows how the same mathematical statistical model can sometimes be implemented in different ways • Offers more detailed explanations of the mathematics in optional sections • Provides the R package on the author’s website and GitHub K23919 w w w . c r c p r e s s . c o m Texts in Statistical Science Statistical Rethinking A Bayesian Course with Examples in R and Stan Richard McElreath S t a t i s t i c a l R e t h i n k i n g M c E l r e a t h K23919_cover.indd 1 11/6/15 10:27 AM
Statistical Rethinking A Bayesian Course with Examples in R and Stan
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 Statistical Theory: A Concise Introduction F. Abramovich and Y. Ritov Practical Multivariate Analysis, Fifth Edition A. Afifi, S. May, and V.A. Clark Practical Statistics for Medical Research D.G. Altman Interpreting Data: A First Course in Statistics A.J.B. Anderson Introduction to Probability with R K. Baclawski Linear Algebra and Matrix Analysis for Statistics S. Banerjee and A. Roy Mathematical Statistics: Basic Ideas and Selected Topics, Volume I, Second Edition P. J. Bickel and K. A. Doksum Mathematical Statistics: Basic Ideas and Selected Topics, Volume II P. J. Bickel and K. A. Doksum Analysis of Categorical Data with R C. R. Bilder and T. M. Loughin Statistical Methods for SPC and TQM D. Bissell Introduction to Probability J. K. Blitzstein and J. Hwang Bayesian Methods for Data Analysis, Third Edition B.P. Carlin and T.A. Louis Second Edition R. Caulcutt The Analysis of Time Series: An Introduction, Sixth Edition C. Chatfield Introduction to Multivariate Analysis C. Chatfield and A.J. Collins Problem Solving: A Statistician’s Guide, Second Edition C. Chatfield Statistics for Technology: A Course in Applied Statistics, Third Edition C. Chatfield Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians R. Christensen, W. Johnson, A. Branscum, and T.E. Hanson Modelling Binary Data, Second Edition D. Collett Modelling Survival Data in Medical Research, Third Edition D. Collett Introduction to Statistical Methods for Clinical Trials T.D. Cook and D.L. DeMets Applied Statistics: Principles and Examples D.R. Cox and E.J. Snell Multivariate Survival Analysis and Competing Risks M. Crowder Statistical Analysis of Reliability Data M.J. Crowder, A.C. Kimber, T.J. Sweeting, and R.L. Smith An Introduction to Generalized Linear Models, Third Edition A.J. Dobson and A.G. Barnett Nonlinear Time Series: Theory, Methods, and Applications with R Examples R. Douc, E. Moulines, and D.S. Stoffer Introduction to Optimization Methods and Their Applications in Statistics B.S. Everitt Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models J.J. Faraway Linear Models with R, Second Edition J.J. Faraway A Course in Large Sample Theory T.S. Ferguson
Multivariate Statistics: A Practical Approach B. Flury and H. Riedwyl Readings in Decision Analysis S. French Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition D. Gamerman and H.F. Lopes Bayesian Data Analysis, Third Edition A. Gelman, J.B. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari, and D.B. Rubin Multivariate Analysis of Variance and Repeated Measures: A Practical Approach for Behavioural Scientists D.J. Hand and C.C. Taylor Practical Longitudinal Data Analysis D.J. Hand and M. Crowder Logistic Regression Models J.M. Hilbe Richly Parameterized Linear Models: Additive, Time Series, and Spatial Models Using Random Effects J.S. Hodges Statistics for Epidemiology N.P. Jewell Stochastic Processes: An Introduction, Second Edition P.W. Jones and P. Smith The Theory of Linear Models B. Jørgensen Principles of Uncertainty J.B. Kadane Graphics for Statistics and Data Analysis with R K.J. Keen Mathematical Statistics K. Knight Introduction to Multivariate Analysis: Linear and Nonlinear Modeling S. Konishi Nonparametric Methods in Statistics with SAS Applications O. Korosteleva Modeling and Analysis of Stochastic Systems, Second Edition V.G. Kulkarni Exercises and Solutions in Biostatistical Theory L.L. Kupper, B.H. Neelon, and S.M. O’Brien Exercises and Solutions in Statistical Theory L.L. Kupper, B.H. Neelon, and S.M. O’Brien Design and Analysis of Experiments with R J. Lawson Design and Analysis of Experiments with SAS J. Lawson A Course in Categorical Data Analysis T. Leonard Statistics for Accountants S. Letchford Introduction to the Theory of Statistical Inference H. Liero and S. Zwanzig Statistical Theory, Fourth Edition B.W. Lindgren Stationary Stochastic Processes: Theory and Applications G. Lindgren Statistics for Finance E. Lindström, H. Madsen, and J. N. Nielsen The BUGS Book: A Practical Introduction to Bayesian Analysis D. Lunn, C. Jackson, N. Best, A. Thomas, and D. Spiegelhalter Introduction to General and Generalized Linear Models H. Madsen and P. Thyregod Time Series Analysis H. Madsen Pólya Urn Models H. Mahmoud Randomization, Bootstrap and Monte Carlo Methods in Biology, Third Edition B.F.J. Manly Introduction to Randomized Controlled Clinical Trials, Second Edition J.N.S. Matthews Statistical Rethinking: A Bayesian Course with Examples in R and Stan R. McElreath Statistical Methods in Agriculture and Experimental Biology, Second Edition R. Mead, R.N. Curnow, and A.M. Hasted Statistics in Engineering: A Practical Approach A.V. Metcalfe Statistical Inference: An Integrated Approach, Second Edition H. S. Migon, D. Gamerman, and F. Louzada
Beyond ANOVA: Basics of Applied Statistics R.G. Miller, Jr. A Primer on Linear Models J.F. Monahan Applied Stochastic Modelling, Second Edition B.J.T. Morgan Elements of Simulation B.J.T. Morgan Probability: Methods and Measurement A. O’Hagan Introduction to Statistical Limit Theory A.M. Polansky Applied Bayesian Forecasting and Time Series Analysis A. Pole, M. West, and J. Harrison Statistics in Research and Development, Time Series: Modeling, Computation, and Inference R. Prado and M. West Introduction to Statistical Process Control P. Qiu Sampling Methodologies with Applications P.S.R.S. Rao A First Course in Linear Model Theory N. Ravishanker and D.K. Dey Essential Statistics, Fourth Edition D.A.G. Rees Stochastic Modeling and Mathematical Statistics: A Text for Statisticians and Quantitative Scientists F.J. Samaniego Statistical Methods for Spatial Data Analysis O. Schabenberger and C.A. Gotway Bayesian Networks: With Examples in R M. Scutari and J.-B. Denis Large Sample Methods in Statistics P.K. Sen and J. da Motta Singer Spatio-Temporal Methods in Environmental Epidemiology G. Shaddick and J.V. Zidek Decision Analysis: A Bayesian Approach J.Q. Smith Analysis of Failure and Survival Data P. J. Smith Applied Statistics: Handbook of GENSTAT Analyses E.J. Snell and H. Simpson Applied Nonparametric Statistical Methods, Fourth Edition P. Sprent and N.C. Smeeton Data Driven Statistical Methods P. Sprent Generalized Linear Mixed Models: Modern Concepts, Methods and Applications W. W. Stroup Survival Analysis Using S: Analysis of Time-to-Event Data M. Tableman and J.S. Kim Applied Categorical and Count Data Analysis W. Tang, H. He, and X.M. Tu Elementary Applications of Probability Theory, Second Edition H.C. Tuckwell Introduction to Statistical Inference and Its Applications with R M.W. Trosset Understanding Advanced Statistical Methods P.H. Westfall and K.S.S. Henning Statistical Process Control: Theory and Practice, Third Edition G.B. Wetherill and D.W. Brown Generalized Additive Models: An Introduction with R S. Wood Epidemiology: Study Design and Data Analysis, Third Edition M. Woodward Practical Data Analysis for Designed Experiments B.S. Yandell
Texts in Statistical Science Statistical Rethinking A Bayesian Course with Examples in R and Stan Richard McElreath Max Planck Institute for Evolutionary Anthropology Leipzig, Germany
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