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Statistical Rethinking

Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds readers' knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today's model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their 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. By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling. Web Resource The book is accompanied by an R package (rethinking) that is available on the author's website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.
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Table of Contents

The Golem of Prague Statistical golems Statistical rethinking Three tools for golem engineering Summary Small Worlds and Large Worlds The garden of forking data Building a model Components of the model Making the model go Summary Practice Sampling the Imaginary Sampling from a grid-approximate posterior Sampling to summarize Sampling to simulate prediction Summary Practice Linear Models Why normal distributions are normal A language for describing models A Gaussian model of height Adding a predictor Polynomial regression Summary Practice Multivariate Linear Models Spurious association Masked relationship When adding variables hurts Categorical variables Ordinary least squares and lm Summary Practice Overfitting, Regularization, and Information Criteria The problem with parameters Information theory and model performance Regularization Information criteria Using information criteria Summary Practice Interactions Building an interaction Symmetry of the linear interaction Continuous interactions Interactions in design formulas Summary Practice Markov Chain Monte Carlo Good King Markov and His island kingdom Markov chain Monte Carlo Easy HMC: map2stan Care and feeding of your Markov chain Summary Practice Big Entropy and the Generalized Linear Model Maximum entropy Generalized linear models Maximum entropy priors Summary Counting and Classification Binomial regression Poisson regression Other count regressions Summary Practice Monsters and Mixtures Ordered categorical outcomes Zero-inflated outcomes Over-dispersed outcomes Summary Practice Multilevel Models Example: Multilevel tadpoles Varying effects and the underfitting/overfitting trade-off More than one type of cluster Multilevel posterior predictions Summary Practice Adventures in Covariance Varying slopes by construction Example: Admission decisions and gender Example: Cross-classified chimpanzees with varying slopes Continuous categories and the Gaussian process Summary Practice Missing Data and Other Opportunities Measurement error Missing data Summary Practice Horoscopes

About the Author

Richard McElreath is the director of the Department of Human Behavior, Ecology, and Culture at the Max Planck Institute for Evolutionary Anthropology. He is also a professor in the Department of Anthropology at the University of California, Davis. His work lies at the intersection of evolutionary and cultural anthropology, specifically how the evolution of fancy social learning in humans accounts for the unusual nature of human adaptation and extraordinary scale and variety of human societies.


"... I am quite impressed by Statistical Rethinking ... I like the highly personal style with clear attempts to make the concepts memorable for students by resorting to external concepts. ... it introduces Bayesian thinking and critical modeling through specific problems and spelled out R codes, if not dedicated datasets. Statistical Rethinking manages this all-inclusive most nicely ... an impressive book that I do not hesitate recommending for prospective data analysts and applied statisticians!" -Christian Robert (Universite Paris-Dauphine, PSL Research University, and University of Warwick) on his blog, April 2016 "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 "This is an exceptional book. The author is very clear that this book has been written as a course . . . Strengths of the book include this clear conceptual exposition of statistical thinking as well as the focus on applying the material to real phenomena." -Paul Hewson, Plymouth University, 2016 "The book contains a good selection of extension activities, which are labelled according to difficulty. There are occasional paragraphs labelled `rethinking' or `overthinking' that contain finer details. The presentation is replete with metaphors ranging from the `statistical Golems' in Chapter 1 through `Monsters and Mixtures' in Chapter 11 and `Adventures in Covariance' in Chapter 13." -Diego Andres Perez Ruiz, University of Manchester

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