Statistical Rethinking : A Bayesian Course with Examples in R and Stan
(Chapman & Hall/crc Texts in Statistical Science Series ; : 122)
Chapman & Hall 2015/12
469 p. 113 illus. 27 cm.
This book provides a more elementary introduction to Bayesian analysis than the Gelman book and is more suitable for graduate students in disciplines other than statistics.
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.
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