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Statistical rethinking: a Bayesian course with examples in R and Stan

By: McElreath, Richard.
Material type: materialTypeLabelBookSeries: Texts in Statistical Science. Publisher: Boca Raton CRC Press 2016Description: xvii, 469 p.ISBN: 9781482253443.Subject(s): Bayesian statistical decision theory | R - Computer program languageDDC classification: 519.542 Summary: 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. (https://www.crcpress.com/Statistical-Rethinking-A-Bayesian-Course-with-Examples-in-R-and-Stan/McElreath/p/book/9781482253443)
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Table of Contents:

1.The Golem of Prague

Statistical golems
Statistical rethinking
Three tools for golem engineering
Summary

2.Small Worlds and Large Worlds

The garden of forking data
Building a model
Components of the model
Making the model go
Summary
Practice

3.Sampling the Imaginary

Sampling from a grid-approximate posterior
Sampling to summarize
Sampling to simulate prediction
Summary
Practice

4.Linear Models

Why normal distributions are normal
A language for describing models
A Gaussian model of height
Adding a predictor
Polynomial regression
Summary
Practice

5.Multivariate Linear Models

Spurious association
Masked relationship
When adding variables hurts
Categorical variables
Ordinary least squares and lm
Summary
Practice

6.Overfitting, Regularization, and Information Criteria

The problem with parameters
Information theory and model performance
Regularization
Information criteria
Using information criteria
Summary
Practice

7.Interactions

Building an interaction
Symmetry of the linear interaction
Continuous interactions
Interactions in design formulas
Summary
Practice

8.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

9.Big Entropy and the Generalized Linear Model

Maximum entropy
Generalized linear models
Maximum entropy priors
Summary

10.Counting and Classification

Binomial regression
Poisson regression
Other count regressions
Summary
Practice

11.Monsters and Mixtures

Ordered categorical outcomes
Zero-inflated outcomes
Over-dispersed outcomes
Summary
Practice

12.Multilevel Models

Example: Multilevel tadpoles
Varying effects and the underfitting/overfitting trade-off
More than one type of cluster
Multilevel posterior predictions
Summary
Practice

13.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

14.Missing Data and Other Opportunities

Measurement error
Missing data
Summary
Practice

15.Horoscopes

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.

(https://www.crcpress.com/Statistical-Rethinking-A-Bayesian-Course-with-Examples-in-R-and-Stan/McElreath/p/book/9781482253443)

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