Statistical Rethinking: A Bayesian Course with Examples in R and STAN 2nd Edition, ISBN-13: 978-0367139919

Description

Statistical Rethinking: A Bayesian Course with Examples in R and STAN 2nd Edition, ISBN-13: 978-0367139919

[PDF eBook eTextbook]

• Publisher: ‎ Chapman and Hall/CRC; 2nd edition (March 16, 2020)
• Language: ‎ English
• 594 pages
• ISBN-10: ‎ 036713991X
• ISBN-13: ‎ 978-0367139919

Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds your knowledge of and confidence in making inferences from data. Reflecting the need for scripting 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 causal inference and generalized linear multilevel models from a simple Bayesian perspective that builds on information theory and maximum entropy. The core material ranges from the basics of regression to advanced multilevel models. It also presents measurement error, missing data, and Gaussian process models for spatial and phylogenetic confounding.

The second edition emphasizes the directed acyclic graph (DAG) approach to causal inference, integrating DAGs into many examples. The new edition also contains new material on the design of prior distributions, splines, ordered categorical predictors, social relations models, cross-validation, importance sampling, instrumental variables, and Hamiltonian Monte Carlo. It ends with an entirely new chapter that goes beyond generalized linear modeling, showing how domain-specific scientific models can be built into statistical analyses.

Features

• Integrates working code into the main text
• Illustrates concepts through worked data analysis examples
• Emphasizes understanding assumptions and how assumptions are reflected in code
• Offers more detailed explanations of the mathematics in optional sections
• Presents examples of using the dagitty R package to analyze causal graphs

Table of Contents

Cover

Half Title

Series Page

Title Page

Copyright Page

Table of Contents

Preface to the Second Edition

Preface

Audience

Teaching strategy

How to use this book

Installing the rethinking R package

Acknowledgments

Chapter 1. The Golem of Prague

1.1. Statistical golems

1.2. Statistical rethinking

1.3. Tools for golem engineering

1.4. Summary

Chapter 2. Small Worlds and Large Worlds

2.1. The garden of forking data

2.2. Building a model

2.3. Components of the model

2.4. Making the model go

2.5. Summary

2.6. Practice

Chapter 3. Sampling the Imaginary

3.1. Sampling from a grid-approximate posterior

3.2. Sampling to summarize

3.3. Sampling to simulate prediction

3.4. Summary

3.5. Practice

Chapter 4. Geocentric Models

4.1. Why normal distributions are normal

4.2. A language for describing models

4.3. Gaussian model of height

4.4. Linear prediction

4.5. Curves from lines

4.6. Summary

4.7. Practice

Chapter 5. The Many Variables & The Spurious Waffles

5.1. Spurious association

5.2. Masked relationship

5.3. Categorical variables

5.4. Summary

5.5. Practice

Chapter 6. The Haunted DAG & The Causal Terror

6.1. Multicollinearity

6.2. Post-treatment bias

6.3. Collider bias

6.4. Confronting confounding

6.5. Summary

6.6. Practice

Chapter 7. Ulysses’ Compass

7.1. The problem with parameters

7.2. Entropy and accuracy

7.3. Golem taming: regularization

7.4. Predicting predictive accuracy

7.5. Model comparison

7.6. Summary

7.7. Practice

Chapter 8. Conditional Manatees

8.1. Building an interaction

8.2. Symmetry of interactions

8.3. Continuous interactions

8.4. Summary

8.5. Practice

Chapter 9. Markov Chain Monte Carlo

9.1. Good King Markov and his island kingdom

9.2. Metropolis algorithms

9.3. Hamiltonian Monte Carlo

9.4. Easy HMC: ulam

9.5. Care and feeding of your Markov chain

9.6. Summary

9.7. Practice

Chapter 10. Big Entropy and the Generalized Linear Model

10.1. Maximum entropy

10.2. Generalized linear models

10.3. Maximum entropy priors

10.4. Summary

Chapter 11. God Spiked the Integers

11.1. Binomial regression

11.2. Poisson regression

11.3. Multinomial and categorical models

11.4. Summary

11.5. Practice

Chapter 12. Monsters and Mixtures

12.1. Over-dispersed counts

12.2. Zero-inflated outcomes

12.3. Ordered categorical outcomes

12.4. Ordered categorical predictors

12.5. Summary

12.6. Practice

Chapter 13. Models With Memory

13.1. Example: Multilevel tadpoles

13.2. Varying effects and the underfitting/overfitting trade-off

13.3. More than one type of cluster

13.4. Divergent transitions and non-centered priors

13.5. Multilevel posterior predictions

13.6. Summary

13.7. Practice

Chapter 14. Adventures in Covariance

14.1. Varying slopes by construction

14.2. Advanced varying slopes

14.3. Instruments and causal designs

14.4. Social relations as correlated varying effects

14.5. Continuous categories and the Gaussian process

14.6. Summary

14.7. Practice

Chapter 15. Missing Data and Other Opportunities

15.1. Measurement error

15.2. Missing data

15.3. Categorical errors and discrete absences

15.4. Summary

15.5. Practice

Chapter 16. Generalized Linear Madness

16.1. Geometric people

16.2. Hidden minds and observed behavior

16.3. Ordinary differential nut cracking

16.4. Population dynamics

16.5. Summary

16.6. Practice

Chapter 17. Horoscopes

Endnotes

Bibliography

Citation index

Topic index

Richard McElreath studies human evolutionary ecology and is a Director at the Max Planck Institute for Evolutionary Anthropology in Leipzig, Germany. He has published extensively on the mathematical theory and statistical analysis of social behavior, including his first book (with Robert Boyd), Mathematical Models of Social Evolution.

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