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Statistical Rethinking: A Bayesian Course with Examples in R and STAN 2nd edition [Kõva köide]

(Max Planck Institute for Evolutionary Anthropology, Leipzig, Germany)
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Winner of the 2024 De Groot Prize awarded by the International Society for Bayesian Analysis (ISBA)

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.



Provides the rethinking R package on the author's website and on GitHub.

Arvustused

"The first edition (and this second edition) of *Statistical Rethinking* beautifully outlines the key steps in the statistical analysis cycle, starting from formulating the research question. I find that many statistics textbooks omit the issue of problem formulation and either jump into data acquisition or further into analysis after the fact. McElreath has created a fantastic text for students of applied statistics to not only learn about the Bayesian paradigm, but also to gain a deep appreciation for the statistical thought process. I also found that many students appreciated McElreaths engaging writing style and humor, and personally found the infusion of humor quite refreshing." - Adam Loy, Carleton College

"(The chapter) Generalized Linear Madness represents another great chapter of an even better edition of an already awesome textbook." - Benjamin K. Goodrich, Columbia University

"(Chapter 16) is a worthy concluding chapter to a masterful book. Eminently readable and enjoyable. Brimful of small thought-provoking bits which may inspire deeper studies, but first and foremost a window on the trial and error process involved in building a statistical model or rather, indeed, any scientific theory." - Josep Fortiana Gregori, University of Barcelona

"I do regard the manuscript as technically correct, clearly written, and at an appropriate level of difficulty. The technical approaches and the R codes of the book are perfect for our students. They can learn concepts of Bayesian models, data analysis, and model validation methods through using the R codes. The codes help students to have better understanding of the models and data analysis process." - Nguyet Nguyen, Youngstown State University

"As a textbook it successfully brings the statisticians toolbox to a wider audience with an accessible style and good humour. It should be recommended to statistics students, both old and new."

- Nathan Green, Journal of the Royal Statistical Society, 2021, https://doi.org/10.1111/rssa.12755

"In conclusion, Statistical Rethinking frames usual methods and tools taught in graduate statistical courses into a different way to encourage the reader to understand the details and appreciate the underlying assumptions. The accompanying R package offers example codes for some interesting problems that are not available in standard library or other popular packages. This book can be used as a supplement to a graduate course or it can be used by practitioners wanting to brush up their knowledge with better understanding of statistical techniques."

- Abhirup Mallik in Technometrics, August 2021 "The first edition (and this second edition) of *Statistical Rethinking* beautifully outlines the key steps in the statistical analysis cycle, starting from formulating the research question. I find that many statistics textbooks omit the issue of problem formulation and either jump into data acquisition or further into analysis after the fact. McElreath has created a fantastic text for students of applied statistics to not only learn about the Bayesian paradigm, but also to gain a deep appreciation for the statistical thought process. I also found that many students appreciated McElreaths engaging writing style and humor, and personally found the infusion of humor quite refreshing." ~Adam Loy, Carleton College

"(The chapter) Generalized Linear Madness represents another great chapter of an even better edition of an already awesome textbook." ~Benjamin K. Goodrich, Columbia University

"(Chapter 16) is a worthy concluding chapter to a masterful book. Eminently readable and enjoyable. Brimful of small thought-provoking bits which may inspire deeper studies, but first and foremost a window on the trial and error process involved in building a statistical model or rather, indeed, any scientific theory." ~Josep Fortiana Gregori, University of Barcelona

"I do regard the manuscript as technically correct, clearly written, and at an appropriate level of difficulty. The technical approaches and the R codes of the book are perfect for our students. They can learn concepts of Bayesian models, data analysis, and model validation methods through using the R codes. The codes help students to have better understanding of the models and data analysis process." ~Nguyet Nguyen, Youngstown State University

"In conclusion, Statistical Rethinking frames usual methods and tools taught in graduate statistical courses into a different way to encourage the reader to understand the details and appreciate the underlying assumptions. The accompanying R package offers example codes for some interesting problems that are not available in standard library or other popular packages. This book can be used as a supplement to a graduate course or it can be used by practitioners wanting to brush up their knowledge with better understanding of statistical techniques." ~Abhirup Mallik in Technometrics, August 2021

"As a textbook it successfully brings the statisticians toolbox to a wider audience with an accessible style and good humour. It should be recommended to statistics students, both old and new." ~ Nathan Green, Journal of the Royal Statistical Society, 2021

Preface to the Second Edition ix
Preface xi
Audience xi
Teaching strategy xii
How to use this book xii
Installing the rethinking R package xvi
Acknowledgments xvi
Chapter 1 The Golem of Prague
1(18)
1.1 Statistical golems
1(3)
1.2 Statistical rethinking
4(6)
1.3 Tools for golem engineering
10(7)
1.4 Summary
17(2)
Chapter 2 Small Worlds and Large Worlds
19(30)
2.1 The garden of forking data
20(8)
2.2 Building a model
28(4)
2.3 Components of the model
32(4)
2.4 Making the model go
36(10)
2.5 Summary
46(1)
2.6 Practice
46(3)
Chapter 3 Sampling the Imaginary
49(22)
3.1 Sampling from a grid-approximate posterior
52(1)
3.2 Sampling to summarize
53(8)
3.3 Sampling to simulate prediction
61(7)
3.4 Summary
68(1)
3.5 Practice
68(3)
Chapter 4 Geocentric Models
71(52)
4.1 Why normal distributions are normal
72(5)
4.2 A language for describing models
77(1)
4.3 Gaussian model of height
78(13)
4.4 Linear prediction
91(19)
4.5 Curves from lines
110(10)
4.6 Summary
120(1)
4.7 Practice
120(3)
Chapter 5 The Many Variables & The Spurious Waffles
123(38)
5.1 Spurious association
125(19)
5.2 Masked relationship
144(9)
5.3 Categorical variables
153(5)
5.4 Summary
158(1)
5.5 Practice
159(2)
Chapter 6 The Haunted DAG & The Causal Terror
161(30)
6.1 Multicollinearity
163(7)
6.2 Post-treatment bias
170(6)
6.3 Collider bias
176(7)
6.4 Confronting confounding
183(6)
6.5 Summary
189(1)
6.6 Practice
189(2)
Chapter 7 Ulysses' Compass
191(46)
7.1 The problem with parameters
193(9)
7.2 Entropy and accuracy
202(12)
7.3 Golem taming: regularization
214(3)
7.4 Predicting predictive accuracy
217(8)
7.5 Model comparison
225(10)
7.6 Summary
235(1)
7.7 Practice
235(2)
Chapter 8 Conditional Manatees
237(26)
8.1 Building an interaction
239(11)
8.2 Symmetry of interactions
250(2)
8.3 Continuous interactions
252(8)
8.4 Summary
260(1)
8.5 Practice
260(3)
Chapter 9 Markov Chain Monte Carlo
263(36)
9.1 Good King Markov and his island kingdom
264(3)
9.2 Metropolis algorithms
267(3)
9.3 Hamiltonian Monte Carlo
270(9)
9.4 Easy HMC: ulam
279(8)
9.5 Care and feeding of your Markov chain
287(9)
9.6 Summary
296(1)
9.7 Practice
296(3)
Chapter 10 Big Entropy and the Generalized Linear Model
299(24)
10.1 Maximum entropy
300(12)
10.2 Generalized linear models
312(9)
10.3 Maximum entropy priors
321(1)
10.4 Summary
321(2)
Chapter 11 God Spiked the Integers
323(46)
11.1 Binomial regression
324(21)
11.2 Poisson regression
345(14)
11.3 Multinomial and categorical models
359(6)
11.4 Summary
365(1)
11.5 Practice
366(3)
Chapter 12 Monsters and Mixtures
369(30)
12.1 Over-dispersed counts
369(7)
12.2 Zero-inflated outcomes
376(4)
12.3 Ordered categorical outcomes
380(11)
12.4 Ordered categorical predictors
391(6)
12.5 Summary
397(1)
12.6 Practice
397(2)
Chapter 13 Models With Memory
399(36)
13.1 Example: Multilevel tadpoles
401(7)
13.2 Varying effects and the underfitting/overfitting trade-off
408(7)
13.3 More than one type of cluster
415(5)
13.4 Divergent transitions and non-centered priors
420(6)
13.5 Multilevel posterior predictions
426(5)
13.6 Summary
431(1)
13.7 Practice
431(4)
Chapter 14 Adventures in Covariance
435(54)
14.1 Varying slopes by construction
437(10)
14.2 Advanced varying slopes
447(8)
14.3 Instruments and causal designs
455(7)
14.4 Social relations as correlated varying effects
462(5)
14.5 Continuous categories and the Gaussian process
467(18)
14.6 Summary
485(1)
14.7 Practice
485(4)
Chapter 15 Missing Data and Other Opportunities
489(36)
15.1 Measurement error
491(8)
15.2 Missing data
499(17)
15.3 Categorical errors and discrete absences
516(5)
15.4 Summary
521(1)
15.5 Practice
521(4)
Chapter 16 Generalized Linear Madness
525(28)
16.1 Geometric people
526(5)
16.2 Hidden minds and observed behavior
531(5)
16.3 Ordinary differential nut cracking
536(5)
16.4 Population dynamics
541(9)
16.5 Summary
550(1)
16.6 Practice
550(3)
Chapter 17 Horoscopes
553(4)
Endnotes 557(16)
Bibliography 573(12)
Citation index 585(4)
Topic index 589
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.