mathematics

Statistical Rethinking

Statistical Rethinking is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Statistical Rethinking rather than just read about it. In short: Statistical Rethinking: A Bayesian Course with Examples in R and Stan is an applied Bayesian statistics textbook by Richard McElreath. A second edition of the book was published in 2020 with a considerable update to the text.

Key takeaways

Statistical Rethinking belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Statistical Rethinking to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Statistical Rethinking from memory before moving on to harder problems.

Reference excerpt

Statistical Rethinking: A Bayesian Course with Examples in R and Stan is an applied Bayesian statistics textbook by Richard McElreath. A second edition of the book was published in 2020 with a considerable update to the text. This edition has more emphasis on using prior predictive simulation to understand prior distribution choices and illustrating additional statistical models (smoothing splines, robust regression, and models not within the generalized linear mixed model framework).

Reception Both editions of the book generally have positive reviews. A book review in the Journal of the Royal Statistical Society Series A: Statistics in Society comments that this is "an exceptional book". Although the book is directed at working researchers and advanced doctoral students, the review suggests that this book "deserves to be read carefully by a much wider audience even if it must be read from cover to cover". The reviewer ends by saying they would "unreservedly recommend this book to a wide audience interested in the principles of modern statistical modelling." The second edition of the book was reviewed in the Journal of Statistics Education and highlights McElreath's storytelling skills, exposition of the Bayesian material, and "colorful manner of providing intuition into the Bayesian concepts". The review concludes with saying the book is an "excellent introduction to modern applied Bayesian modeling" and is "a valuable resource for practitioners in the applied sciences". One concern from the review in the Journal of Statistics Education highlights the lack of mathematical rigor a doctoral student in statistics may need in developing Bayesian methodology and the reliance on the author's rethinking R package.

Awards 2023 DeGroot Prize by the International Society for Bayesian Analysis (ISBA)

Publication history McElreath, Richard (2015). Statistical Rethinking: A Bayesian Course with Examples in R and Stan (1st ed.). Chapman & Hall (published December 21, 2015). doi:10.1201/9781315372495. ISBN 978-1-4822-5344-3. OL 20743446W. McElreath, Richard (2020). Statistical Rethinking: A Bayesian Course with Examples in R and STAN (2nd ed.). New York (published March 16, 2020). doi:10.1201/9780429029608. ISBN 978-0-367-13991-9. OCLC 1145123627. OL 28056868M.{{cite book}}: CS1 maint: location missing publisher (link)

References

External links Richard McElreath's Official Website Lectures and notes for Statistical Rethinking (2024 Edition) rethinking on GitHub

Worked examples

Example 1 — a first encounter with Statistical Rethinking

Start with the simplest possible case. Write down what Statistical Rethinking claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Statistical Rethinking before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Statistical Rethinking ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Statistical Rethinking

In research: Statistical Rethinking appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Statistical Rethinking in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Statistical Rethinking is common in secondary-school and first-year university syllabi. It links to neighbouring topics 2015 non-fiction books, Bayesian statistics, R (programming language), so understanding it makes those chapters shorter.
In everyday life: Look for Statistical Rethinking outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Statistical Rethinking in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Statistical Rethinking means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Statistical Rethinking out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Statistical Rethinking in simple terms?

Why does Statistical Rethinking matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Statistical Rethinking?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Statistical Rethinking.