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Think Bayes

Allen B. Downey

Beijing

Boston Farnham Sebastopol

Tokyo

Think Bayes

By Allen B. Downey

Printed in the United States of America.

Published by O’Reilly Media, Inc., 1005 Gravenstein Highway North, Sebastopol, CA 95472.

O’Reilly books may be purchased for educational, business, or sales promotional use. Online editions are

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Editors:

Mike Loukides and Ann Spencer

Production Editor:

Melanie Yarbrough

Proofreader:

Jasmine Kwityn

Indexer:

Allen Downey

September, 2013:

First Edition

Interior Designer:

David Futato

Cover Designer:

Randy Comer

Illustrator:

Rebecca Demarest

Revision History for the First Edition

2013-09-10:

2014-02-10:

2014-08-22:

2016-06-03:

First release

Second release

Third release

Fourth release

See

http://oreilly.com/catalog/errata.csp?isbn=9781449370787

for release details.

The O’Reilly logo is a registered trademark of O’Reilly Media, Inc.

Think Bayes,

the cover image of a red

striped mullet, and related trade dress are trademarks of O’Reilly Media, Inc.

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instructions contained in this work are accurate, the publisher and the authors disclaim all responsibility

for errors or omissions, including without limitation responsibility for damages resulting from the use of

or reliance on this work. Use of the information and instructions contained in this work is at your own

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thereof complies with such licenses and/or rights.

Think Bayes

is available under the Creative Commons Attribution-NonCommercial 3.0 Unported

License. The author maintains an online version at

http://thinkbayes.com.

978-1-449-37078-7

[LSI]

Table of Contents

Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

Bayes’s Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Conditional probability

Conjoint probability

The cookie problem

Bayes’s theorem

The diachronic interpretation

The M&M problem

The Monty Hall problem

Discussion

Distributions

The cookie problem

The Bayesian framework

The Monty Hall problem

Encapsulating the framework

The M&M problem

Discussion

Exercises

The dice problem

The locomotive problem

What about that prior?

An alternative prior

Credible intervals

Computational Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

iii

Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

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