Think Bayes, 2nd Edition

Copyright
Table of Contents
Preface
	Who Is This Book For?
	Modeling
	Working with the Code
	Installing Jupyter
	Conventions Used in This Book
	O’Reilly Online Learning
	How to Contact Us
	Contributor List
Chapter 1. Probability
	Linda the Banker
	Probability
	Fraction of Bankers
	The Probability Function
	Political Views and Parties
	Conjunction
	Conditional Probability
	Conditional Probability Is Not Commutative
	Condition and Conjunction
	Laws of Probability
		Theorem 1
		Theorem 2
		Theorem 3
		The Law of Total Probability
	Summary
	Exercises
Chapter 2. Bayes’s Theorem
	The Cookie Problem
	Diachronic Bayes
	Bayes Tables
	The Dice Problem
	The Monty Hall Problem
	Summary
	Exercises
Chapter 3. Distributions
	Distributions
	Probability Mass Functions
	The Cookie Problem Revisited
	101 Bowls
	The Dice Problem
	Updating Dice
	Summary
	Exercises
Chapter 4. Estimating Proportions
	The Euro Problem
	The Binomial Distribution
	Bayesian Estimation
	Triangle Prior
	The Binomial Likelihood Function
	Bayesian Statistics
	Summary
	Exercises
Chapter 5. Estimating Counts
	The Train Problem
	Sensitivity to the Prior
	Power Law Prior
	Credible Intervals
	The German Tank Problem
	Informative Priors
	Summary
	Exercises
Chapter 6. Odds and Addends
	Odds
	Bayes’s Rule
	Oliver’s Blood
	Addends
	Gluten Sensitivity
	The Forward Problem
	The Inverse Problem
	Summary
	More Exercises
Chapter 7. Minimum, Maximum, and Mixture
	Cumulative Distribution Functions
	Best Three of Four
	Maximum
	Minimum
	Mixture
	General Mixtures
	Summary
	Exercises
Chapter 8. Poisson Processes
	The World Cup Problem
	The Poisson Distribution
	The Gamma Distribution
	The Update
	Probability of Superiority
	Predicting the Rematch
	The Exponential Distribution
	Summary
	Exercises
Chapter 9. Decision Analysis
	The Price Is Right Problem
	The Prior
	Kernel Density Estimation
	Distribution of Error
	Update
	Probability of Winning
	Decision Analysis
	Maximizing Expected Gain
	Summary
	Discussion
	More Exercises
Chapter 10. Testing
	Estimation
	Evidence
	Uniformly Distributed Bias
	Bayesian Hypothesis Testing
	Bayesian Bandits
	Prior Beliefs
	The Update
	Multiple Bandits
	Explore and Exploit
	The Strategy
	Summary
	More Exercises
Chapter 11. Comparison
	Outer Operations
	How Tall Is A?
	Joint Distribution
	Visualizing the Joint Distribution
	Likelihood
	The Update
	Marginal Distributions
	Conditional Posteriors
	Dependence and Independence
	Summary
	Exercises
Chapter 12. Classification
	Penguin Data
	Normal Models
	The Update
	Naive Bayesian Classification
	Joint Distributions
	Multivariate Normal Distribution
	A Less Naive Classifier
	Summary
	Exercises
Chapter 13. Inference
	Improving Reading Ability
	Estimating Parameters
	Likelihood
	Posterior Marginal Distributions
	Distribution of Differences
	Using Summary Statistics
	Update with Summary Statistics
	Comparing Marginals
	Summary
	Exercises
Chapter 14. Survival Analysis
	The Weibull Distribution
	Incomplete Data
	Using Incomplete Data
	Light Bulbs
	Posterior Means
	Posterior Predictive Distribution
	Summary
	Exercises
Chapter 15. Mark and Recapture
	The Grizzly Bear Problem
	The Update
	Two-Parameter Model
	The Prior
	The Update
	The Lincoln Index Problem
	Three-Parameter Model
	Summary
	Exercises
Chapter 16. Logistic Regression
	Log Odds
	The Space Shuttle Problem
	Prior Distribution
	Likelihood
	The Update
	Marginal Distributions
	Transforming Distributions
	Predictive Distributions
	Empirical Bayes
	Summary
	More Exercises
Chapter 17. Regression
	More Snow?
	Regression Model
	Least Squares Regression
	Priors
	Likelihood
	The Update
	Marathon World Record
	The Priors
	Prediction
	Summary
	Exercises
Chapter 18. Conjugate Priors
	The World Cup Problem Revisited
	The Conjugate Prior
	What the Actual?
	Binomial Likelihood
	Lions and Tigers and Bears
	The Dirichlet Distribution
	Summary
	Exercises
Chapter 19. MCMC
	The World Cup Problem
	Grid Approximation
	Prior Predictive Distribution
	Introducing PyMC3
	Sampling the Prior
	When Do We Get to Inference?
	Posterior Predictive Distribution
	Happiness
	Simple Regression
	Multiple Regression
	Summary
	Exercises
Chapter 20. Approximate Bayesian Computation
	The Kidney Tumor Problem
	A Simple Growth Model
	A More General Model
	Simulation
	Approximate Bayesian Computation
	Counting Cells
	Cell Counting with ABC
	When Do We Get to the Approximate Part?
	Summary
	Exercises
Index
About the Author
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