Bayesian Statistics the Fun Way

Table of contents

1. Cover Page
2. Title Page
3. Copyright Page
4. Dedication
5. About the Author
6. About the Technical Reviewer
7. Brief Contents
8. Contents in Detail
9. Acknowledgments
10. Introduction
    1. Why Learn Statistics?
    2. What Is “Bayesian” Statistics?
    3. What’s in This Book
    4. Background for Reading the Book
    5. Now Off on Your Adventure!
11. Part I: Introduction to Probability
12. 1. Bayesian Thinking and Everyday Reasoning
    1. Reasoning About Strange Experiences
    2. Gathering More Evidence and Updating Your Beliefs
    3. Comparing Hypotheses
    4. Data Informs Belief; Belief Should Not Inform Data
    5. Wrapping Up
    6. Exercises
13. 2. Measuring Uncertainty
    1. What Is a Probability?
    2. Calculating Probabilities by Counting Outcomes of Events
    3. Calculating Probabilities as Ratios of Beliefs
    4. Wrapping Up
    5. Exercises
14. 3. The Logic of Uncertainty
    1. Combining Probabilities with AND
    2. Combining Probabilities with OR
    3. Wrapping Up
    4. Exercises
15. 4. Creating a Binomial Probability Distribution
    1. Structure of a Binomial Distribution
    2. Understanding and Abstracting Out the Details of Our Problem
    3. Counting Our Outcomes with the Binomial Coefficient
    4. Example: Gacha Games
    5. Wrapping Up
    6. Exercises
16. 5. The Beta Distribution
    1. A Strange Scenario: Getting the Data
    2. The Beta Distribution
    3. Reverse-Engineering the Gacha Game
    4. Wrapping Up
    5. Exercises
17. Part II: Bayesian Probability and Prior Probabilities
18. 6. Conditional Probability
    1. Introducing Conditional Probability
    2. Conditional Probabilities in Reverse and Bayes’ Theorem
    3. Introducing Bayes’ Theorem
    4. Wrapping Up
    5. Exercises
19. 7. Bayes’ Theorem with LEGO
    1. Working Out Conditional Probabilities Visually
    2. Working Through the Math
    3. Wrapping Up
    4. Exercises
20. 8. The Prior, Likelihood, and Posterior of Bayes’ Theorem
    1. The Three Parts
    2. Investigating the Scene of a Crime
    3. Considering Alternative Hypotheses
    4. Comparing Our Unnormalized Posteriors
    5. Wrapping Up
    6. Exercises
21. 9. Bayesian Priors and Working with Probability Distributions
    1. C-3PO’s Asteroid Field Doubts
    2. Determining C-3PO’s Beliefs
    3. Accounting for Han’s Badassery
    4. Creating Suspense with a Posterior
    5. Wrapping Up
    6. Exercises
22. Part III: Parameter Estimation
23. 10. Introduction to Averaging and Parameter Estimation
    1. Estimating Snowfall
    2. Means for Measurement vs. Means for Summary
    3. Wrapping Up
    4. Exercises
24. 11. Measuring the Spread of Our Data
    1. Dropping Coins in a Well
    2. Finding the Mean Absolute Deviation
    3. Finding the Variance
    4. Finding the Standard Deviation
    5. Wrapping Up
    6. Exercises
25. 12. The Normal Distribution
    1. Measuring Fuses for Dastardly Deeds
    2. The Normal Distribution
    3. Solving the Fuse Problem
    4. Some Tricks and Intuitions
    5. “N Sigma” Events
    6. The Beta Distribution and the Normal Distribution
    7. Wrapping Up
    8. Exercises
26. 13. Tools of Parameter Estimation: The PDF, CDF, and Quantile Function
    1. Estimating the Conversion Rate for an Email Signup List
    2. The Probability Density Function
    3. Introducing the Cumulative Distribution Function
    4. The Quantile Function
    5. Wrapping Up
    6. Exercises
27. 14. Parameter Estimation with Prior Probabilities
    1. Predicting Email Conversion Rates
    2. Taking in Wider Context with Priors
    3. Prior as a Means of Quantifying Experience
    4. Is There a Fair Prior to Use When We Know Nothing?
    5. Wrapping Up
    6. Exercises
28. PART IV: Hypothesis Testing: The Heart of Statistics
29. 15. From Parameter Estimation to Hypothesis Testing: Building a Bayesian A/B Test
    1. Setting Up a Bayesian A/B Test
    2. Monte Carlo Simulations
    3. Wrapping Up
    4. Exercises
30. 16. Introduction to the Bayes Factor and Posterior Odds: The Competition of Ideas
    1. Revisiting Bayes’ Theorem
    2. Building a Hypothesis Test Using the Ratio of Posteriors
    3. Wrapping Up
    4. Exercises
31. 17. Bayesian Reasoning in the Twilight Zone
    1. Bayesian Reasoning in the Twilight Zone
    2. Using the Bayes Factor to Understand the Mystic Seer
    3. Developing Our Own Psychic Powers
    4. Wrapping Up
    5. Exercises
32. 18. When Data Doesn’t Convince You
    1. A Psychic Friend Rolling Dice
    2. Arguing with Relatives and Conspiracy Theorists
    3. Wrapping Up
    4. Exercises
33. 19. From Hypothesis Testing to Parameter Estimation
    1. Is the Carnival Game Really Fair?
    2. Building a Probability Distribution
    3. From the Bayes Factor to Parameter Estimation
    4. Wrapping Up
    5. Exercises
34. A. A Quick Introduction to R
    1. R and RStudio
    2. Creating an R Script
    3. Basic Concepts in R
    4. Functions
    5. Random Sampling
    6. Defining Your Own Functions
    7. Creating Basic Plots
    8. Exercise: Simulating a Stock Price
    9. Summary
35. B. Enough Calculus to Get By
    1. Functions
    2. The Fundamental Theorem of Calculus
36. C. Answers to the Exercises
37. Index