Bayesian Statistics the Fun Way: Understanding Statistics and Probability with Star Wars, LEGO, and Rubber Ducks

by Will Kurt

Overview

Fun guide to learning Bayesian statistics and probability through unusual and illustrative examples.

Probability and statistics are increasingly important in a huge range of professions. But many people use data in ways they don't even understand, meaning they aren't getting the most from it. Bayesian Statistics the Fun Way will change that.

This book will give you a complete understanding of Bayesian statistics through simple explanations and un-boring examples. Find out the probability of UFOs landing in your garden, how likely Han Solo is to survive a flight through an asteroid shower, how to win an argument about conspiracy theories, and whether a burglary really was a burglary, to name a few examples.

By using these off-the-beaten-track examples, the author actually makes learning statistics fun. And you'll learn real skills, like how to:

- How to measure your own level of uncertainty in a conclusion or belief
- Calculate Bayes theorem and understand what it's useful for
- Find the posterior, likelihood, and prior to check the accuracy of your conclusions
- Calculate distributions to see the range of your data
- Compare hypotheses and draw reliable conclusions from them

Next time you find yourself with a sheaf of survey results and no idea what to do with them, turn to Bayesian Statistics the Fun Way to get the most value from your data.

Product Details

ISBN-13:	9781593279561
Publisher:	No Starch Press
Publication date:	07/09/2019
Pages:	256
Sales rank:	59,840
Product dimensions:	7.00(w) x 9.20(h) x 0.70(d)

About the Author

Will Kurt currently works as a Senior Data Scientist at Bombora, and has been using Bayesian statistics to solve real business problems for over half a decade. He frequently blogs about probability on his website, CountBayesie.com. Will is the author of Get Programming with Haskell (Manning Publications) and lives in Reno, Nevada.

Table of Contents

Acknowledgments xv

Introduction XVII

Why Learn Statistics? xviii

What Is "Bayesian" Statistics? xix

What's in This Book xix

Part I Introduction to Probability xix

Part II Bayesian Probability and Prior Probabilities xx

Part III Parameter Estimation xxi

Part IV Hypothesis Testing: The Heart of Statistics xxi

Background for Reading the Book xxii

Now Off on Your Adventure! xxii

Part I Introduction to Probability

1 Bayesian Thinking and Everyday Reasoning 3

Reasoning About Strange Experiences 4

Observing Data 4

Holding Prior Beliefs and Conditioning Probabilities 5

Forming a Hypothesis 6

Spotting Hypotheses in Everyday Speech 8

Gathering More Evidence and Updating Your Beliefs 8

Comparing Hypotheses 9

Data Informs Belief; Belief Should Not Inform Data 10

Wrapping Up 11

Exercises 11

2 Measuring Uncertainty 13

What is a Probability? 14

Calculating Probabilities by Counting Outcomes of Events 15

Calculating Probabilities as Ratios of Beliefs 16

Using Odds to Determine Probability 17

Solving for the Probabilities 17

Measuring Beliefs in a Coin Toss 18

Wrapping Up 19

Exercises 20

3 The Logic of Uncertainty 21

Combining Probabilities with AND 22

Solving a Combination of Two Probabilities 22

Applying the Product Rule of Probability 24

Example: Calculating the Probability of Being Late 25

Combining Probabilities with OR 26

Calculating OR for Mutually Exclusive Events 26

Using the Sum Rule for Non-Mutually Exclusive Events 28

Example: Calculating the Probability of Getting a Hefty Fine 29

Wrapping Up 30

Exercises 31

4 Creating a Binomial Probability Distribution 33

Structure of a Binomial Distribution 34

Understanding and Abstracting Out the Details of Our Problem 35

Counting Our Outcomes with the Binomial Coefficient 36

Combinatorics: Advanced Counting with the Binomial Coefficient 37

Calculating the Probability of the Desired Outcome 38

Example: Gacha Games 41

Wrapping Up 43

Exercises 43

5 The Beta Distribution 45

A Strange Scenario: Getting the Data 46

Distinguishing Probability, Statistics, and Inference 46

Collecting Data 46

Calculating the Probability of Probabilities 47

The Beta Distribution 50

Breaking Down the Probability Density Function 50

Applying the Probability Density Function to Our Problem 51

Quantifying Continuous Distributions with Integration 52

Reverse-Engineering the Gacha Game 53

Wrapping Up 55

Exercises 55

Part II Bayesian Probability and Prior Probabilities

6 Conditional Probability 59

Introducing Conditional Probability 60

Why Conditional Probabilities Are Important 60

Dependence and the Revised Rules of Probability 61

Conditional Probabilities in Reverse and Bayes' Theorem 62

Introducing Bayes' Theorem 64

Wrapping Up 65

Exercises 66

7 Bayes' Theorem with Lego 67

Working Out Conditional Probabilities Visually 70

Working Through the Math 71

Wrapping Up 72

Exercises 72

8 The Prior, Likelihood, and Posterior Of Bayes' Theorem 73

The Three Parts 74

Investigating the Scene of a Crime 74

Solving for the Likelihood 75

Calculating the Prior 75

Normalizing the Data 76

Considering Alternative Hypotheses 78

The Likelihood for Our Alternative Hypothesis 78

The Prior for Our Alternative Hypothesis 78

The Posterior for Our Alternative Hypothesis 79

Comparing Our Unnormalized Posteriors 80

Wrapping Up 81

Exercises 81

9 Bayesian Priors and Working with Probability Distributions 83

C-3PO's Asteroid Field Doubts 84

Determining C-3PO's Beliefs 84

Accounting for Han's Badassery 85

Creating Suspense with a Posterior 87

Wrapping Up 88

Exercises 89

Part III Parameter Estimation

10 Introduction to Averaging and Parameter Estimation 93

Estimating Snowfall 94

Averaging Measurements to Minimize Error 94

Solving a Simplified Version of Our Problem 95

Solving a More Extreme Case 97

Estimating the True Value with Weighted Probabilities 98

Defining Expectation, Mean, and Averaging 99

Means for Measurement vs. Means for Summary 100

Wrapping Up 101

Exercises 101

11 Measuring the Spread of Our Data 103

Dropping Coins in a Well 104

Finding the Mean Absolute Deviation 104

Finding the Variance 106

Finding the Standard Deviation 107

Wrapping Up 109

Exercises 109

12 The Normal Distribution 111

Measuring Fuses for Dastardly Deeds 112

The Normal Distribution 114

Solving the Fuse Problem 116

Some Tricks and Intuitions 118

"N Sigma" Events 120

The Beta Distribution and the Normal Distribution 121

Wrapping Up 122

Exercises 122

13 Tools of Parameter Estimation: The PDF, CDF, and Quantile Function 123

Estimating the Conversion Rate for an Email Signup List 124

The Probability Density Function 124

Visualizing and Interpreting the PDF 125

Working with the PDF in R 126

Introducing the Cumulative Distribution Function 127

Visualizing and Interpreting the CDF 130

Finding the Median 130

Approximating Integrals Visually 131

Estimating Confidence Intervais 132

Using the CDF in R 133

The Quantile Function 133

Visualizing and Understanding the Quantile Function 134

Calculating Quantiles in R 135

Wrapping Up 135

Exercises 136

14 Parameter Estimation with Prior Probabilities 137

Predicting Email Conversion Rates 138

Taking in Wider Context with Priors 139

Prior as a Means of Quantifying Experience 143

Is There a Fair Prior to Use When We Know Nothing? 144

Wrapping Up 146

Exercises 146

Part IV Hypothesis Testing: The Heart of Statistics

15 From Parameter Estimation to Hypothesis Testing: Building a Bayesian A/B Test 149

Setting Up a Bayesian A/B Test 150

Finding Our Prior Probability 150

Collecting Data 151

Monte Carlo Simulations 152

In How Many Worlds Is ? the Better Variant? 153

How Much Better Is Each Variant ? Than Each Variant A? 154

Wrapping Up 156

Exercises 156

16 Introduction to the Bayes Factor and Posterior Odds: The Competition Of Ideas 157

Revisiting Bayes' Theorem 158

Building a Hypothesis Test Using the Ratio of Posteriors 159

The Bayes Factor 159

Prior Odds 159

Posterior Odds 160

Wrapping Up 164

Exercises 165

17 Bayesian Reasoning in the Twilight Zone 167

Bayesian Reasoning in the Twilight Zone 168

Using the Bayes Factor to Understand the Mystic Seer 168

Measuring the Bayes Factor 169

Accounting for Prior Beliefs 170

Developing Our Own Psychic Powers 171

Wrapping Up 173

Exercises 173

18 When Data Doesn't Convince You 175

A Psychic Friend Rolling Dice 176

Comparing Likelihoods 176

Incorporating Prior Odds 177

Considering Alternative Hypotheses 178

Arguing with Relatives and Conspiracy Theorists 179

Wrapping Up 181

Exercises 181

19 From Hypothesis Testing to Parameter Estimation 183

Is the Carnival Game Really Fair? 184

Considering Multiple Hypotheses 186

Searching for More Hypotheses with R 186

Adding Priors to Our Likelihood Ratios 188

Building a Probability Distribution 190

From the Bayes Factor to Parameter Estimation 191

Wrapping Up 194

Exercises 194

A A Quick Introduction to R 195

R and RStudio 196

Creating an R Script 197

Basic Concepts in R 197

Data Types 197

Missing Values 200

Vectors 200

Functions 201

Basic Functions 202

Random Sampling 206

The runif() Function 206

The rnorm() Function 207

The sample() Function 207

Using set.seed() for Predictable Random Results 208

Defining Your Own Functions 209

Creating Basic Plots 210

Exercise: Simulating a Stock Price 213

Summary 214

B Enough Calculus to Get By 215

Functions 216

Determining How Far You've Run 217

Measuring the Area Under the Curve: The Integral 219

Measuring the Rate of Change: The Derivative 223

The Fundamental Theorem of Calculus 227

Index 229

Editorial Reviews

"An excellent introduction to subjects critical to all data scientists."
—Inside Big Data

"The author uses great examples to clarify key concepts . . . I would highly recommend as a supplement for any stats student or professional looking to refresh on Bayesian statistics."
—Stan T., Design Collective

From the Publisher