Bayesian Statistics The Fun Way: Understanding Statistics And Probability With Star Wars, LEGO, And Rubber Ducks

Description

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. BAYESIAN STATISTICS THE FUN WAY......Page 2 About the Technical Reviewer......Page 4 ACKNOWLEDGMENTS......Page 5 WHY LEARN STATISTICS?......Page 6 Part I: Introduction to Probability......Page 7 Part III: Parameter Estimation......Page 8 BACKGROUND FOR READING THE BOOK......Page 9 NOW OFF ON YOUR ADVENTURE!......Page 10 PART I INTRODUCTION TO PROBABILITY......Page 11 REASONING ABOUT STRANGE EXPERIENCES......Page 12 Holding Prior Beliefs and Conditioning Probabilities......Page 13 Forming a Hypothesis......Page 14 GATHERING MORE EVIDENCE AND UPDATING YOUR BELIEFS......Page 15 COMPARING HYPOTHESES......Page 16 DATA INFORMS BELIEF; BELIEF SHOULD NOT INFORM DATA......Page 17 EXERCISES......Page 18 WHAT IS A PROBABILITY?......Page 20 CALCULATING PROBABILITIES BY COUNTING OUTCOMES OF EVENTS......Page 21 CALCULATING PROBABILITIES AS RATIOS OF BELIEFS......Page 22 Solving for the Probabilities......Page 23 Measuring Beliefs in a Coin Toss......Page 24 EXERCISES......Page 25 3 THE LOGIC OF UNCERTAINTY......Page 26 Solving a Combination of Two Probabilities......Page 27 Applying the Product Rule of Probability......Page 29 Example: Calculating the Probability of Being Late......Page 31 Calculating OR for Mutually Exclusive Events......Page 32 Using the Sum Rule for Non–Mutually Exclusive Events......Page 33 Example: Calculating the Probability of Getting a Hefty Fine......Page 34 EXERCISES......Page 35 STRUCTURE OF A BINOMIAL DISTRIBUTION......Page 36 UNDERSTANDING AND ABSTRACTING OUT THE DETAILS OF OUR PROBLEM......Page 37 COUNTING OUR OUTCOMES WITH THE BINOMIAL COEFFICIENT......Page 38 Combinatorics: Advanced Counting with the Binomial Coefficient......Page 39 Calculating the Probability of the Desired Outcome......Page 40 EXAMPLE: GACHA GAMES......Page 42 WRAPPING UP......Page 44 EXERCISES......Page 45 Distinguishing Probability, Statistics, and Inference......Page 46 Calculating the Probability of Probabilities......Page 47 Breaking Down the Probability Density Function......Page 51 Applying the Probability Density Function to Our Problem......Page 52 Quantifying Continuous Distributions with Integration......Page 53 REVERSE-ENGINEERING THE GACHA GAME......Page 54 WRAPPING UP......Page 55 EXERCISES......Page 56 PART II BAYESIAN PROBABILITY AND PRIOR PROBABILITIES......Page 57 INTRODUCING CONDITIONAL PROBABILITY......Page 58 Dependence and the Revised Rules of Probability......Page 59 CONDITIONAL PROBABILITIES IN REVERSE AND BAYES’ THEOREM......Page 60 INTRODUCING BAYES’ THEOREM......Page 61 WRAPPING UP......Page 62 EXERCISES......Page 63 7 BAYES’ THEOREM WITH LEGO......Page 64 WORKING OUT CONDITIONAL PROBABILITIES VISUALLY......Page 67 WORKING THROUGH THE MATH......Page 68 EXERCISES......Page 69 THE THREE PARTS......Page 70 Solving for the Likelihood......Page 71 Normalizing the Data......Page 72 The Likelihood for Our Alternative Hypothesis......Page 74 The Posterior for Our Alternative Hypothesis......Page 75 WRAPPING UP......Page 76 EXERCISES......Page 77 C-3PO’S ASTEROID FIELD DOUBTS......Page 78 DETERMINING C-3PO’S BELIEFS......Page 79 ACCOUNTING FOR HAN’S BADASSERY......Page 80 CREATING SUSPENSE WITH A POSTERIOR......Page 82 WRAPPING UP......Page 83 EXERCISES......Page 84 PART III PARAMETER ESTIMATION......Page 85 ESTIMATING SNOWFALL......Page 86 Solving a Simplified Version of Our Problem......Page 87 Solving a More Extreme Case......Page 90 Estimating the True Value with Weighted Probabilities......Page 92 Defining Expectation, Mean, and Averaging......Page 93 WRAPPING UP......Page 94 EXERCISES......Page 95 DROPPING COINS IN A WELL......Page 96 FINDING THE MEAN ABSOLUTE DEVIATION......Page 97 FINDING THE STANDARD DEVIATION......Page 99 WRAPPING UP......Page 100 EXERCISES......Page 101 MEASURING FUSES FOR DASTARDLY DEEDS......Page 102 THE NORMAL DISTRIBUTION......Page 104 SOLVING THE FUSE PROBLEM......Page 107 SOME TRICKS AND INTUITIONS......Page 110 THE BETA DISTRIBUTION AND THE NORMAL DISTRIBUTION......Page 112 EXERCISES......Page 114 THE PROBABILITY DENSITY FUNCTION......Page 115 Visualizing and Interpreting the PDF......Page 116 INTRODUCING THE CUMULATIVE DISTRIBUTION FUNCTION......Page 118 Finding the Median......Page 121 Approximating Integrals Visually......Page 122 Estimating Confidence Intervals......Page 123 Using the CDF in R......Page 124 Visualizing and Understanding the Quantile Function......Page 125 Calculating Quantiles in R......Page 126 EXERCISES......Page 127 PREDICTING EMAIL CONVERSION RATES......Page 128 TAKING IN WIDER CONTEXT WITH PRIORS......Page 130 PRIOR AS A MEANS OF QUANTIFYING EXPERIENCE......Page 134 IS THERE A FAIR PRIOR TO USE WHEN WE KNOW NOTHING?......Page 135 EXERCISES......Page 137 PART IV HYPOTHESIS TESTING: THE HEART OF STATISTICS......Page 138 SETTING UP A BAYESIAN A/B TEST......Page 139 Collecting Data......Page 140 In How Many Worlds Is B the Better Variant?......Page 142 How Much Better Is Each Variant B Than Each Variant A?......Page 143 EXERCISES......Page 145 REVISITING BAYES’ THEOREM......Page 146 Prior Odds......Page 147 Posterior Odds......Page 148 Testing for a Loaded Die......Page 149 Self-Diagnosing Rare Diseases Online......Page 150 EXERCISES......Page 152 USING THE BAYES FACTOR TO UNDERSTAND THE MYSTIC SEER......Page 153 Measuring the Bayes Factor......Page 154 Accounting for Prior Beliefs......Page 155 DEVELOPING OUR OWN PSYCHIC POWERS......Page 156 WRAPPING UP......Page 157 EXERCISES......Page 158 A PSYCHIC FRIEND ROLLING DICE......Page 159 Incorporating Prior Odds......Page 160 Considering Alternative Hypotheses......Page 161 ARGUING WITH RELATIVES AND CONSPIRACY THEORISTS......Page 162 WRAPPING UP......Page 163 EXERCISES......Page 164 IS THE CARNIVAL GAME REALLY FAIR?......Page 165 Searching for More Hypotheses with R......Page 167 Adding Priors to Our Likelihood Ratios......Page 169 BUILDING A PROBABILITY DISTRIBUTION......Page 171 FROM THE BAYES FACTOR TO PARAMETER ESTIMATION......Page 173 EXERCISES......Page 176 R AND RSTUDIO......Page 177 CREATING AN R SCRIPT......Page 178 Doubles......Page 179 Strings......Page 180 Missing Values......Page 181 Vectors......Page 182 FUNCTIONS......Page 183 Basic Functions......Page 184 The sum(), cumsum(), and diff() Functions......Page 185 The : operator and the seq() Function......Page 186 The ifelse() Function......Page 187 The runif() Function......Page 188 The sample() Function......Page 189 DEFINING YOUR OWN FUNCTIONS......Page 190 CREATING BASIC PLOTS......Page 192 EXERCISE: SIMULATING A STOCK PRICE......Page 195 SUMMARY......Page 196 FUNCTIONS......Page 197 Determining How Far You’ve Run......Page 199 Measuring the Area Under the Curve: The Integral......Page 200 Measuring the Rate of Change: The Derivative......Page 205 THE FUNDAMENTAL THEOREM OF CALCULUS......Page 209 ABOUT THE AUTHOR......Page 211