Statistical Inference for Everyone

Description

Approaching an introductory statistical inference textbook in a novel way, this book is motivated by the perspective of "probability theory as logic". Targeted to the typical "Statistics 101" college student this book covers the topics typically treated in such a course - but from a fresh angle. This book walks through a simple introduction to probability, and then applies those principles to all problems of inference. Topics include hypothesis testing, data visualization, parameter inference, and model comparison. Statistical Inference for Everyone is freely available under the Creative Commons License, and includes a software library in Python for making calculations and visualizations straightforward. Proposal......Page 29 Introduction to Probability......Page 33 Models and Data......Page 34 What is Probability?......Page 35 Conditional Probability......Page 39 Rules of Probability......Page 40 Venn Mnemonic for the Rules of Probability......Page 49 Lessons from Bayes' Rule - A First Look......Page 50 Cancer and Probability......Page 53 Weather......Page 55 Adding Dice......Page 56 The Birthday Problem......Page 58 The Lottery Problem or Rare Things Are Common......Page 62 Monte Hall Problem......Page 64 Exercises......Page 66 Some Philosophical Applications......Page 67 Computer Examples......Page 72 Coin Flipping......Page 75 Some Philosophical Applications......Page 82 Visualization of Data......Page 87 Computer Examples......Page 92 The High/Low Deck Game......Page 95 Multiple Hypotheses......Page 102 Disease Testing......Page 109 M&M's......Page 112 Psychic Octopi......Page 114 Monty Hall Problem......Page 117 Bent Coins......Page 121 Priors versus Data......Page 124 Moving Toward the Continuous......Page 125 MAP and Areas......Page 127 Quartiles......Page 129 Best Estimates......Page 131 Uncertainty in the Best Estimates......Page 133 Exercises......Page 134 Computer Examples......Page 135 Binomial and Beta Distributions......Page 139 The Normal Distribution - Properties......Page 140 The Normal Distribution - Estimating From Data......Page 146 Normal Approximation......Page 149 Summary......Page 154 Computer Examples......Page 155 z-test......Page 159 What it means and doesn't mean......Page 161 Student-t-test......Page 162 Computer Examples......Page 163 Normal Model - Inference about Means......Page 165 Normal Model Again - Inference about Means and Deviations......Page 166 Beta Model - Inference About Proportions......Page 170 Model Construction......Page 173 Computer Examples......Page 180 Simple Linear Regression......Page 193 Multiple regression......Page 199 Computer Examples......Page 202 One-Dimensional Models......Page 211 Multi-Dimensional Models......Page 213 Hierarchical Model Example - Kruschke BEST Test......Page 215 Where have we come?......Page 219 Where are we going?......Page 220 Bibliography......Page 221 Computational Analysis......Page 223 Some Math Notation......Page 225 Qualitative labels to probability values......Page 227 Uniform......Page 229 Beta......Page 232 Normal (Gaussian)......Page 233 Credible Intervals for Standard Normal Distribution......Page 235 Credible Intervals for Student's t Distribution......Page 236 Cumulative Standard Normal Distribution......Page 238