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.
Author(s): Brian S. Blais
Publisher: Save The Broccoli Publishing
Year: 2018
Language: English
Pages: 242
Tags: Statistical Inference
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
