Statistical inference for data science
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Last updated on 20160524
About the Book
The ideal reader for this book will be quantitatively literate and has a basic understanding of statistical concepts and R programming. The book gives a rigorous treatment of the elementary concepts in statistical inference from a classical frequentist perspective. After reading this book and performing the exercises, the student will understand the basics of hypothesis testing, confidence intervals and probability. Check out the status of the book at github https://github.com/bcaffo/LittleInferenceBook
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The book + videos + homework videos + github repos
This contains the book, the videos for the course, the homework solutions and the course repositories. Not necessary if you want to get the videos on YouTube or Coursera and the repos from github.
Includes:
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This is all of the homework videos downloadable. The filename contains the problem numbers. These are all available on YouTube as well.
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This contains the github repo for the Coursera Class and the homework.
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Table of Contents

 About this book
 About the picture on the cover

1. Introduction
 Before beginning
 Statistical inference defined
 Summary notes
 The goals of inference
 The tools of the trade
 Different thinking about probability leads to different styles of inference
 Exercises

2. Probability
 Where to get a more thorough treatment of probability
 Kolmogorov’s Three Rules
 Consequences of The Three Rules
 Random variables
 Probability mass functions
 Probability density functions
 CDF and survival function
 Quantiles
 Exercises

3. Conditional probability
 Conditional probability, motivation
 Conditional probability, definition
 Bayes’ rule
 Diagnostic Likelihood Ratios
 Independence
 IID random variables
 Exercises

4. Expected values
 The population mean for discrete random variables
 The sample mean
 Continuous random variables
 Simulation experiments
 Summary notes
 Exercises

5. Variation
 The variance
 The sample variance
 Simulation experiments
 The standard error of the mean
 Data example
 Summary notes
 Exercises

6. Some common distributions
 The Bernoulli distribution
 Binomial trials
 The normal distribution
 The Poisson distribution
 Exercises

7. Asymptopia
 Asymptotics
 Limits of random variables
 The Central Limit Theorem
 CLT simulation experiments
 Confidence intervals
 Simulation of confidence intervals
 Poisson interval
 Summary notes
 Exercises

8. t Confidence intervals
 Small sample confidence intervals
 Gosset’s t distribution
 The data
 Independent group t confidence intervals
 Confidence interval
 Mistakenly treating the sleep data as grouped
 Unequal variances
 Summary notes
 Exercises

9. Hypothesis testing
 Hypothesis testing
 Types of errors in hypothesis testing
 Discussion relative to court cases
 Building up a standard of evidence
 General rules
 Two sided tests
 T test in R
 Connections with confidence intervals
 Two group intervals
 Exact binomial test
 Exercises

10. Pvalues
 Introduction to Pvalues
 What is a Pvalue?
 The attained significance level
 Binomial Pvalue example
 Poisson example
 Exercises

11. Power
 Power
 Question
 Notes
 Ttest power
 Exercises

12. The bootstrap and resampling
 The bootstrap
 The bootstrap principle
 Group comparisons via permutation tests
 Permutation tests
 Variations on permutation testing
 Permutation test B v C
 Exercises
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