Statistical inference for data science
This book is 99% complete
Last updated on 2016-05-24
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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This is the book plus all of the videos in MP4 format. Not necessary if you just want to watch the videos on YouTube or Coursera.
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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.
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Video lectures associated with the book.
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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
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- 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
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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
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3. Conditional probability
- Conditional probability, motivation
- Conditional probability, definition
- Bayes’ rule
- Diagnostic Likelihood Ratios
- Independence
- IID random variables
- Exercises
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4. Expected values
- The population mean for discrete random variables
- The sample mean
- Continuous random variables
- Simulation experiments
- Summary notes
- Exercises
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5. Variation
- The variance
- The sample variance
- Simulation experiments
- The standard error of the mean
- Data example
- Summary notes
- Exercises
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6. Some common distributions
- The Bernoulli distribution
- Binomial trials
- The normal distribution
- The Poisson distribution
- Exercises
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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
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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
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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
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10. P-values
- Introduction to P-values
- What is a P-value?
- The attained significance level
- Binomial P-value example
- Poisson example
- Exercises
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11. Power
- Power
- Question
- Notes
- T-test power
- Exercises
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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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