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Material for Statistical inference for data science

A companion to the Coursera Statistical Inference Course

Brian Caffo

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Author

About the Author

Brian Caffo

Brian Caffo, PhD is a professor in the Department of Biostatistics at the Johns Hopkins Bloomberg School of Public Health. Along with Roger Peng and Jeff Leek, Dr. Caffo created the Data Science Specialization on Coursera. Dr. Caffo is leading  expert in statistics and biostatistics and is the recipient of the PECASE award, the highest honor given by the US Government for early career scientists and engineers.

Leanpub Podcast

Episode 21

An Interview with Brian Caffo

Contents

Table of Contents

1. Introduction

  1. Before beginning
  2. About the picture on the cover
  3. Statistical inference defined
  4. Motivating example: who’s going to win the election?
  5. Motivating example: predicting the weather
  6. Motivating example: brain activation
  7. Summary notes
  8. Exercise 1
  9. The goals of inference
  10. Exercise 2
  11. The tools of the trade
  12. Exercise 3
  13. Different thinking about probability leads to different styles of inference
  14. Exercise 4
  15. Paper Exercises
  16. Exercise 5
  17. Quiz 1

2. Probability

  1. Exercise 6
  2. Where to get a more thorough treatment of probability
  3. Kolmogorov’s Three Rules
  4. Exercise 7
  5. Consequences of The Three Rules
  6. Example of Implementing Probability Calculus
  7. Exercise 8
  8. Random variables
  9. Probability mass functions
  10. Example
  11. Exercise 9
  12. Probability density functions
  13. Example
  14. Exercise 10
  15. CDF and survival function
  16. Example
  17. Exercise 11
  18. Quantiles
  19. Example
  20. Exercise 12
  21. Paper Exercises
  22. Quiz 2

3. Conditional probability

  1. Conditional probability, motivation
  2. Conditional probability, definition
  3. Example
  4. Exercise 13
  5. Bayes’ rule
  6. Diagnostic tests
  7. Example
  8. Exercise 14
  9. Diagnostic Likelihood Ratios
  10. HIV example revisited
  11. Exercise 15
  12. Independence
  13. Example
  14. Case Study
  15. Exercise 16
  16. IID random variables
  17. Exercise 17
  18. Paper Exercises
  19. Quiz 3

4. Expected values

  1. The population mean for discrete random variables
  2. The sample mean
  3. Example Find the center of mass of the bars
  4. The center of mass is the empirical mean
  5. Example of a population mean, a fair coin
  6. What about a biased coin?
  7. Example Die Roll
  8. Exercise 18
  9. Continuous random variables
  10. Example
  11. Facts about expected values
  12. Simulation experiments
  13. Standard normals
  14. Averages of x die rolls
  15. Averages of x coin flips
  16. Exercise 19
  17. Summary notes
  18. Exercise 20
  19. Paper Exercises
  20. Exercise 21
  21. Quiz 4

5. Variation

  1. The variance
  2. Example
  3. Example
  4. Exercise 22
  5. The sample variance
  6. Exercise 23
  7. Simulation experiments
  8. Simulating from a population with variance 1
  9. Variances of x die rolls
  10. Exercise 24
  11. The standard error of the mean
  12. Summary notes
  13. Simulation example 1: standard normals
  14. Simulation example 2: uniform density
  15. Simulation example 3: Poisson
  16. Simulation example 4: coin flips
  17. Exercise 25
  18. Data example
  19. Exercise 26
  20. Summary notes
  21. Exercise 27
  22. Paper Exercises
  23. Quiz 5

6. Some common distributions

  1. The Bernoulli distribution
  2. Exercise 28
  3. Binomial trials
  4. Example
  5. Exercise 29
  6. The normal distribution
  7. Reference quantiles for the standard normal
  8. Shifting and scaling normals
  9. Example
  10. Example
  11. Example
  12. Exercise 30
  13. The Poisson distribution
  14. Rates and Poisson random variables
  15. Example
  16. Poisson approximation to the binomial
  17. Example, Poisson approximation to the binomial
  18. Exercise 31
  19. Paper Exercises
  20. Exercise 32
  21. Quiz 6

7. Asymptopia

  1. Asymptotics
  2. Limits of random variables
  3. Law of large numbers in action
  4. Law of large numbers in action, coin flip
  5. Discussion
  6. Exercise 33
  7. The Central Limit Theorem
  8. CLT simulation experiments
  9. Die rolling
  10. Coin CLT
  11. Exercise 34
  12. Confidence intervals
  13. Example CI
  14. Example using sample proportions
  15. Example
  16. Exercise 35
  17. Simulation of confidence intervals
  18. Exercise 36
  19. Poisson interval
  20. Example
  21. Simulating the Poisson coverage rate
  22. Exercise 37
  23. Summary notes
  24. Exercise 38
  25. Paper Exercises
  26. Quiz 7

8. t Confidence intervals

  1. Small sample confidence intervals
  2. Gosset’s t distribution
  3. Code for manipulate
  4. Summary notes
  5. Example of the t interval, Gosset’s sleep data
  6. Exercise 39
  7. The data
  8. Exercise 40
  9. Independent group t confidence intervals
  10. Confidence interval
  11. Exercise 41
  12. Mistakenly treating the sleep data as grouped
  13. ChickWeight data in R
  14. Exercise 42
  15. Unequal variances
  16. Exercise 43
  17. Summary notes
  18. Exercise 44
  19. Paper Exercises
  20. Exercise 45
  21. Quiz 8

9. Hypothesis testing

  1. Hypothesis testing
  2. Example
  3. Exercise 46
  4. Types of errors in hypothesis testing
  5. Exercise 47
  6. Discussion relative to court cases
  7. Building up a standard of evidence
  8. Exercise 48
  9. General rules
  10. Summary notes
  11. Example reconsidered
  12. Exercise 49
  13. Two sided tests
  14. Exercise 50
  15. T test in R
  16. Exercise 51
  17. Connections with confidence intervals
  18. Two group intervals
  19. Example chickWeight data
  20. Exercise 52
  21. Exact binomial test
  22. Exercise 53
  23. Paper Exercises
  24. Exercise 54
  25. Quiz 9

10. P-values

  1. Introduction to P-values
  2. What is a P-value?
  3. Exercise 55
  4. The attained significance level
  5. Exercise 56
  6. Binomial P-value example
  7. Exercise 57
  8. Poisson example
  9. Exercise 58
  10. Paper Exercises
  11. Exercise 59
  12. Quiz 10

11. Power

  1. Power
  2. Exercise 60
  3. Question
  4. Exercise 61
  5. Notes
  6. Exercise 62
  7. T-test power
  8. Exercise 63
  9. Paper Exercises
  10. Quiz 11

12. The bootstrap and resampling

  1. The bootstrap
  2. Example Galton’s fathers and sons dataset
  3. Exercise 64
  4. The bootstrap principle
  5. The bootstrap in practice
  6. Nonparametric bootstrap algorithm example
  7. Example code
  8. Summary notes on the bootstrap
  9. Exercise 65
  10. Group comparisons via permutation tests
  11. Permutation tests
  12. Exercise 66
  13. Variations on permutation testing
  14. Permutation test B v C
  15. Exercise 67
  16. Paper Exercises
  17. Exercise 68
  18. Quiz 12

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