Statistical inference for data science
Course Info
This course includes 5 attempts.
The ideal reader for this course will be quantitatively literate and has a basic understanding of statistical concepts and R programming. The course gives a rigorous treatment of the elementary concepts in statistical inference from a classical frequentist perspective. After reading this course 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
Course Material
- 1. Introduction
- Before beginning
- About the picture on the cover
- Statistical inference defined
- Motivating example: who’s going to win the election?
- Motivating example: predicting the weather
- Motivating example: brain activation
- Summary notes
- Exercise 1
- The goals of inference
- Exercise 2
- The tools of the trade
- Exercise 3
- Different thinking about probability leads to different styles of inference
- Exercise 4
- Paper Exercises
- Exercise 5
- Quiz 13 attempts allowed
- 2. Probability
- Exercise 6
- Where to get a more thorough treatment of probability
- Kolmogorov’s Three Rules
- Exercise 7
- Consequences of The Three Rules
- Example of Implementing Probability Calculus
- Exercise 8
- Random variables
- Probability mass functions
- Example
- Exercise 9
- Probability density functions
- Example
- Exercise 10
- CDF and survival function
- Example
- Exercise 11
- Quantiles
- Example
- Exercise 12
- Paper Exercises
- Quiz 23 attempts allowed
- 3. Conditional probability
- Conditional probability, motivation
- Conditional probability, definition
- Example
- Exercise 13
- Bayes’ rule
- Diagnostic tests
- Example
- Exercise 14
- Diagnostic Likelihood Ratios
- HIV example revisited
- Exercise 15
- Independence
- Example
- Case Study
- Exercise 16
- IID random variables
- Exercise 17
- Paper Exercises
- Quiz 33 attempts allowed
- 4. Expected values
- The population mean for discrete random variables
- The sample mean
- Example Find the center of mass of the bars
- The center of mass is the empirical mean
- Example of a population mean, a fair coin
- What about a biased coin?
- Example Die Roll
- Exercise 18
- Continuous random variables
- Example
- Facts about expected values
- Simulation experiments
- Standard normals
- Averages of x die rolls
- Averages of x coin flips
- Exercise 19
- Summary notes
- Exercise 20
- Paper Exercises
- Exercise 21
- Quiz 43 attempts allowed
- 5. Variation
- The variance
- Example
- Example
- Exercise 22
- The sample variance
- Exercise 23
- Simulation experiments
- Simulating from a population with variance 1
- Variances of x die rolls
- Exercise 24
- The standard error of the mean
- Summary notes
- Simulation example 1: standard normals
- Simulation example 2: uniform density
- Simulation example 3: Poisson
- Simulation example 4: coin flips
- Exercise 25
- Data example
- Exercise 26
- Summary notes
- Exercise 27
- Paper Exercises
- Quiz 53 attempts allowed
- 6. Some common distributions
- The Bernoulli distribution
- Exercise 28
- Binomial trials
- Example
- Exercise 29
- The normal distribution
- Reference quantiles for the standard normal
- Shifting and scaling normals
- Example
- Example
- Example
- Exercise 30
- The Poisson distribution
- Rates and Poisson random variables
- Example
- Poisson approximation to the binomial
- Example, Poisson approximation to the binomial
- Exercise 31
- Paper Exercises
- Exercise 32
- Quiz 63 attempts allowed
- 7. Asymptopia
- Asymptotics
- Limits of random variables
- Law of large numbers in action
- Law of large numbers in action, coin flip
- Discussion
- Exercise 33
- The Central Limit Theorem
- CLT simulation experiments
- Die rolling
- Coin CLT
- Exercise 34
- Confidence intervals
- Example CI
- Example using sample proportions
- Example
- Exercise 35
- Simulation of confidence intervals
- Exercise 36
- Poisson interval
- Example
- Simulating the Poisson coverage rate
- Exercise 37
- Summary notes
- Exercise 38
- Paper Exercises
- Quiz 73 attempts allowed
- 8. t Confidence intervals
- Small sample confidence intervals
- Gosset’s t distribution
- Code for manipulate
- Summary notes
- Example of the t interval, Gosset’s sleep data
- Exercise 39
- The data
- Exercise 40
- Independent group t confidence intervals
- Confidence interval
- Exercise 41
- Mistakenly treating the sleep data as grouped
- ChickWeight data in R
- Exercise 42
- Unequal variances
- Exercise 43
- Summary notes
- Exercise 44
- Paper Exercises
- Exercise 45
- Quiz 83 attempts allowed
- 9. Hypothesis testing
- Hypothesis testing
- Example
- Exercise 46
- Types of errors in hypothesis testing
- Exercise 47
- Discussion relative to court cases
- Building up a standard of evidence
- Exercise 48
- General rules
- Summary notes
- Example reconsidered
- Exercise 49
- Two sided tests
- Exercise 50
- T test in R
- Exercise 51
- Connections with confidence intervals
- Two group intervals
- Example chickWeight data
- Exercise 52
- Exact binomial test
- Exercise 53
- Paper Exercises
- Exercise 54
- Quiz 93 attempts allowed
- 10. P-values
- Introduction to P-values
- What is a P-value?
- Exercise 55
- The attained significance level
- Exercise 56
- Binomial P-value example
- Exercise 57
- Poisson example
- Exercise 58
- Paper Exercises
- Exercise 59
- Quiz 103 attempts allowed
- 11. Power
- Power
- Exercise 60
- Question
- Exercise 61
- Notes
- Exercise 62
- T-test power
- Exercise 63
- Paper Exercises
- Quiz 113 attempts allowed
- 12. The bootstrap and resampling
- The bootstrap
- Example Galton’s fathers and sons dataset
- Exercise 64
- The bootstrap principle
- The bootstrap in practice
- Nonparametric bootstrap algorithm example
- Example code
- Summary notes on the bootstrap
- Exercise 65
- Group comparisons via permutation tests
- Permutation tests
- Exercise 66
- Variations on permutation testing
- Permutation test B v C
- Exercise 67
- Paper Exercises
- Exercise 68
- Quiz 123 attempts allowed
Instructors
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.
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