Statistical inference for data science (The Course)
Course Info
This course includes 5 attempts.
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
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
- The goals of inference
- The tools of the trade
- Different thinking about probability leads to different styles of inference
- Paper Exercises
- 2. Probability
- Where to get a more thorough treatment of probability
- Kolmogorov’s Three Rules
- Consequences of The Three Rules
- Example of Implementing Probability Calculus
- Random variables
- Probability mass functions
- Example
- Probability density functions
- Example
- CDF and survival function
- Example
- Quantiles
- Example
- Paper Exercises
- 3. Conditional probability
- Conditional probability, motivation
- Conditional probability, definition
- Example
- Bayes’ rule
- Diagnostic tests
- Example
- Diagnostic Likelihood Ratios
- HIV example revisited
- Independence
- Example
- Case Study
- IID random variables
- Paper Exercises
- 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
- Continuous random variables
- Example
- Facts about expected values
- Simulation experiments
- Standard normals
- Averages of x die rolls
- Averages of x coin flips
- Summary notes
- Paper Exercises
- 5. Variation
- The variance
- Example
- Example
- The sample variance
- Simulation experiments
- Simulating from a population with variance 1
- Variances of x die rolls
- 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
- Data example
- Summary notes
- Paper Exercises
- 6. Some common distributions
- The Bernoulli distribution
- Binomial trials
- Example
- The normal distribution
- Reference quantiles for the standard normal
- Shifting and scaling normals
- Example
- Example
- Example
- The Poisson distribution
- Rates and Poisson random variables
- Example
- Poisson approximation to the binomial
- Example, Poisson approximation to the binomial
- Paper Exercises
- 7. Asymptopia
- Asymptotics
- Limits of random variables
- Law of large numbers in action
- Law of large numbers in action, coin flip
- Discussion
- The Central Limit Theorem
- CLT simulation experiments
- Die rolling
- Coin CLT
- Confidence intervals
- Example CI
- Example using sample proportions
- Example
- Simulation of confidence intervals
- Poisson interval
- Example
- Simulating the Poisson coverage rate
- Summary notes
- Paper Exercises
- 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
- The data
- Independent group t confidence intervals
- Confidence interval
- Mistakenly treating the sleep data as grouped
- ChickWeight data in R
- Unequal variances
- Summary notes
- Paper Exercises
- 9. Hypothesis testing
- Hypothesis testing
- Example
- Types of errors in hypothesis testing
- Discussion relative to court cases
- Building up a standard of evidence
- General rules
- Summary notes
- Example reconsidered
- Two sided tests
- T test in R
- Connections with confidence intervals
- Two group intervals
- Example chickWeight data
- Exact binomial test
- Paper Exercises
- 10. P-values
- Introduction to P-values
- What is a P-value?
- The attained significance level
- Binomial P-value example
- Poisson example
- Paper Exercises
- 11. Power
- Power
- Question
- Notes
- T-test power
- Paper Exercises
- 12. The bootstrap and resampling
- The bootstrap
- Example Galton’s fathers and sons dataset
- The bootstrap principle
- The bootstrap in practice
- Nonparametric bootstrap algorithm example
- Example code
- Summary notes on the bootstrap
- Group comparisons via permutation tests
- Permutation tests
- Variations on permutation testing
- Permutation test B v C
- Paper Exercises
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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