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 1
3 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 2
3 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 3
3 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 4
3 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 5
3 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 6
3 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 7
3 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 8
3 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 9
3 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 10
3 attempts allowed
11. Power
Power
Exercise 60
Question
Exercise 61
Notes
Exercise 62
T-test power
Exercise 63
Paper Exercises
Quiz 11
3 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 12
3 attempts allowed
Statistical inference for data science
A companion to the Coursera Statistical Inference Course
Statistical inference for data science
A companion to the Coursera Statistical Inference Course
This course gives a brief, but rigorous, treatment of statistical inference intended for practicing Data Scientists.
The instructor is letting you choose the price you pay for this course!
The instructor is letting you choose the price you pay for this course!
This course gives a brief, but rigorous, treatment of statistical inference intended for practicing Data Scientists.
About
About the Course
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
Categories
Price
Course Price
Minimum price
$129.00
$179.00
You pay
$179.00Author earns
$143.20Instructor
About the Instructor
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.
Episode 21
An Interview with Brian Caffo
Material
Course Material
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