Preamble
1
Axioms of Probability Theory
1.1
Manipulation of Sets
1.2
Venn and Euler diagrams
2
Discrete Probability Spaces
2.1
Bernoulli trials
2.2
Sampling without replacement
2.3
Pólya’s urn model
2.4
Factorials and binomials coefficients
3
Distributions on the Real Line
4
Discrete Distributions
4.1
Uniform distributions
4.2
Binomial distributions
4.3
Geometric distributions
4.4
Poisson distributions
5
Continuous Distributions
5.1
Uniform distributions
5.2
Normal distributions
5.3
Exponential distributions
5.4
Normal approximation to the binomial
6
Multivariate Distributions
6.1
Multinomial distribution
6.2
Uniform distributions
6.3
Normal distributions
7
Expectation and Concentration
7.1
Concentration inequalities
8
Convergence of Random Variables
8.1
Law of Large Numbers
8.2
Central Limit Theorem
8.3
Extreme Value Theory
9
Stochastic Processes
9.1
Markov chains
9.2
Simple random walk
9.3
Galton–Watson processes
10
Sampling and Simulation
10.1
Monte Carlo simulations
10.2
Monte Carlo integration
10.3
Rejection sampling
10.4
Markov chain Monte Carlo
11
Data Collection
11.1
Survey sampling
11.1.1
Sampling according to prescribed inclusion probabilities
11.1.2
Cluster sampling
11.1.3
Stratified sampling
11.2
Experimental design
11.3
Observational studies
12
Models, Estimators, and Tests
12.1
Confidence intervals
12.2
Tests
13
Properties of Estimators and Tests
13.1
Comparing estimators
13.2
Uniformly most powerful tests
14
One Proportion
14.1
Comparing various confidence intervals
15
Multiple Proportions
15.1
One-sample goodness-of-fit testing
15.2
Association studies
15.3
Matched-pair experiment
16
One Numerical Sample
16.1
Quantiles and other summary statistics
16.2
Empirical distribution function
16.3
Histogram
16.4
Confidence interval for the median
16.5
Bootstrap confidence interval
16.6
Kernel density estimation
16.7
Kaplan–Meier estimator
17
Multiple Numerical Samples
17.1
An example of A/B testing
17.1.1
Boxplots
17.1.2
Histograms
17.1.3
Welch–Student test
17.1.4
Rank tests
18
Paired Numerical Samples
18.1
Scatterplot
18.2
Testing for symmetry
18.3
Repeated measures
19
Correlation Analysis
19.1
Scatterplot
19.2
Sample correlations
19.3
Correlations tests
19.4
Distance covariance (and test)
20
Multiple Testing
20.1
An example from genetics
20.1.1
Adjusted p-values
20.1.2
Rejections
20.2
An example from meta-analysis
20.2.1
Cochran–Mantel–Haenszel test
20.2.2
Combination tests
21
Regression Analysis
21.1
Regression
21.1.1
Kernel smoothing
21.1.2
Choice of bandwidth by cross-validation
21.1.3
Local linear regression
21.1.4
Polynomial regression
21.2
Classification
21.2.1
Nearest neighbor classifier
21.2.2
Linear classification
22
Foundational Issues
Principles of Statistical Analysis: R Companion
22
Foundational Issues
(Nothing here at the moment.)