NOTES ON STATISTICS AND PROBABILITY:
DISTRIBUTIONS:
Ditributions and their stories
Uniform Distribution and the Probability Integral Transform
Moment Generating Functions (MGF)
Probability Generating Functions (PGF)
Multivariate Gaussian Distribution
Multivariate Gaussian Distribution: Random Sampling and the Cholesky
INFERENCE:
One-Sample Mean compared to Population & Confidence Intervals
Independent Samples Means Test
PROPORTIONS:
Confidence Interval and Margin of Error
Comparing Sample Proportion to Population: Z-test proportions, CI and margin of error
Comparing Sample Proportions to Population: Exact Multinomial (Goodness of Fit)
Comparing Sample Proportions: Fisher Exact; Chi square; G-test; Z-test
Chi Square: Test of Independence and Homogeneity
Chi Square: Testing Standard Deviation (Variance)
Chi Square Test in R: Monte Carlo Option
Grading on the curve: detectable with GoF test
Monte Carlo Validation of the Z Test of Proportions
Monte Carlo alternative to Chi Square
REGRESSION:
Global and individual predictors p-values of explained variance in a linear model
Variance-Covariance Matrix and A transpose A
Calculating Sts. Error, t value and Pr(>|t|) of coefficients
Manual calculation ANOVA OLS lm Models
Confidence Intervals & p-values of OLS
Interpretation of Output in Linear Model with Interactions
Comparing Models with Mixed Effects
Predict Function in Mixed Effects
Model Matrices in Mixed Effects
Confounders, Control Variables, Endogeneity
NON-PARAMETRIC:
On the meaning of Parametric v Nonparametric
MACHINE LEARNING:
TIME SERIES:
Random walk - Return to origin
Time Series: Variance, Covariance and Correlation
PROBABILITY TOPICS:
OTHER:
Alternate formula variance (raw moments)
Convolution or pdf of Z = X + Y
Simpson's Paradox and Random Effects
Natural phenomena are not Gaussian
A Practical Example of Markov Chain Monte Carlo (MCMC)
LINEAR ALGEBRA:
Systems of linear equations and basis for the four spaces