NOTES ON STATISTICS AND PROBABILITY:
INFERENCE:
One-Sample Mean compared to Population & Confidence Intervals
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
PROPORTIONS:
Confidence Interval and Margin of Error
Comparing Sample Proportion to Population: Z test of proportions and Binomial test
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:
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
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