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
What test to use & how to code it in R
One-Sample Mean compared to Population & Confidence Intervals
Independent Samples Means Test
Calculating Power and Sample Size
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
Global and individual predictors p-values of explained variance in a linear model
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
Variance of Estimated Parameters
Interrrupted Time Series (ITS) & Poisson Regression
Conditional Logistic Regression
CO2 and Global Temperature: Model analysis, autocorrelation and time series
On the meaning of Parametric v Nonparametric
Stochastic processes - general concepts
Random walk - Return to origin
Time Series: Variance, Covariance and Correlation
How to calculate manually ACF and PACFs
Alternate formula variance (raw moments)
Convolution or pdf of Z = X + Y
Simpson’s Paradox and Random Effects
Natural phenomena are not Gaussian
Markov Chains (Stochastic Matrices) & Ergodicity
A Practical Example of Markov Chain Monte Carlo (MCMC)
Discrete Fourier transform (DFT)
Modular Forms and Möbius transformation
Zeta Function: Functional Equation and Analytical Continuation
Systems of linear equations and basis for the four spaces
Variance-Covariance Matrix and A transpose A
Tensors Linearization of Multilinear map
dx as a covector (linear functional)
covectors, 1-forms and gradient
Covariant gradient field transformation
Covariant, Contravariant Forms and Metric Tensor
Tensors in physics: The Metric Tensor
Riemann Tensor for a Sphere and Schwarzschild Christoffel Symbols
Tensors in physics: Lorentz transformations
NOTE: These are tentative notes on different topics for personal use - expect mistakes and misunderstandings.