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variance-covariance matrix

contour ellipsoids of a projected MND

Multivariate Normal Distributions – I – Basics and a random vector of independent Gaussians

This post series is about mathematical aspects of so called “Multivariate Normal Distributions“. In the literature two abbreviations are common: MNDs or MVNs. I will use both synonymously. To get an easy access I want to introduce MNDs as the result of a linear transformations applied to random vectors whose components can be described by independent 1-dimensional normal distributions. Afterward… Read More »Multivariate Normal Distributions – I – Basics and a random vector of independent Gaussians

Probability density function of a Bivariate Normal Distribution – derived from assumptions on marginal distributions and functional factorization

For a better understanding of ML experiments regarding a generator of human faces based on a convolutional autoencoder we need an understanding of multivariate and bivariate normal distributions and their probability densities. This post is about the probability density function of a bivariate normal distribution depending on two correlated random variables X and Y. Most derivations of the mathematical form… Read More »Probability density function of a Bivariate Normal Distribution – derived from assumptions on marginal distributions and functional factorization