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BVD

Confidence ellipses based on covariance matrix

How to compute confidence ellipses – I – simple method based on the Pearson correlation coefficient

This post was motivated by a publication of Carsten Schelp [1]. Actually, a long time ago. I used his results in 2021, when I had to plot confidence ellipses during the analysis of statistical (multivariate) vector distributions produced a Machine Learning algorithm. So, all acknowledgements belong to Schelp’s work. However, his ideas have also triggered some of my own efforts… Read More »How to compute confidence ellipses – I – simple method based on the Pearson correlation coefficient

Confidence ellipses for an approximate BVD

Bivariate Normal Distribution – integrated probability up to a given Mahalanobis distance, the Chi-squared distribution and confidence ellipses

In previous posts of this blog we have discussed the general form of the probability density function [pdf] of a Bivariate Normal Distribution [BVD]. In this post we consider the integral over a BVD’s pdf up to a defined value of the Mahalanobis Distance. A given value of the latter defines an elliptic contour line of constant probability density. With… Read More »Bivariate Normal Distribution – integrated probability up to a given Mahalanobis distance, the Chi-squared distribution and confidence ellipses

BVD contour ellipses

Bivariate Normal Distribution – Mahalanobis distance and contour ellipses

I continue with my posts on Bivariate Normal Distributions [BVDs]. In this post we consider the exponent of a BVD’s probability density function [pdf]. This function is governed by a central matrix Σ-1, the inverse of the variance-covariance matrix of the BVD’s random vector. We define the so called Mahalanobis distance dm for BVD vectors. A constant value of the… Read More »Bivariate Normal Distribution – Mahalanobis distance and contour ellipses

Contours of a bivariate normal distribution

Bivariate normal distribution – explicit reconstruction of a BVD random vector via Cholesky decomposition of the covariance matrix

In other posts of this blog I have discussed the general form of a Bivariate Normal Distribution [BVD] . For a centered Cartesian coordinate system [CCS] (see below), we have already seen the following: In this post I will give you a recipe to explicitly construct two random variables X, Y of a BVD from 1-dimensional Gaussians Z1, Z2 with… Read More »Bivariate normal distribution – explicit reconstruction of a BVD random vector via Cholesky decomposition of the covariance matrix