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Pearson correlation coefficient

How to compute confidence ellipses – III – 4 alternative construction methods

In previous mathematical posts of this blog, we have studied some core properties of Bivariate Normal Distributions [BVDs]. During the rather mathematical tour de force we have come across various methods to construct and plot confidence ellipses for a given confidence level and respective Mahalanobis distance from the distribution’s center. We have also covered the mathematical derivation of the methods.… Read More »How to compute confidence ellipses – III – 4 alternative construction methods

How to compute confidence ellipses – II – equivalence of Schelp’s basic construction method for confidence ellipse with other approaches

In the 1st post of this series, I have motivated a simple method for constructing confidence ellipses for assumedly Bivariate Normal Distributions [BVD] or at least approximate BVDs. A reader has asked me, whether one can prove more rigidly that the proposed method of C. Schelp is equivalent to other BVD-based methods. Well, in this post we show that the… Read More »How to compute confidence ellipses – II – equivalence of Schelp’s basic construction method for confidence ellipse with other approaches

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

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