2D Gaussian distribution: confidence rectangles and ellipses (Matlab example)

Antonio Sala, UPV

Difficulty: ** ,       Relevance: ,      Duration: 18:51

Summary:

This video illustrates the computation of the ‘maximum likelihood per unit area’ region for a 2D standard normal distribution (that is, a multivariate Gaussian probability distribution with identity covariance matrix), using the ${\chi }^2$ formula. Such a region is, indeed, a ‘confidence circle’ given the circular contours of the density function.

We also compute ‘marginal’ confidence regions by studying each variable separately (e.g., $\pm 1.96\sigma$ would give the 95% confidence interval). Multiplying the probabilities of an interval would calculate the probabilities of a confidence ’rectangle’ (square in this unit variance case). The final part of the video discusses the confidence ellipse that would come out with a covariance diag([1 4]), and the resulting rectangles. The calculations if the variance-covariance matrix were not diagonal would not be valid; this is discussed in more detail in the video [cfrcwrongEN], a continuation of this one.

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.