Question on the normality assumption of the predictor variable and the covariance matrix of the likelihood

Asked Jul 23 '23 at 10:09

Active Jul 25 '23 at 01:24

Viewed 24 times

Suppose you are trying to fit a continuous variable y depending on some input x ( es y= ax+b) and you are using a multivariate distribution as likelihood for the fitting.

Does using a multinormal distribution with a non diagonal covariance matrix as likelihood means necessarily that the target variable y is not normally distributed around its true value ? in other words, the assumption that the predictive uncertainty is gaussian is still valid?

edited Jul 25 '23 at 01:24

kjetil b halvorsen

77,844

asked Jul 23 '23 at 10:09

Alucard

Do you mean the distribution of $(Y\vert X=x)$ when $(X,Y)\sim N((\mu_X, \mu_Y), \Sigma)$ for non-diagonal covariance matrix $\Sigma?$ That distribution is Gaussian, yes. – Dave Jul 23 '23 at 16:41
2

JFYI: non-zero off-diagonal elements of the covariance matrix simply imply correlation. Nothing more and nothing less. – Durden Jul 25 '23 at 00:05

Question on the normality assumption of the predictor variable and the covariance matrix of the likelihood

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