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Jun 17, 2020 at 16:46 comment added Prototank Thank you for your thorough answer as well as the references. You expressed things very cleanly!
Jun 17, 2020 at 16:45 vote accept Prototank
Jun 16, 2020 at 21:25 comment added chang_trenton Yes, indeed, the multivariate normal PDF replaces the $\frac{x - \mu}{\sigma}$ in the exponential with $(x-\mu)^\top \Sigma^{-1} (x - \mu)$; hence, $p(x)$ in a multivariate normal is a function of the Mahalanobis distance.
Jun 16, 2020 at 21:21 comment added Firebug This term also appears in the Multivariate Normal log-likelihood, so there's another interpretation possible from there.
Jun 16, 2020 at 21:08 history edited chang_trenton CC BY-SA 4.0
clarified preliminaries
Jun 16, 2020 at 21:03 history answered chang_trenton CC BY-SA 4.0