While reading on Gaussian Discriminant Analysis, I came across a derivation of the parameters (specifically, $\sum$) using Maximum Likelihood Estimation that claimed that the MLE of $\sum$ is equivalent to the MLE of $\sum^{-1}$, $\sum$ being the covariance matrix of the multivariate Gaussian distribution.

Though I am able to reach the same result without using the above, I want to know:

  1. Why does this hold true?
  2. Does this hold true for any positive definite matrix $A \in \mathbb S_{++}^{n}$, or does the fact that $\sum$ is a covariance matrix play a role in proving this.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.