a neat EM resolution

Read (and answered) this question on X validation about finding the maximum likelihood estimator of a 2×2 Gaussian covariance matrix when some observations are partly missing. The neat thing is that, in this case, the maximisation step is identical to the maximum likelihood estimation of the 2×2 Gaussian covariance matrix by redefining the empirical covariance matrix into Z and maximising

$-n\log|\Sigma|-\text{trace}(Z\Sigma^{-1})$

in Σ. Nothing involved but fun to explain, nonetheless. (In my final exam this year, no student even approached the EM questions!)

This entry was posted on February 3, 2021 at 12:21 am and is filed under Books, Kids, Statistics, University life with tags cross validated, EM algorithm, final exam, maximum likelihood estimation, missing data, MLE, normal model. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

Xi'an's Og