In his book on the minimum message length (MML) theory of inference, Wallace shows how one may derive MML estimates and message length formulae for many popular parametric distributions. An important example is the multivariate Gaussian distribution given in section 6.2.1 of the book. Here, Wallace derives the commonly used Wallace-Freeman (or MML87) message length formula and parameter estimates for the p-variate Gaussian using conjugate priors. After noticing a minor typographical error in the Fisher information formula (pp. 262), I decided to re-examine the MML87 treatment of the Gaussian from scratch. The first draft of my attempt is available here.
I hope this document will be useful to researchers interested in learning more about the the MML principle.
Update (24/07/2014): I have written MATLAB code to compute MML estimates and the message length. I have also done minor updates to the document.