MAP for multivariate gaussian?

mort.motes

The standard multivariate gaussian is given by:

http://upload.wikimedia.org/math/1/c...416333d07f.png

taken from:

http://en.wikipedia.org/wiki/Multiva...l_distribution

The parameters can be estimated using:

http://en.wikipedia.org/wiki/Estimat...l_distribution

and:

http://en.wikipedia.org/wiki/Normal_..._of_parameters

But given those parameters how are MAP (maximum posterior) or the "mode" computed? Again from wiki:


"The parameter μ is at the same time the mean, the median and the mode of the normal distribution"

In a bayes context MAP can somtimes be estimated as:

MAP = ML*Prior