Archive for maximum a posteriori

posterior distribution missing the MLE

Posted in Books, Kids, pictures, Statistics with tags , , , , , , , on April 25, 2019 by xi'an

An X validated question as to why the MLE is not necessarily (well) covered by a posterior distribution. Even for a flat prior… Which in restrospect highlights the fact that the MLE (and the MAP) are invasive species in a Bayesian ecosystem. Since they do not account for the dominating measure. And hence do not fare well under reparameterisation. (As a very much to the side comment, I also managed to write an almost identical and simultaneous answer to the first answer to the question.)