Michael Evans and Gun Ho Jang posted an arXiv paper where they discuss the connection between MAP, least relative surprise (or maximum profile likelihood) estimators, and loss functions. I posted a while ago my perspective on MAP estimators, followed by several comments on the Bayesian nature of those estimators, hence will not reproduce them here, but the core of the matter is that neither MAP estimators, nor MLEs are really justified by a decision-theoretic approach, at least in a continuous parameter space. And that the dominating measure [arbitrarily] chosen on the parameter space impacts the value of the MAP, as demonstrated by Druihlet and Marin in 2007.
Archive for MLE
MAP, MLE and loss
Posted in Statistics with tags intrinsic losses, loss functions, MAP estimators, measure theory, MLE on April 25, 2011 by xi'anExamen
Posted in Kids, pictures, University life with tags exam, MLE, Montpellier on February 19, 2011 by xi'an
I was visiting Jean-Michel Marin over the past two days in order to finalise our paper on ABC model choice and I noticed this very special exam on his wall. It was a copy made by his son, who is currently learning his letters, of a true exam Jean-Michel was grading a few weeks ago. Even though the picture is over-zoomed, it is possible to identify the (correct!) resolution of the MLE of the upper bound of a uniform distribution. A very cute rendering that also qualifies as Art brut! (In the spirit of Pierre Ménard, Borges’ short story about re-creation)
