## X entropy

**A**nother discussion on X validated related to the maximum entropy priors and their dependence on the dominating measure μ chosen to define the score. With the same electrical engineering student as previously. In the wee hours at Casa Matematicà Oaxaca. As I took the [counter-]example of a Lebesgue dominating measure versus a Normal density times the Lebesgue measure producing the same maximum entropy distribution [with obviously the same density wrt to the Lebesgue measure] when the constraints involve the second moment, this confused the student and I spent some time constructing another example with different outcomes, when the Lebesgue measure versus the [artificial] dx/√|x| measure.

I am actually surprised at how limited the discussion of that point occurs in the literature (or at least in my googling attempt). Just a mention made in Bayesian Analysis in Statistics and Econometrics.

November 16, 2018 at 5:05 pm

something like picking a dominating measure is in PT:LOS though; IIRC it’s picking the limiting density of sets of discrete points on which we are willing to put constant probability mass as the number of points in the sets increases without bound