X entropy

Another 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.

One Response to “X entropy”

  1. 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

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.