Greg Dobler (UCSB) gave the astro seminar today, on the WMAP, Fermi, and now Planck haze at the center of the Milky Way. My take-away is that, energetically, it is not hard to explain, but specifically it has morphological features that are hard to explain. That's like so damned much in astrophysics!
Not much other work got done, except I shocked (shocked!) the crowd at stats school by saying that it is almost never the case that you want to select models based on chi-squared per degree of freedom. You can show that your models are bad fits that way, but you can't really choose among models that way. It is related to Gould's intemperate comment about accuracy vs precision: Model selection is a precision question, not an accuracy question.
Chi^2/DOF seems closely related to AIC and that kind of thing. So you *could* use it for model selection if you wanted.
ReplyDeleteI don't believe in AIC though so I wouldn't advocate that.
I think you can't really select on chi^2 / dof, because in things like AIC and BIC you want to be adding numbers of parameters (times something) to chi^2. you don't want to be *dividing* chi^2 by anything. I think, ever. Because chi^2 is a log likelihood, dividing it by something is like taking the likelihood to a power, which just seems wrong.
ReplyDeleteYou're right.
ReplyDelete