Periodic model parameters? about emcee

[dfm]

Thanks for the compliments! I'm glad that it's helpful!

I think that your intuition is correct about the fact that this is a significant problem. emcee is definitely not very good at dealing with problems with identical maxima like that. I would just restrict the phases to [0, 2 * pi) using you prior (just return -numpy.inf from lnpost if the parameter falls out of the range). This should work just fine in practice unless most of the mass is right around the break. In that case, it should still also work in theory but I expect that the convergence would be much less efficient.

Let me know if this helps or if you have any other questions.

[vallis]

Sure, that may be the most straightforward solution. But what about renormalizing the periodic variables after they're updated (say, at line 176 of ensemble.py), so that, for instance, a phase updated to 2 pi + 0.1 wraps over to 0.1?

[davidwhogg]

If you have an amplitude A and a phase phi, the phase is periodic, but x = A cos phi and y = A sin phi is a coordinate transformation that is not periodic. It works in most cases of periodic signals. See our paper (Hou et al, with me and Goodman) for a transformation for exoplanet orbits that works very well. Similar things can be done for any periodic signal, I suspect.

[eggplantbren]

"Sure, that may be the most straightforward solution. But what about renormalizing the periodic variables after they're updated (say, at line 176 of ensemble.py), so that, for instance, a phase updated to 2 pi + 0.1 wraps over to 0.1?"

This sounds better in my opinion, especially if there are lots of these periodic parameters in your model. Once you get into large dimensions with lots of hard edges in your prior, the rejection rate gets pretty high. The above strategy would give no rejections whatsoever for a flat likelihood.