A model with calibration uncertainties

[kbarbary]

In thinking about the API, we asked if the current setup could handle a model where there are calibration uncertainties. Such a model would have a set of global parameters specifying the zeropoint for each filter used in the photometric observations.

@rbiswas4 drew a PGM for this; can you post it in this thread?

[rbiswas4]

Yes, I was going to post it .... here it is:

[kbarbary]

Some background: the theta_c represent calibration parameters, such as the zeropoint of each instrument/bandpass combination. These parameters would have a prior that represents the measurement uncertainty of the calibration.

I think this would cause a Problem for importance sampling, since the theta_c parameters directly affect the photometry, rather than going through intermediate SN parameters like the other global parameters.

Any thoughts, @drphilmarshall? I think this is a really important use case, so we might need a different approach.

[kbarbary]

To summarize the discussion today at KIPAC: Yes. (Yes, it is a problem for importance sampling)

[drphilmarshall]

I started reading about Population Monte Carlo: in this scheme we would
approximate the density, perhaps with a Gaussian Mixture Model fit to the
samples, and then use that to iteratively improve the overall posterior
sampling. I'm not clear on the details, but cheap GMMs in general might be
something to think about. Its possible that once you have a GMM we could
either draw more samples cheaply (PMC style), or perhaps even do integrals
analytically, if the target conditional PDF were also a GMM (and the
interim prior was uniform or a GMM as well). I think...

On Fri, Mar 20, 2015 at 6:05 PM, Kyle Barbary notifications@github.com
wrote:

To summarize the discussion today at KIPAC: Yes. (Yes, it is a problem
for importance sampling)

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