modeling noise

At group meeting my new student Dun Wang (NYU) showed very nice results in which he has used linear combinations of the brightness histories of Kepler pixels to predict the brightness histories of other Kepler pixels. The idea is that inasmuch as pixels coming from other stars co-vary with the pixel of interest, that co-variability must be caused by the satellite and instrument. That is, this is a way of calibrating out the coherent calibration "noise" that comes from the fact that the observations are being made with a time-varying device.

After group meeting, Michael Cushing (Toledo) showed up to discuss fitting spectra. Like in previous conversations with Czekala and with Johnson, we talked about making a flexible model of calibration and an accurate noise model. We talked through the relative merits of putting complexity into the covariance function (as with Gaussian Processes) or into a parameterized model of calibration (which you fit simultaneously with everything else). These issues—of modeling calibration "noise" in spectroscopy and photometry—come up so much, I feel like we should organize a workshop. One thing that's nice about Cushing's plan is that he wants to use the expected intensity (not the observed intensity) to set the variance of the Poisson term in his noise model. That's the Right Thing To Do (tm). Of course it makes the likelihood function more complicated in some ways.