I did lots of small things today. Perhaps the least small was to help a tiny bit with Bovy's proposal to change SDSS-III BOSS quasar target selection over to a method that makes principled use of extreme deconvolution (XD). The Bovy method has several advantages over the current method, including:
- It is lightweight. The model is completely specified by a (large) number of Gaussians in photometry space; it can be implemented by any code easily given those Gaussian parameters.
- It is the best performing method of all those tested by the Collaboration.
- It does not, in any sense, convolve the model with the errors twice. Most empirical distribution function descriptions are descriptions of the error-convolved distribution; when you compare with a new data point you effectively apply the uncertainty convolution to the distribution twice. Not so for XD.
- It is the easiest method to extend in various ways including the following: You can modify the priors easily, even as a function of position on the sky. You can add data from GALEX or UKIDSS or variability studies straightforwardly. You can apply a utility to make the method prefer quasars that are more useful for the measurements of interest.
In general, when you need to do classification you should—if you have measurements with uncertainties you believe—model distribution functions for the classes, and when you want to model distribution functions using uncertainty information correctly you should use XD!