A Likely Result

In SDSS-III, the BOSS project is targeting 160,000 quasars (QSOs) at redshifts between 2.2 and 3.5. A color-color plot of spectroscopically confirmed QSOs (green) and stars (red). You can see that the quasars and stars have regions of overlap in the color space, and are therefore difficult to distinguish from each other.

David Schlegel suggested using a likelihood estimator to select quasars from stars. The basic idea is to have a templates of "quasar objects" and "all other objects" we would expect to see in the Sloan data set. We then take a "test object," one which we are trying to determine if it is a quasar or not, and compute a likelihood between it and the two templates. The likelihood of a test object (i) is for a set of template data (j) with color filters (f) is defined as follows:

where x is the flux of an object in the template data and mu is the flux of your test object and sigma if the error in your test object flux measurement.

I computed this likelihood with a set of test object where I knew if they were quasars or not. Below is a plot of the above likelihood computed on the test objects with a "quasar template" and a "everything else template." I am plotting the likelihood of the test objects with everything else (on the x axis) versus with quasars (on the y axis). Because I know what these test objects are, I can color the quasars (green) and the stars (blue). You can see that I get a clear separation in likelihood-likelihood space of these populations, where the quasars fall along a higher likelihood for quasars and the stars fall along a higher likelihood for everything else: