likelihood functions for stellar age relations

Bird (Vanderbilt) and I pair-coded a likelihood function for the age–velocity relation in the Milky Way Disk. After that, I coded up a likelihood function for the star-formation history in the Milky Way disk, given very noisy age estimates (from The Cannon). By the end of the day, Bird was successfully MCMC sampling his parameters, and my inference was going massively unstable. I am sure I have a simple bug.

Price-Whelan, Rix, and I discussed a brute-force search for stellar streams in stellar catalogs called KingKong. It samples randomly in orbit space for a trial or toy potential and asks, for each orbit, how many stars have observations that are consistent with being on that orbit. The method is simple. But it is all about implementation details.

black holes and weird pixel effects

In group meeting, Huppenkothen argued out the projects we discussed on Monday related to machine classification of black-hole accretion states of GRS 1915. We talked about all three levels of project: Using supervised methods to transfer classifications for a couple of years of data onto all the other years of data, using unsupervised methods to find out how many classes there plausibly are for the state, and building some kind of generative model either for state transitions or for literally the time-domain photon data. We discussed feature selection for the first and second projects.

Also at group meeting, Foreman-Mackey showed a new Earth-like exoplanet he has discovered in the Kepler data! Time to open our new Twitter (tm) account. He also showed that a lot of his false positives relate to un-discovered discontinuities in the Kepler photometry of stars. After lunch, we spent time investigating these and building (hacky, heuristic) code to find them.

Here are the symptoms of these events (which are sometimes called "sudden pixel sensitivity drops"): They are very fast (within one half-hour data point) changes to the brightness of the star. Although the star brightness drops, in detail if you look at the pixel level, some pixels brighten and some get fainter at the same time. These events appear to have signs and amplitudes that are consistent with a sudden change in telescope pointing. However, they are not shared by all stars on the focal plane, or even on the CCD. Insane! It is like just a few stars jump all at once, and nothing else does. I am confused.

Anyway, we now have code to find these and (in our usual style) split the data at their locations.

finding tiny planets, Kepler jumps, papers

Foreman-Mackey and I had a long and wide-ranging conversation about exoplanet search. He has search completeness in regimes of exoplanet period heretofore unexplored, and more completeness at small radii than anyone previously, as far as we can tell. However, his search still isn't as sensitive as we would like. We are doing lots of hacky and heuristic things ("ad hockery" as Jaynes and Rix both like to say), so there is definitely room for improvement. All that said, we might find a bunch of smaller and longer-period planets than anyone before. I am so stoked.

In related news, we looked at a Kepler star that suffered an instantaneous change in brightness. We went back to the pixel level, and found the discontinuity exists in every pixel in the star's image, but the discontinuity has different amplitudes including different signs in the different pixels. It is supposed to be some kind of CCD defect, but it is as if the star jumped in position (but its fellow stars on the CCD didn't). It is just so odd. When you do photometry at this level of precision, so many crazy thing appear.

Late in the day I caught up on reading and commenting on papers people have sent me, including a nice paper by Megan Shabram (PSU) et al on a hierarchical Bayesian model for exoplanet eccentricities, a draft paper (with my name on it) by Jessi Cisewski (CMU) et al on likelihood-free inference for the initial mass function of stars, a draft paper by Dustin Lang (CMU) and myself on principled probabilistic source detection, a paper by John Jenkins (Ames) et al on optimal photometry from a jittery spacecraft (think Kepler), and the draft paper by Melissa Ness et al on The Cannon.

interatively reweighted least squares: Gaussian Process edition

Yesterday and today, Mykytyn and I worked out the generalization of iteratively reweighted least squares (a method for down-weighting outliers that is slightly, slightly better than sigma-clipping) to the case of a Gaussian Process noise model. We take the standard algorithm and replace the residual scaled by the noise with the deviation from the conditional mean prediction scaled by the sum in quadrature of the observational noise and the GP conditional variance. We implemented this simple algorithm on Mykytyn's quasar time-series data and it looks like it works beautifully. Now he is going to see if our inferences look better with the re-weighted uncertainties.