In a low-research day, Jiang and I discussed the idea of using continuity to understand galaxy evolution. That is, changes in the number density of any population of galaxies should be quantitatively explained by sources of galaxies in that population, sinks, and evolution within the population. We can measure each of these terms for some galaxy populations, so there is a rich set of projects here.
I spoke with Jonathan Goodman, Jonathan Weare (NYU, Chicago), and Hou about exoplanets generally and hierarchical models more specifically. Late in the day I wrote a document to try out some notation and check consistency of my vague thinking.
A day of proposal planning with Lang was interrupted by a beautiful PhD defense by Ke Xiao, on optical tweezers, holography, transport in non-trivial force landscapes, and thermal ratcheting. Very nice; congratulations Dr Xiao.
Mondays are check-in-with-everyone days. For example, today Hou was as surprised as I was about the format of the reduced MARVELS data from SDSS-III. Late in the day I worked out a notational framework for describing the hierarchical-Bayesian methodology we could adopt for his PhD dissertation. I also retrieved my copy of Gelman et al to brush up on the relevant stuff.
On the plane home, I continued reading Ke Xiao's dissertation and wrote a bit about model complexity. I worked on an example from Yann LeCun (NYU) that illustrates very clearly that model complexity is not directly related to the number of free parameters. It is related to the range of (reasonable) observables that could be fit by the model, which—for non-linear models—is related to the sensitivity of the observables to the parameters, and not the number of parameters per se.
I had a great time visiting the astrophysics group at JPL today. There is so much going on, and so much sophisticated working with and thinking about challenging data sets and challenging data analysis programs. I spoke with people working on Planck, HST, Spitzer, weak lensing, exoplanets, the Galactic Center, and numerical relativity. It was a way too-short visit. On the plane to LA I read parts of the dissertation of Ke Xiao (NYU), on brownian motion in the presence of non-trivial potential and force landscapes.
Price-Whelan made a remarkable discovery today—which may be false or an error of some kind, so don't quote me—that commercial digital cameras do not always subtract the dark frame, and the dark currents of the pixels are significant and vary from pixel to pixel. If this is right, we are going to be able to vastly improve the sensitivity of the cameras we have. Time to start writing the paper!
Aside from administration of the Department's undergraduate program—which took almost all of my working day—I had a conversation with Coryn Bailer-Jones (MPIA, Harvard) about the creation, evaluation, and truth content of scientific theories.
My only research contribution today was a short discussion with Jagannath and Price-Whelan about how to control or adjust adaptively the sampling of a numerically computed curve in non-linear curve fitting to data. The curve is not an analytic function, in general, so we have to choose a sampling. This sampling will matter if we aren't careful, but it is equally easy to over-compute and slow things down incredibly.
Whew! I didn't want to go three days without something. I helped Hou find the SDSS-III MARVELS data; and later in the day Bovy pointed out to me that we could do a fast project with them based on our predictions of Hipparcos star radial velocities (from our moving groups work). I had lunch with Jagannath, where we talked about the origins of tidal streams (and the collapse of the wave function, which I am suspicious never happens). This afternoon, Price-Whelan and I got robust median-absolute-difference estimates for image noise implemented because we want to be very robust and very precise in our analysis of the noise in commercial digital camera images.
Adrian Price-Whelan and I figured out today the dependence of the RAW-file median levels and noise on exposure time and ISO for the Canon Digital Rebel XSi cameras we have been testing. We are trying to build a noise models for the pixels—on average and individually—as a function of illumination and camera settings. I have always wondered if changing the ISO setting on a digital camera changes the bias or anything else about the readout electronics, or whether it just changes the way the camera converts the RAW file into a human-viewable JPEG. We started to get some evidence today that it actually changes the bias on the CCD, but we haven't built a noise model yet. That's the project for the coming week.
Started work on a document about fitting points to a curve in d dimensions, when you have non-trivial and covariant errors in all dimensions, different for every point. This is the generic situation for science, and especially astronomy, for example when we fit the GD-1 stream to a Milky Way orbit.
I spoke for a few seconds today with Hou, about using clustering of a set of samplers running in parallel (for an adaptive sampling technique) to find and eliminate trapping by local minima. This might be a very simple and effective technique for search, optimization, and sampling in dynamics problems.
Jiang and I tried to understand differences he is finding between A–B and B–A cross-correlations in the SDSS data. These differences look like bugs, but how to find out? I am confused.
Jerry Sellwood (Rutgers) gave a talk today at AMNH in which I learned a huge amount about spiral structure. He showed that disks have various kinds of linear and nonlinear instabilities to create spiral structure, and the structure tends to be transient. Nonetheless, a transient spiral pattern has an effective pattern speed and can drive resonant evolution at an inner and an outer resonance. These drive stars to eccentric orbits and plausibly cause some of the kinematic structure we see in the disk. After the talk, Sellwood, Bovy, and I talked about our differences and agreements in this literature. It turns out we don't really have differences at this point.
Not much got done in the last two days (I didn't have to post yesterday because I posted on the previous Sunday; see rules). But I did get a few minutes to talk with Bovy about his centroiding tests; he confirmed that Lupton's centroiding trick in SDSS Photo performs surprisingly well relative to the best that can possibly be done with a compact point-spread function.
I spoke with Jiang about his cross-correlations. After a conversation with Blanton we decided to do every small–big cross-correlation corresponding to each of the big–small cross-correlations we are doing. This permits us to check our results (there are symmetry relations), and it also permits us to compute a death rate analogous to the accretion rates we are currently measuring. Think big fish eating small fish, and small fish getting eaten!
George Lewis (NYU) had a candidacy exam about understanding QCD backgrounds for Higgs events at LHC ATLAS. He and Kyle Cranmer (NYU) are looking at a set of data-driven methods to constrain QCD events, since precise QCD calculations are impossible for many of the relevant interactions. Of course I am a huge supporter of data-driven data analysis at LHC; I am certain this is a necessary part of any precise measurements with that incredibly complicated machine.