Christian Schwab (Heidelberg) came by today and he, Hou, and I had lunch to talk about stellar radial velocities. We spent a bit of time talking about how the extraction of the radial velocities might be made more precise. I would love to work on that problem; the only question is whether Hou could be convinced.
Lang and I still haven't passed all our unit tests (some of which are pretty damned stringent) on our orbital elements and phase-space coordinates code. However, we passed a pretty strong one: We can reproduce the conversions performed by the JPL Solar System Dynamics group to machine precision. I was pleased.
[Today is the 5th birthday of this research diary. Here's the first post.]
Fengji Hou showed me plausibly converged MCMC chains for a two-body exoplanet radial velocity system today, along with plausible posterior probability distribution estimates. I am pretty excited because his code is much, much faster than mine was (when I did this a few months ago).
Lang came in to New York to spend the day writing unit tests and functions (in that order, supposedly) for conversions between phase-space coordinates (position and velocity) and orbital elements (semi-major axis, eccentricity, inclination, longitude of the ascending node, argument of perihelion, and mean anomaly). We were able to pass the unit tests for most cases, but failed on a few edge cases where some of the angles become undefined. Rooting these issues out is not trivial. Also, there are some numerical instabilities which require analysis. I definitely feel like we are reinventing a wheel, but at the same time, we are learning a lot.
In the afternoon, I discussed with Itay Yavin and Kyle Cranmer fast methods for fitting exoplanet orbits to stellar radial velocity data using Fourier or periodogram approaches. We were inspired by Bretthorst's book on Bayesian spectral analysis. In the morning, I discussed with Blanton and Demitri Muna (NYU) the detection in real time of supernovae (or other anomalies) in the SDSS-III BOSS spectroscopic data stream.
I had a nice discussion with Bovy, Neal Weiner, and Ilias Cholis (NYU) about doing astronomy with the Fermi satellite, in particular the kinds of astronomy that might make the mission much more sensitive to dark matter annihilation than any of the standard dark-matter analyses will make it. Unfortunately, everything I would like to do involves Roweis-like technology, so I am not sure how to proceed.
In the morning, with Blanton, Yosi Gelfand, and Ingyin Zaw (NYU), I discussed possible big astronomy projects we could undertake as part of NYU Abu Dhabi. We concentrated on radio, where start-up costs can be far lower. In the afternoon, with Yann LeCun (NYU) and Lang (in separate conversations), I discussed on-line learning (which for some reason also in some contexts gets the name
stochastic gradient) and how it might make possible our
Theory of Everything and Open-Source Sky Survey projects. These are all long-term projects, but I need to think long-term now that everything has changed.
My collaborator of ten years—and friend of twenty-five years—Sam Roweis died on 2010 January 12 in New York City. Anyone who has even glanced at this blog will know that he was involved in almost everything I have been thinking about scientifically. What you might not know is that Roweis also was an absolutely wonderful friend to me.
It was working with Roweis that made me formulate the following principle: All scientific projects are interesting. So choose not what you want to work on, but rather who you want to work with.
It has been my greatest privilege to work with people I love, and—above all—Sam Roweis.
[I think this post violates the rules.]
On the airplane to Abu Dhabi, I checked my calculations for transformations between position and velocity three-vectors and the standard orbital elements for Keplerian orbits. Lang and I need these for our Holmes project.
Lang, Roweis, and I spent the full day in Princeton, to talk about and work on extensions and next steps for Astrometry.net. The range of things we talked about was very large, from daily operations to very long-term plans like our conceivable Open-Source Sky Survey.
The problem we talked most about and worked most on was what we call, internally, "tweak". This is the problem of determining the astrometric distortions in an image away from a basic tangent-plane projection of the sky; these distortions are a product of atmosphere and optics and are among the fundamental limitations of cameras. There is a good product out there for determining these distortions called SCAMP (by Bertin and collaborators), and we usually point users to that (we even generate the proper input files that SCAMP wants to see). However, there are issues with all such packages: They need extremely good first guesses to get the correspondences right—the correspondences between sources in the image and sources in whatever catalog is being treated as "truth". Most images that fail for any system fail because of bad correspondences, usually near the edges or in highly distorted parts of the images.
Since linear fitting is trivial, it is not an exaggeration to say that all of the difficulty of fine astrometric calibration is in the finding, managing, and handling of image–catalog correspondences. Even better, we could replace distortion-conveying FITS WCS standards with simply a list of true correspondences (since that encodes all the information we have about astrometric distortions—any polynomial fit to that information is just an approximate description of the information you actually have, which is the correspondences themselves). So we came up with a few ways to nail (in a Bayesian way) the correspondences and hope to implement these in the next little while. (Note how vague I am being; that's because we aren't sure what will work or how well.)
Lang and I spent part of the day deciding that we had to write functions that convert back and forth between position and velocity and standard "osculating" orbital elements. We didn't write them; we just decided that we had to write them!
Matt Kleban (NYU) and I discussed the fractal Universe today, in the context of my polemic. He questioned a number of things, including whether the fractal dimension could be less than three but only very slightly, and what would that mean? Also, if you believe some forms of inflation, the Universe sort-of has to be a fractal on super-super-horizon scales; is that an issue? Of course I don't think either of those issues is so important, because neither conflicts with CDM (the theory I would love to be wrong), but he brought up some very relevant points. One of these is whether the fact that there are always order-unity density fluctuations possible on all scales means that it might be hard to define or understand the mean density in any single realization. But it remains true that there are no GR calculations of any observables in any expanding Universe with a distribution of matter with fractal dimension significantly different from three on large scales. That lack is a substantial hindrance to the success of any model that is fractal in that sense (for the reasons I try to give in the polemic).
Jagannath and I worked on our new how-similar-are-two-orbits project with what I think is a pretty general formalism. The formalism is inspired by Gaussian statistics, because I expect the project to evolve into an inference project.
Roweis is not afraid of large numbers of parameters! He modeled the spectrograph output with a trace model that has more parameters than pixel rows, and a psf model with 200 times as many parameters as pixels! That is, far more parameters than data. Because he put on strong smoothness priors, he was able to optimize (on his laptop) no problem. He and I spent lunch discussing spectral modeling. Roweis noted that there are many ways to make the problem scale; in particular you can compute the gradient in parameter space for small blocks of data, make small steps, one for each data block, and iterate over all the data. Apparently this still optimizes the system just fine, and you never have to get everything into memory at once. We assigned me more writing tasks and set the goal of extracting one BOSS fiber by the end of the month.
I wrote some words in Roweis and my spectroscopic calibration document, mainly about modeling of spectral traces. Our current plans will lead (I'm pretty sure) to a non-linear fit, which doesn't worry me in terms of local optimization, but it does worry me in terms of convexity. I don't see any simple way to keep the problem we are trying to solve—a spectral reduction pipeline that learns its own calibration information as it goes—convex. That's not a drop-dead requirement, but it sure is nice to know that you are at a global optimum.