I didn't do much research today because it was my last day at the MPIA in Heidelberg. What a great summer!
My one substantive scientific discussion was with Rix about understanding open clusters—their ages and mass functions—through astrometry. It is an old subject, but it hasn't really been tapped for all it is worth. And there are a lot of data.
Visualize me doing that NFL-style end-zone post-touchdown dance. The faint-source proper motion paper Measuring the undetectable
(link should come live on 2008-09-01) is submitted to The Astronomical Journal and to the arXiv. Lang, Jester, and Rix all did some last-minute pulling together to get that done. Thanks, team! Now, does anyone want to follow up our brown dwarfs with infrared spectroscopy?
We realized today that we were slightly mis-using the SDSS Southern Stripe Coadd Catalog, and the parent sample for our faint-source proper motion paper went from 1500 sources to less than 100. But that's good, because now some of our statistics make much more sense.
I contemplated putting in a truly insane letter of intent to the Spitzer Cycle 6 (warm mission) call for proposals, which is for 10,000 hours of imaging at 3.6 and 4.5 microns. My contemplation was carried out while reading observing strategy cookbooks (thanks, Spitzer Science Center).
Lang computed infrared colors (from UKIDSS and SDSS-II) for the very faint, fast-moving sources to compare with the less-fast-moving sources at the same magnitude. Although all are very red in i−z, they vary hugely in z−J, with the faster-moving redder. This is good.
After a few edits to the faint-motion paper, I had a long conversation with Adam Bolton (Hawaii) about constraining cosmological models (on small scales) with data (such as galaxy positions, redshifts, weak lensing, and the like). He wants to advocate an approach in which we find all (or a representative sample of) realizations of the density field that are consistent with the data, and ask whether they (or any of them) are consistent with the fundamental model, for model testing. This is in contrast to the usual techniques of computing statistics on the observations, statistics on the model, and comparing them. This standard technique rarely gets you close to saturating the available information, and given the quality of the CDM model, if you want to find problems you are probably going to have to come close to saturating the information available.
Jester, Rix, and I had various conversations today about how we can demonstrate that Lang and my method for measuring the astrometric variations of extremely faint sources can be used to speed, cheapen, and facilitate upcoming science projects, especially PanSTARRS. I am now working on paper modifications based on these discussions.
What little work I did today was mainly preoccupied with computer issues, and not ones of an intellectually engaging nature.
Rix "bled" all over the faint proper-motion paper this weekend (think: lots of red ink). I got started mopping it up today.
I finished my PCA polemic; it is too theoretical and needs to be threaded with real examples of failures and improvements and alternatives applied to real data sets. That is a long-term project, of course.
I poster-ified Lang and my paper faint-source proper motions for the SDSS Symposium next week in Chicago.
I finished everything I could do on my project on the monopole term in the transparency with More; that project will now wait until he returns. I worked on writing up a principled approach to a side project that Lang and I have been discussing on finding variable sources in pure photon time streams.
As my loyal reader knows, I have been bashing PCA and hyping jackknife. As I was responding to some local comments on our paper on faint-source proper-motions, I found myself adding the words principal components
to a discussion of how well jackknife works! This is because if you have d parameters, and you want to measure the d×d covariance matrix, you will rarely have enough jackknife trials to fill in every element of the matrix precisely. To do so, you would need N much larger than d, and even then you would only do well if the covariance matrix describes a variance that is close to spherical.
However, the jackknife (except in pathological situations) will return a sampling of the covariance matrix that gets the principal components correct. This is because the principal components will dominate the variance (by definition, in some sense). And for error propagation, all you care about are the dominant directions in the space, as defined by the true covariance matrix; this is a rare case where the concept of PCA is good: it is a rare case where you care most about the directions of largest variance.
This relates to one of my unwritten polemics: uncertainties should be communicated via samplings, not analytic descriptions of multi-dimensional confidence regions.
I wrote more of my PCA polemic, in part preparing myself for a possible assault on the emission lines in SDSS spectra, parallel to the PCA stuff I have been doing with Tsalmantza.
Work finishing the faint proper-motion paper has been halted by computer problems. The Astrometry.net project is trying to run as a web service, and we run the service and our project management and our source code repository all out of the same few machines. One of these machines is failing frequently, and we may have to harden substantially our web serving technology. Right now, we are running with home-built stuff and hoping for good luck, but that isn't sustainable. Anyone want to donate us some enterprise-scale uptime foo?
In other news, Bunn and I finished our comment on cosmological redshifts. Comments greatly appreciated.
I started to write my polemic about PCA today. I decided that it was a worthwhile paper, or part thereof.
Today, Wu found a population of galaxies that are clearly forming stars (significant H-alpha emission, star-formation line ratio diagnostics), not strongly extincted in the optical (H-alpha to H-beta ratio near 3), but with very little GALEX NUV flux. There is pretty-much no way to make such galaxies, so we suspect that we have issues with either the SDSS data or the GALEX data or their intercomparison (for example, overlapping sources, or star-formation offset from the nucleus, etc.). But I am now confident that we will either be able to refine our procedures so that we can use GALEX to find post-starburst galaxies, or else we will discover a new and interesting galaxy sub-population. Either way, I am happy.
Ted Bunn (Richmond) and I finished the first draft of a piece on cosmological redshifts today. We argue—against prevailing wisdom—that the redshifts of distant sources can be regarded as kinematic, that is, as due to recession velocities. We hope to be ready to put it on the arXiv soon.
Lang and I spent more time discussing how one measures the information in an image. It turns out that despite the fact that information is a quantitative property, how one calculates it depends on what parts of the data stream are expected to contain the information, and very different quantities are produced when you make different assumptions. For example, the information in an image, by the usual methods, does not change if you randomize the pixel order, even though most of us would say that the randomized picture contains much less information! That is because most methods for measuring the information consider only the pixel histogram, and not the pixel adjacency relations.
