highly parameterized models of data

As my loyal reader knows, I have no fear when it comes to models with huge numbers of parameters; indeed the ubercalibration project is effectively a fit with hundreds of millions of parameters, and we can prove that we got the global optimum (in the sense that we made sure the problem is guaranteed to be convex). Today Roweis pitched a generalization of all this, in which one creates a very flexible linear model space, where parameters are tied to or in a hierarchy of meta-data, such that some parameters are tied to, say, the date, some to the airmass, some to the seeing, some to the camera column, and so on. Then the model discovers which parameters are necessary for accurate modeling of the data and thereby discovers important meta-data, dependencies of the data on artificial issues, and bad data. We tentatively agreed to run this on the new BOSS spectra from SDSS-III.

more sampling

Iain Murray gave another nice talk today, this time in the machine learning group, about a high-end sampling method called elliptical slice sampling, optimized for gaussian process modeling, where calls to the prior probability distribution function are more expensive than likelihood calls. It was a very nice talk and got me thinking about slice sampling in general, which might be very useful to us.

distinguishable orbits

I assigned Jagannath the following problem: What can you learn about the gravitational potential of a gravitating system in which you yourself lie (think the Milky Way) if all you have are streams of stars that trace out orbits, and all you can measure about those streams are their trajectories in angular coordinates (think RA, Dec). That is, what can you do if you get a snapshot of a few orbits, but you only get the angular shapes of those orbits? We went back and forth a bit between the answer everything and the answer nothing. I think it is the former, but of course it will depend strongly on the precision of the measurements! In some sense, all the answers are known; we are just on an intuition-building adventure.

talking

I spent an irresponsible morning talking non-stop to (at?) Iain Murray and Jo Bovy, about our various inference projects, current and future. Murray and Bovy have spent the last week figuring stuff out about our Solar System project, and are producing a much deeper (and more useful) paper; it shows that different parameterizations of phase-space distribution functions lead to different results, but (a) not very different, when stated in terms of reasonable probability intervals, and (b) you can put all possible parameterizations into the model and marginalize over them, without harming the results. What a pleasure it is that I can count hanging out all morning discussing such niceties as performing crucial functions of my job!

At lunch time, Jeff Allen (NYU) gave a status update from the Pierre Auger Observatory for ultra-high energy cosmic rays. There are now conflicting bits of evidence about their sources and composition, which is tantalizing, although the GZK cutoff did really appear is it had to.

ephemeris, sampling

I fielded email today from various undergrads to whom I pitched (on Wednesday) a big project to build a precise probabilistic ephemeris for the Solar System. I am hoping to execute a huge project with a team of undergrads handling all the important parts.

At group meeting (before lunch), Iain Murray (Toronto, Edinburgh), who is one of our Bayesian consultants, gave a talk on sampling for inference, reviewing a few simple methods and then some hard pitfalls. A bit of an argument broke out about how you deal with well-separated maxima, with Roweis and me more on the side of "you never know if you have found the true maximum so you have to figure out how to do science without knowing that" and Scoccimarro and Blanton more on the side of "you have to keep working until you are sure".

history of cosmology

Jim Peebles (Princeton) visited today. Roweis and I spent an hour or so advertising to him our data analysis projects. Late in the day he gave a talk on the history of cosmology, which made a number of remarkable points, like that Hoyle was (almost) the first person to identify the cosmic microwave background (despite the fact that he thought it was impossible). An argument broke out about the importance of Friedman; Peebles takes the (tough) view that to be really important in cosmology you must have not just done theory but connected it directly to experiment, or not just done experiment but had the theorists realize that it was relevant. That's a high bar.

eccentricities

Zolotov and I worked on estimating eccentricities for stars in N-body simulations. This is not trivial—not even well defined—because there is no overall, unique potential (let alone a spherical one!).

sampling and Gaia

I spoke with Bovy about the possibility of doing an ambitious analysis of what is possible with Gaia. I spoke with Iain Murray (Edinburgh), who is visiting, about sampling, where he is one of the world's experts. I asked him to tell me what we can do if likelihood calls are outrageously expensive (so converged samplings of the posterior PDF are impossible).

out sick

I was on vacation on Friday and out sick today. That's not research.

grant proposal and infrared emission

Today was devoted to an NSF proposal, which, according to the rules, is not research. The only research activity of the day was a talk by Nadia Zakamska (IAS) about infrared emission lines and what they have to say about the physics of galaxies. She has some beautiful results, especially that the PAH emission and the H₂ emission in the interstellar medium are differently affected by dust extinction. This is odd, because they are both strongly correlated with star formation and one another. So they are strongly correlated but not co-spatial. Odd.

Comet Holmes

Lang and I worked on (that is, pair coded) making figures for our somewhat strange Comet Holmes project. We started by re-running everything from scratch (find images on web, download, source extract, calibrate) and made this, one of several images of the individual-image footprints on the sky. In this image, the brighter footprints are the more constraining footprints; axis units are degrees on the sky from some reference point.

fractals

My only research time today was spent fielding email about fractal universes, emails that were inspired by my arXiv submission yesterday. It turns out—contrary to what I wrote in that note—that there have been some serious attempts to compute observables in inhomogeneous models. I think my conclusions are still safe, but my language might have been a bit strong.

Roger Blandford

I spent all day today at the meeting in honor of Roger Blandford, which I played an embarrassingly microscopic effort in organizing. The meeting was incredibly well attended, with many old friends in attendance from all over the world. There were talks across the whole electromagnetic spectrum and covering a large range of astrophysical processes, all of which I enjoyed. In particular, Maxim Lyutikov (Purdue) gave just about the perfect description of Blandford the advisor (Lyutikov and I are coeval). Chris Kochanek (OSU) described a brute-force generative modeling of microlensing light curves that made my Bayesian heart sing. I spoke about model selection in cosmology, in a general way; I put my remarks on the arXiv here.

modeling galaxies with galaxies

I spent a long time on the phone with Lang, who is building quantitative models of galaxy images using other galaxy images. We spoke about the free parameters, and the robustness of the fitting (given that there are some random superimposed stars and the like), and so on. He has some nice results already, and this has only been underway for a few days now. At the end of the day I gave a big public talk here in Buffalo.

Buffalo

I worked on two talks for Buffalo and one for Stanford today; I also gave one of the Buffalo talks.