proposals

I spent the day at the Spitzer Science Center participating in a review of preparations for Spitzer's proposal to the NASA Senior Review, which is empowered to continue or terminate the ongoing missions. I also wrote text for the NSF proposal being submitted by Geha, Johnston, and me.

data science; data-driven models

Today I turned down an invitation to the White House. That might not be research, but it sure is a first for me! I turned it down to hang out more with Vanderplas (UW). I hope he appreciates that! At the White House Office of Science and Technology Policy (okay, perhaps this is just on the White House grounds), there was an announcement today of the Moore-Sloan Data Science Environment at NYU, UW, and Berkeley. This is the project I was working on all summer; it has come to fruition, and we start hiring this Spring. Look for our job ads, which will be for fellowship postdocs, software engineering and programming positions, quantitative evaluation (statistics) positions, and even tenure-track faculty positions (the latter coming from NYU, not Moore and Sloan, but related).

At lunch, Vanderplas, Foreman-Mackey, Fadely, and I discussed alternative publication models and how they relate to our research. Foreman-Mackey reasserted his goal of having any exoplanet discoveries we make come out on Twitter before we write them up. Vanderplas is wondering if there could be a scientific literature on blogs that would "play well" with the traditional literature.

Earlier in the morning, Vanderplas gave us some good feedback on our data-driven model of the Kepler focal plane. He had lots to say about these "uninterpretable" models. How do you use them as if they provide just a calibration, when what they really do is fit out all the signals without prejudice (or perhaps with extreme prejudice)? Interestingly, the Kepler community is already struggling with this, whether they know it or not: The Kepler PDC photometry is based on the residuals away from a data-driven model fit to the data.

objective filter design, Bayes

Jake Vanderplas (UW), internet-famous computational data-driven astrophysicist, showed up at NYU for a couple of days today. He showed us some absolutely great results on objective design of photometric systems for future large imaging surveys (like LSST). His method follows exactly my ideas about how this should be done—it is a scoop, from my perspective—he computes the information delivered by the photometric bandpasses about the quantities of interest from the observed objects, as a function of exposure time. Fadely, Vanderplas, and I discussed what things about the bandpasses and the survey observing strategy he should permit to vary. Ideally, it would be everything, at fixed total mission cost! He has many non-trivial results, not the least of which is that the bandpasses you want depend on the signal-to-noise at which you expect to be working.

In the afternoon, Hou, Goodman, Fadely, Vanderplas, and I had a conversation about Hou's recent work on full marginalization of the likelihood function. In the case of exoplanet radial-velocity data, he has been finding that our simple "multi-canonical" method is faster and more accurate than the much more sophisticated "nested sampling" method he has implemented. We don't fully understand all the differences and trade-offs yet, but since the multi-canonical method is novel for astrophysics, we decided to raise its priority in Hou's paper queue.

HST WFC3 PSF

In a day of proposal and letter writing, Fadely came by for a work meeting. We discussed all his projects and publications and priorities. On the HST WFC3 self-calibration project, he is finding that the TinyTim PSF model is not good enough for our purposes: If we use it we will get a very noisy pixel-level flat. So we decided we have to suck it up and build our own model. Then we realized that in any small patch of the detector, we can probably make a pretty good model just empirically from all the stellar sources we see; the entire HST Archive is quite a bit of data. Other decisions include: We will model the pixel-convolved PSF, not the optical PSF alone. There is almost no reason to ever work with anything other than the pixel-convolved PSF; it is easier to infer (smoother) and also easier to use (you just sample it, you don't have to convolve it). We will work on a fairly fine sub-pixel grid to deal with the fact that the detector is badly sampled. We will only do a regularized maximum likelihood or MAP point estimate, using convex optimization. If all that works, this won't set us back too far.

potential expansions

Late in the day I zoomed up to Columbia to discuss streams with Bonaca, Johnston, Küpper, and Price-Whelan. We discussed things related to our upcoming NSF proposal. One idea in the proposal is too look at models of the Milky Way gravitational potential that make use of expansions. In these kinds of problems, issues arise regarding what expansion to use, and what order to go to. On the former, choices include expansions that are orthogonal in something you care about, like the potential or density, or expansions that are orthogonal in the context of the data you have. That is, the data constrain the potential incompletely, so an expansion that is orthogonal in the potential basis will not have coefficients that are independently constrained by the data; there will be data-induced covariances in the uncertainties. On the latter (what order), choices include, at one extreme, just making a heuristic or educated guess, and on the other extreme, going fully non-parametric and inferring an infinity of parameters. You can guess what I want to try! But we will probably put more modest goals in the proposal, somewhere in-between. Amusingly, both of these problems (orthogonal expansions for incomplete observations, and choices about expansion order) come up in cosmology and have been well studied there.

centering

Jeffrey Mei (NYUAD) came by to discuss his project to infer the dust extinction law from SDSS spectra of F stars. We talked about a "centering" issue: We are regressing out g-band brightness (flux; a brightness or distance proxy), H-delta equivalent width (a temperature proxy), and extinction amplitude from the Schlegel, Finkbeiner, & Davis map. The coefficient of the latter will be interpretable in terms of the extinction law (the dust law). Because we have regressed out the observed g-band brightness, we get that the mean effect of extinction is zero in the g-band; that is, our results about the dust extinction are distorted by what we choose, precisely, to regress out. Another way to put it: The brightness is a function of distance, temperature, and extinction. So if you regress that out, you distort your extinction results. The point is obvious, but it took us a while to figure that simple thing out! We have a fix, and Mei is implementing.

goose egg

It's job season. Nothing to report!

marginalizing over images

MJ Vakili delivered to me a draft manuscript on his prior over galaxy images. In the introduction, it notes that the only other times things like this have been done it has been to reduce the dimensionality of the space in which galaxy images are modeled or represented. This is a baby step, of course, towards a prior on images, but only a baby step, because principal component coefficients don't, in themselves, have a probabilistic interpretation or result in a generative model.

On the board in my office, Vakili explained how he would use the prior over images to make the best possible measurement of weak gravitational-lensing shear; it involves marginalizing out the unsheared galaxy image, which requires the prior of which we speak. The cool thing is that this solves—in principle—one of the ideas Marshall and I hatched at KIPAC@10, which was to use the detailed morphological features in galaxies that go beyond just overall ellipticity to measure the shear field. Now that's in principle; will it work in practice? Vakili is going to look at the GREAT3 data.

the (low mass) IMF

Dennis Zaritsky (Arizona, on sabbatical at NYU) gave the astro seminar today, about measuring the IMF for the purposes of understanding the mass-to-light ratios of stellar populations. He is using bound stellar clusters, measuring kinematic masses and visible and infrared photometry. He finds that there seem to be two different IMFs for stellar clusters, one for the oldest clusters and another for those less than 10 Gyr in age. But this difference also more-or-less maps onto metallicity (the older clusters are more metal poor) and onto environment (the younger clusters are Magellanic-Cloud disk clusters, the older clusters are Milky-Way bulge and halo clusters). So it is hard to understand the causal relationships in play. Zaritsky is confident that near-future observations will settle the questions.

At lunch, Fadely proposed that we enter the Strong-Lens Time Delay Challenge. We imagined an entry that involves multi-band Gaussian Processes (like those worked out by Hernitschek, Mykytyn, Patel, Rix, and me this summer) added to multi-band Gaussian Processes. Time to do some math.

forward modeling a coronograph

Fergus, Neil Zimmerman (MPIA), and I chatted on the phone a bit today. Zimmerman wants to write a proposal to build a forward model of a coronographic spectrograph (think P1640 or GPI); he has the intuition (which I share) that if you built such a model, you could calibrate the data far better. Right now calibration is performed before and after observing; the science frames are expected to be in agreement with the calibration meta-data or some interpolation of it, and the data are "corrected" or transformed from the instrument coordinates (two-dimensional pixels) to some calibrated object (three-dimensional imaging spectroscopic boxels). But since flexure and temperature changes can be non-trivial, and since the science frames contain so many photons, it would be better to learn the calibration of the spectrograph from the appropriate combination of the calibration and science data, and it would be better to perform the comparison between models and data at the pixel level. That's a theme of this blog, of course. We discussed what kinds of small, toy, demonstration systems could show this, convincingly enough for a proposal, relevant to the real thing, but easy to set up and use as a little sandbox.

JWST has a finite lifetime

I spent the day at STScI, giving a talk about hierarchical inference, hosted by Lou Strolger (STScI), and also chatting with various. There is so much going on at STScI and JHU; it was a busy day! One theme of my conversations was calibration (of course); CampHogg and STScI are aligned in wanting to make calibration simultaneously more precise and less time-consuming (as in less consuming of observing time). Another theme was the short life of JWST; as a non-serviceable facility with expendables, it has a finite lifetime. This puts pressure not just on calibration, but also on every possible science program. We have to use this facility efficiently. That's a challenge to the whole community, but especially the many teams at STScI.

determinants

Who would have thunk it: I have spent the last 25 years doing astrophysics in some form or another, and now I am preparing to co-write a paper on computing the determinants of matrices. Foreman-Mackey and I met with Mike O'Neil (NYU) and Sivaram Ambikasaran (NYU) (both Applied Math) today about making determinant calculations fast. The crazy thing is that linear algebra packages out there are happy to make matrix inversion fast, but they uniformly discourage, disparage, or express incredulity about the computation of determinants. I understand the issues—determinants have ungodly units and therefore ungodly magnitudes—but we need to compute them if we are going to compute Gaussian probability densities. Our matrices are somewhat sparse, but the key idea behind Ambikasaran's method is that the matrices are smooth (columns are good at predicting other columns), or, equivalently, that the matrices have low-rank sub-matrices inside them. Plus fastness.

prior on galaxy images, bullet

MJ Vakili (NYU) showed me today what he has been working on to generate a data-driven prior probability distribution over galaxies. It is great work. He finds that he can do a shapelet decomposition, truncate it, and then do a dimensionality reduction (again, as it were), and then fit the resulting distribution of components with a mixture of Gaussians. We have yet to show that the model is good, but when he samples from it, the samples look like actual galaxies. The point is this: If you want to measure a shear map (or anything else, for that matter) from galaxy images, you can't do proper inference if you don't have a prior over galaxy images. So we are playing around with the possibility of making one.

In the brown-bag today, Craig Lage (NYU) showed detailed simulations he is doing of the "Bullet Cluster". He is doing by-hand likelihood optimization, with an hours-long simulation inside the loop! But the results are gorgeous: He can reproduce all the large-scale features, and a lot of the small-scale details. He says it isn't a challenge to CDM, but it is a challenge to theories in which there is no dark matter. One of his goals is to test dark-matter interactions; it looks very promising for that.

building photometry from our imaging model

On the airplane home from "The AD", I wrote in our paper about a data-driven model for the Kepler focal plane. I wrote about the following issue: This model is a data-driven, flexible model of the pixels telemetered down from the spacecraft. As such, the model doesn't contain anything within it that could be interpreted as the "flat-field" or as the "point-spread function" or a "source", let alone a source "brightness". But it is a good model! The question is: How to extract photometry? We have a plan, but it is debatable. The fundamental issue is that data-driven models are, almost by definition, uninterpretable (or at least not straightforwardly interpretable). Insane.

nothing

[There is no interpretation of the rules of this blog such that I could count camel racing as research. Thanks to Yosi Gelfand (NYUAD) for that!]