snail models; platykurtic galaxies

Suroor Gandhi (NYU) made me in real time some really nice plots today of what a swarm of stars in phase space do over time. Her plots are for the vertical dynamics of the disk. The very exciting thing is that she can reproduce the qualitative properties of The Snail (the phase-space spiral in the local Milky Way disk). Now we have to look at dependence on initial conditions, time of evolution, and potential parameters.

Dustin Lang (Perimeter) and I spoke for a bit about our old project modeling simple galaxy profiles with mixtures of concentric Gaussians. He is trying to build a truly continuous, interpolate-able model for all Sersic indices, and of course (well it wasn't obvious to me before today) at Sersic index of 0.5, the galaxy profile is exactly a Gaussian, so a mixture of Gaussians makes no sense. And then at indices less than 0.5, the distribution becomes platykurtic, so it can't be fit with a concentric mixture of positive Gaussians. What to do there. Lang wants to add in negative Gaussians! I want to say “don't go there”.

writing

My only accomplishment today was a bit of writing in the method section of the write-up of my project with Kapala and Lang.

image modeling and optimization

The morning began with a talk by Oguz Semerci (Schlumberger-Doll) about optimization and inverse problems in imaging where the data are non trivially related to the image of interest and the problem is under-determined (requiring regularization). He showed examples from medical imaging, airport security, and oil exploration. Unlike many talks I see in these areas, he wasn't restricting to convex problems but still had very good performance. My only complaint would be that he was custom-building optimizers for each problem; I would be surprised if he beats the best industrial optimizers out there. Of course Lang and I are guilty of the same thing in The Tractor! One beautiful idea in his talk is the use of level sets to define the shapes of complex, opaque objects (or image segments).

Mid-day, Maria Kapala (Cape Town), Dustin Lang, and I had a chat about how to proceed on modeling Herschel imaging. Lang agreed to help Kapala get our old code from 2012 working again, and consult on optimization. I promised to start writing the paper (my favorite) and Kapala agreed to gather the relevant data for paper 1. (Somehow the two paragraphs of this research-blog post are more similar than I expected.)

high-resolution dust maps, data-driven SED templates

Maria Kapala (Cape Town) showed up today, to discuss analyses of multi-wavelength imaging. Our idea, which was born years ago in work with Lang, is to build a dust map that constrains dust density and temperature and emission properties using all the Herschel bands, but works at the angular resolution of the best band. The usual practice is to smooth everything to the worst band!

Also had a long conversation with Boris Leistedt (NYU) about learning the templates simultaneously with the redshifts in a template-based photometric-redshift system. This is the right thing to do: It captures the causal model that is inherent in the template-based systems, but also captures the data-driven advantages of a machine-learning method. I am interested to know how accurately and at what resolution we could recover templates in realistic fake-data tests. We scoped a first paper on the subject.

#AstroHackWeek 2015, day 1

We kicked off AstroHackWeek 2015 today, with a huge crowd (some 60-ish) people from all over the world and in all different astrophysics fields (and a range of career stages!). Kyle Barbary (UCB) started the day with an introduction to Python for data analysts and Daniela Huppenkothen (NYU, and the principal organizer of the event) followed with some ideas for exploratory data analysis. They set up Jupyter notebooks for interactive tutorials and the crowd followed along. At some point in the morning, Huppenkothen shocked the crowd by letting them know that admissions to AstroHackWeek had been done (in part) with a random number generator!

In the afternoon, the hacking started: People split up into groups to work on problems brought to the meeting by the participants. Dalya Baron (TAU) and I teamed up to write code to build and project mixtures of Gaussians in preparation for an experiment in classifying and determining the projections (Euler angles) of galaxies. This is the project that Leslie Greengard and I have been discussing at the interface of molecular microscopy and astrophysics; that is, anything we figure out here could be used in many other contexts. By the end of the day we had working mixture-of-Gaussian code and could generate fake images.

JPL, day 3

I spent the morning with Leonidas Moustakas (JPL), a bit of Foreman-Mackey (in Pasadena for the Sagan Fellowship Symposium), and a bit of Andrew Romero-Wolf (JPL) and Curtis McCully (LCOGT) by phone, discussing projects related to strong-lensing time-delay measurements. We discussed two challenging projects. The first is to determine (from as many as we can construct) the best model for quasar time-domain variability. There are claims in the literature that the damped random walk is the best model, but that (very sensible) model hasn't really been competed against all that much. We know how to do this, lets do this! The reason they want good probabilistic generative models is that they want to determine time delays as precisely as possible, using a probabilistic approach.

The second project is to perform high-quality photometry on the (overlapping from the ground) images of a strongly lensed quasar. In this case—when the point-spread functions overlap—you have to do your photometry by simultaneous fitting, but with the variable (and badly known) PSF of ground-based astronomy, I have never seen such photometry that really looks right: There are always fitting-induced covariances of the overlapping-source light curves. I think this is caused by model mismatch (under-fitting), but I don't really know. Romero-Wolf and McCully pointed out that image differencing methods work well in crowded fields, so I formulated an image-modeling approach to the photometry that is as close to image differencing as possible. I promised to write it up into a document. I am kind-of excited about it; it is still just image modeling, but it makes use of the power of image differencing technologies to get flexibility to fit the real PSF as it is.

Late in the day, Adam Miller (JPL) showed me the JPL Mission Control center and a few high bays, filled with awesome stuff (including some fake Mars!).

cosmic origins

Short conversations today with Mei and Lang and Foreman-Mackey. Mei and I decided that we should do the continuum normalization that he is doing at the raw-data stage, before we interpolate the spectra onto the common wavelength grid. This should make the interpolation a bit safer, I think. Lang and I discussed DESI and he showed me some amazing images, plus image models from The Tractor. Foreman-Mackey and I discussed the relevance of his exoplanet research program to the NASA Origins program and the Great Observatories. Can anyone imagine why?

getting funded

A few years ago, I modified The Rules (at right) to permit discussion of proposal writing and related fundraising. I am glad I did that, because otherwise quite a few days might be labeled "not research". Today Foreman-Mackey and I put in a full weekend day on proposal-writing. The big one is for the (excellent, valuable, and influential) NASA Astrophysical Data Analysis Program. This program capitalizes on NASA's public archival data sets by providing funding for individual-investigator re-analyses.

Foreman-Mackey and I are proposing to re-analyze the Kepler data, of course, in order to make it more sensitive (to exoplanets and stellar variability) and more precise. We have four approaches: The first is to build a data-driven pixel-level calibration of the device, in which we use covariances across pixels to model all spacecraft-induced variability. The second is my optimized weighted linear (OWL) photometry, that produces (under strong assumptions) optimal signal-to-noise photometry from the data. The third is our Gaussian-Process code to model stellar (and residual spacecraft) variability or (equivalently) to generalize our exoplanet-transit likelihood function. The fourth is our nascent project to fully model the Kepler focal plane, including point-spread function, sub-pixel flat-field, and the spacecraft Euler Angles. We wrote like the wind.

UnDisLo, day 3

Another impressively productive day just happened in our work bunker on the Central Coast. Conroy (UCSC) came in again, with his student Jieun Choi (UCSC). We discussed ways to generalize "stacking" of spectra in "bins"; it is often (usually?) better to regress. This can be expressed as a wavelength-by-wavelength weighted linear least-square fit. We worked through the linear-regression math in the morning and Choi implemented in the afternoon. The results look sweet. Choi used them to look for consistent residuals in rest-frame (redshifted) and observed-frame (spectrograph) space and it looks like there are effects in both places. At the end of the day, we left Choi with the project of going to quadratic regression.

Marshall (KIPAC) and I worked on extending The Tractor to fit variable point sources, as part of our long-term goal of finding strong gravitational lenses in ground-based data by comparing lens and non-lens explanations of the data. We spent a lot of time understanding inheritance and Lang's pythonisms.

Johnson (UCSC) showed us the results of his Gaussian-Process data-driven calibrations of spectra. They are extremely precise, produce sensible-looking posterior information on spectral properties, and don't seem to erase or interfere with narrow-line issues with the models. We plan to write the method paper this summer.

At the very end of the day, Barclay, Quintana (Ames), and Wolfgang (UCSC) showed up, so I guess we will be talking exoplanets tomorrow! Quintana and Barclay just found the first Earth-radius planet in the habitable zone of a star, and Wolfgang is using physics-based models to fit the radius–period distribution of exoplanets.

Toronto

I spent the day in Toronto, where I gave the Astronomy Colloquium. Ray Carlberg mentioned (perhaps critically) that my talk was a bit more technical than usual for this venue. Oh well! In the morning I spoke with David Law (Dunlap) about how the MANGA project intends to go from spectral pixel data to imaging spectroscopic intensity voxel. They plan to go through a "spectral extraction" step which is very sensible and practical, but probably at least somewhat lossy. We discussed what could be better.

In the afternoon I spoke with Peter Martin (CITA) and Amir Hajian (CITA), both of whom are working with multi-wavelength data of very varied angular resolution, although in very different contexts. I argued for forward modeling (duh!) for both, but also sparse (compressed sensing) dictionary methods for Hajian, whose CMB-contaminating point sources are very distinct in support and spectrum from the CMB.

In the evening, I had dinner with the graduate students. We talked about realism, and the possible reactions to the issue that all models are (or must be) wrong.

intensity vs flux bug

I spent some quality time with Ekta Patel tracking down a bug in our visualization of output from The Tractor. In the end it turned out to be a think-o (as many hard-to-find bugs are) in which I had put in some calibration information as if it calibrated flux, when in fact it calibrates intensity. The flux vs intensity issues have got me many times previously, so I might learn it some day. As my loyal reader knows (from this and this, for example) I feel very strongly that an astronomical image is a measure of intensity not flux! If you don't know what I mean by that, probably it doesn't matter, but the key idea is that intensity is the thing that is preserved by transparent optics; it is the fundamental quantity.

sampling in galaxy shape space

Lang and I pair-coded (although really Lang coded and I stared at the terminal) two extensions for The Tractor today, both related to our hierarchical weak lensing project (now called MBI) with Bard and Marshall and Schneider and Dawson and others. In the first, we extended our mixture of Gaussians approximations to standard galaxy profile to general Sérsic indices; this requires some optimizations, running now in the background. In the second, we built something (that Lang wants to call "Trogdor the Burninator") that very reliably initializes emcee for industrial-scale sampling in galaxy morphological parameters for millions of galaxies. We start with an optimization. A third issue, which we did not address, is that we have four qualitatively different galaxy models (exp, dev, composite exp+dev, and Sérsic) and we would like, ideally, to sample in all four, but this is not totally trivial, given that either we have to make reversible jumps or else compute fully marginalized likelihoods. Right now we just do an early model selection (by BIC) and go with the selected model only. That's a hack, to be sure.

Save Kepler Day, insane imaging precision

Today was Save Kepler Day at Camp Hogg. Through a remarkable set of fortunate events, I had Barclay (Ames), Fergus (NYU), Foreman-Mackey (NYU), Harmeling (MPI-IS), Hirsch (UCL, MPI-IS), Lang (CMU), Montet (Caltech), and Schölkopf (MPI-IS) all working on different questions related to how might we make Kepler more useful in two-wheel mode. We are working towards putting in a white paper to the two-wheel call. The MPI-IS crew got all excited about causal methods, including independent components analysis, autoregressive models, and data-driven discriminative models. By the end of the day, Foreman-Mackey had pretty good evidence that the simplest auto-regressive models are not a good idea. The California crew worked on target selection and repurpose questions. Fergus started to fire up some (gasp) Deep Learning. Lang is driving the Tractor, of course, to generate realistic fake data and ask whether what we said yesterday is right: The loss of pointing precision is a curse (because the system is more variable) but also a blessing (because we get more independent information for system inference).

One thing about which I have been wringing hands for the last few weeks is the possibility that every pixel is different; not just in sensitivity (duh, that's the flat-field) but in shape or intra-pixel sensitivity map. That idea is scary, because it would mean that instead of having one number per pixel in the flat-field, we would have to have many numbers per pixel. One realization I had today is that there might be a multipole expansion available here: The lowest-order effects might appear as dipole and quadrupole terms; this expansion (if relevant) could make modeling much, much simpler

The reason all this matters to Kepler is that—when you are working at insane levels of precision (measured in ppm)—these intra-pixel effects could be the difference between success and failure. Very late in the day I asked Foreman-Mackey to think about these things. Not sure he is willing!

GALEX, SDSS, and WISE

I spent the day in and near AMNH, where Schiminovich and I tried to re-start all our GALEX projects. He proposed that we look at some of the very most recent data, where GALEX is pointing at high stellar density regions of the Milky Way. We were interrupted by Lang, who was finding issues in a SDSS-WISE match. He is making the match in preparation for (as an initialization for) a big fit of the WISE imaging with an SDSS-based model. There are missing objects from SDSS; we tracked (at least some of) them down to the exceedingly complicated definition of SDSS survey primary.

lens-fitting success

Around a nice talk by Daniel Grin (IAS) about estimators for non-Gaussianity in CMB projects and related matters, Marshall and I worked on initialization and optimization of lens models for PanSTARRS data. The optimizer was borked but we figured out it was because the (numerical) derivatives were being taken with step sizes that were too large. Fixed that and it now almost works!

lens Tractor

Marshall and I got Lang on the phone for talk about The Tractor, which Marshall and I are adapting to fit strong lenses (and alternative models) to every source in the PanSTARRS imaging. With help from Lang we got the code running, but it looks like initialization (as usual) is the problem. Late in the day we wrote the abstract of paper 1 on the subject.

cross validation and Bayes

Jake VanderPlas (UW) had the misfortune to be staying in a NYU guest apartment when Hurricane Sandy hit on Monday, taking out subway and then power and then water. In between fulfilling basic human needs for ourselves and our neighbors, we worked on the relationship between cross-validation and Bayes integrals. I think we have something to say here. It might not be original, but it is useful in understanding the relationships of methods. We both wrote some equations and then tried to develop a concordance today. We started a document. While we sheltered in the only location in lower Manhattan with power and internet, I also spoke by Skype with Lang about flexible sky models for The Tractor. Today ended with a discussion on long-term future discounted free-cash flow, about which I really must write an essay sometime very soon.

the fundamental plane

There were talks today by Jim Stone (Princeton), talking about accretion disk physics from simulations, and Lauren Porter (UCSC), talking about the fundamental plane of elliptical galaxies from semi-analytic modeling. Interestingly, Porter was trying to understand the observations of the dependence of galaxy properties as a function of distance from the plane, not within the plane. It is so intriguing that the FP has been around for decades and never really been explained in terms of galaxy formation. Porter finds that it is natural for the duration of star formation to be related to position off the plane. When not in seminars, I was working on my mixture-of-Gaussians paper.

mixture-of-Gaussian galaxies

I actually did real research today, writing and making figures for Lang and my paper on mixture-of-Gaussian approximations to standard two-dimensional galaxy intensity models (think exponential and de Vaucouleurs). I tweaked the figures so their notation matches the paper, I made figure captions, I adjusted the text, and I got the to-do items down to one day's hard work. I am so close! People: Don't use the de Vaucouleurs profile; use my approximation. It is so much better behaved. Details to hit arXiv very soon, I hope.

time for Astrometry.net to rise again

I had two conversations about Astrometry.net today. The first was with Oded Nov (NYU Poly), with whom I plan to put in an engineering proposal to work on citizen science and distributed, untrusted sensors, using Astrometry.net and something about urban sensing as examples.

The second conversation was with Kilian Walsh (NYU), with whom I am trying to get up and running a system to synthesize every submitted image right after we calibrate it. The idea is that the image synthesis (plus a healthy dose of optimization) will tell us, for each submitted image, the sky, bandpass, zeropoint, large-scale flat, and point-spread function. If we can get all that to work (a) we will be Gods on this Earth, and (b) we will be able to search the data for variable stars, transients, and other anomalies.