Over the Thanksgiving break, my only research was providing some comments to Huppenkothen on her paper (in prep) about fitting flexible models to magnetar bursts.
Michael Kesden (UT Dallas) gave a great talk today about black-hole–black-hole binary orbits, and the spin–orbit and spin–spin interactions during inspiral. He showed that he can reduce the dimensionality of the spin interaction problem massively using invariants of the motion, and then obtained a regular, analytic solution for the spin evolution. This new solution will massively speed up post-Newtonian calculations of orbits and gravitational-wave waveforms and also will deliver new insight about relativistic dynamics. Along those lines, he found new resonances (spin-evolution resonances with the orbit) and three qualitatively different behaviors of the spin vectors in three different regimes of spin magnitude and alignment. It is also very related to everything I am teaching this semester!
After a low-research morning, Foreman-Mackey and I retreated to an undisclosed location to work on asteroseismology. We checked (by doing a set of likelihood evaluations) on behalf of Eric Agol (UW) whether there is any chance of measuring asteroseismological modes using a bespoke Gaussian process which corresponds to narrow Gaussians in the Fourier domain. The prospects are good (it seems to work) but the method seemed to degrade with signal-to-noise and sampling worse than I expected. Okay, enough playing around! Back to work.
I worked a bit today on building new capabilities for Kepler and TESS and everything to follow: In one project, we are imagining getting parallax information about stars in Kepler. This has been tried before, and there are many who have foundered on the rocks. We (meaning Foreman-Mackey and I) have a new approach: Let's, on top of a very flexible light-curve model, permit a term proportional to the sine and the cosine of the parallactic angle. Then let's consider the amplitude-squared of those coefficients as something that indicates the parallax. The idea is similar to that of the "reduced proper motion" method for getting distances: No proper motion is a parallax, but closer stars tend to have higher proper motions, so there is work that can be done with them. There the stochastic component is the velocity distribution in the disk. Here the stochastic component is the unmodeled flat-field variations.
In the other project I worked on today, I figured out how we might switch asteroseismology from it's current mode (take data to periodogram, take periodogram to measurements of mode frequencies and amplitudes; take mode frequencies to big and small differences; do science on the frequency differences) to one in which the most important quantity—the big frequency difference—is observed more-or-less directly in the data. I have a method, based on Gaussian Processes and Fourier transforms that I think might possibly work. One cool thing is that it might just might enable asteroseismology measurements on dwarf stars even in Kepler long-cadence data. That would be insane. Both of these projects are also great projects for TESS of course.
Dave Charbonneau (Harvard) was in town today, to give the Big Apple Colloquium, which he did with flair. He emphasized the importance of exoplanets in any study of astrophysics or in any astrophysics group or department. He emphasized the amazing value of M-dwarfs as exoplanet hosts: Exoplanets are abundant around M-dwarfs, they are easier to detect there than around Sun-like stars, they are shorter-period at same temperature, and they tend to host small, rocky planets. He showed beautiful work (with Dressing) on the population statistics and also on the compositions of the small planets, which do indeed seem like they are Earth and Venus-like in their compositions. He also talked about TESS and it reminded me that the projects we have going here on Kepler and K2 should all also be pointed at TESS. It is often said that TESS will not be good for long-period planets, but in fact there is a large part of the sky that is viewed for the full year.
In group meeting we talked more about our crazy asteroseismology ideas. Foreman-Mackey and Fadely explained a recent paper about building Gaussian Processes with kernels that represent power spectra that are mixtures of Gaussians in Fourier space. I have a hope that we can use a model like this to do asteroseismology at very low signal-to-noise, bad cadence, and with massive missing data. Any takers?
In our morning informal talk, Yossi Shvartzvald (TAU) showed us results from a global network of planet-oriented microlensing monitor telescopes. They are observing so many stars in the bulge that there are some 50 events going off at all times in their data, and they are getting a few exoplanet discoveries per year. Awesome! He showed that we can already do some pretty confident planet occurrence rate calculations with the data, and this is the first time that we can constrain the statistics of true Jupiter and Saturn and Uranus analogs: Unlike RV and transits, the discoveries don't require monitoring for decades! Also, he talked about what is called "microlensing parallax", which is something I have been interested in for years, because it so beautifully converts angles into distances.
John Johnson (Harvard) came to NYU today along with a big fraction of his group: Ben Montet, Ruth Angus, Andrew Vanderburg, Yutong Shan. In addition, Fabienne Bastien (PSU), Ian Czekala (Harvard), Boris Leistedt (UCL), and Tim Morton (Princeton) showed up. We pitched early in the day, in the NYU CDS Studio Space, and then hacked all day. Projects included: Doing the occurrence rate stuff we do for planets but for eclipsing binaries, generalizing the Bastien "flicker" method for getting surface gravities for K2 data, building a focal-plane model for K2 to improve lightcurve extraction, documenting and build-testing code, modeling stellar variability using a mixture of Gaussians in Fourier space, and more! Great progress was made, especially on K2 flicker and focal-plane modeling. I very much hope this is the start of a beautiful relationship between our groups.
I also had long conversations with Leistedt about near-future probabilistic approaches to cosmology using our new technologies, Sanderson about series expansions of potentials for Milky Way modeling, Huppenkothen about AstroHackWeek 2015, and Vakili about star centroiding. In somewhat related news, during the morning pitch session, I couldn't stop myself from describing the relationships I see between structured signals, correlation functions, power spectra, Gaussian processes, cosmology, and stellar asteroseismology. I think we might be able to make asteroseismology more productive with smaller data sets.
In the second day, we heard from Ulvestad (NSF) about how budgets are planned at the agencies, from the presidential request through to the divisions and then adjusted over time. It was remarkable and scary! Although the granting is all peer-reviewed, there is a huge amount of decision-making within NSF that is certainly not. That said, astronomy does well at NSF in part because it has well-organized, unified community support for certain big projects.
We spent a long time talking about principles for access to shared facilities and federally funded observatories and surveys and other such projects. One principal principle is transparency, which I love. Another is open data. We also spent a lot of time talking about the possible data we would need to understand the causes of (and solutions to) the related problems of low success rates on grant proposals and the large number of proposals submitted per person per year.
Today was the first day of the Astronomy and Astrophysics Advisory Committee meeting at NSF headquarters. The Committee is established by an act of Congress to oversee the interagency cooperation and interaction and etc between NSF Astronomy and Astrophysics and NASA Astrophysics (and also DOE Cosmic Frontiers). I learned a huge amount about science at the meeting, including about a conflict between VLBI and Hipparcos parallaxes to the Pleaides. That's Huge. Of course we looked at the outrageously awesome ALMA image of HL Tau showing actual Oh-My-God rings. I learned that the black hole at the center of M82 is no longer thought to be a black hole (need to learn more about that!) and that there is a too-massive black hole found at an ultra-compact dwarf galaxy. Wow, science rocks!
We went on to learn that science rocks a lot less than I thought, for various reasons: The proposal success rates in most individual-investigator money grants are at 15 to 20 percent, with DOE being higher but with most of their (DOE's) grants going to groups already working on DOE-priority projects. These low success rates may be distorting the "game" of applying for funding; indeed it appears that proposers are writing more proposals per year than ever before.
I learned (or re-learned) that the federal budgets (primarily from the executive branch) that involve ramping down work on NASA SOFIA are also budgets that involve ramping down the whole NASA Astrophysics budget by the same amount. That is, the honesty of the community and its willingness to make hard choices about what's important leads to budget reductions. Those are some terrible incentives being set up for the community. The agencies and the powers that be above them are creating a world in which honesty and frugality is rewarded with budget cuts. I guess that's why the defense part of the US government is so (a) large and (b) dishonest. Thanks, executive branch! Okay, enough goddamn politics.
I spent the day working finishing my grant proposal to the NSF (due tomorrow). It is about probabilistic approaches to cosmology. In the end, I am very excited about the things that can be enabled if we can find ways to make a generative model of things like the positions of all galaxies or the unlensed shapes of galaxies: We can connect the theoretical model (which generates two-point functions of primordial density fields) to the data (which are positions and shapes of galaxies, among other things). That can only increase our capabilities, with existing and future data.
A highlight of group meeting today was Sander Dieleman (Ghent) explaining to us how he won the kaggle Galaxy Zoo challenge. His blog post about it is great too. We hope to use something like his technology (which he also applies to music analysis) to Kepler light-curves. The convolutional trick is so sensible and clever I can't stand it. His presentation to my group reminds me that no use of deep learning or neural networks in astronomy that I know about so far has ever really been sophisticated. Of course it isn't easy!
Ness and I spent the full afternoon working on The Cannon, although a lot of what we talked about was context and next projects, which informs what we write in our introduction and discussion, and what we focus on for paper 2. One thing we batted around was: What kind of projects can we do with these labels that no-one has done previously? I was asking this because we have various assumptions about our "customer" and if our customer isn't us, we might be making some mistakes. Reminds me of things we talked about at DDD.
In my view, the introduction of a paper should contextualize, bring up, form, and ask questions, and the discussion section at the end should answer them, or fail to, or answer them with caveats. The discussion should say all the respects in which the answers given are or could be or shoud be wrong. We only understand things by understand what they don't do. (And no paper should have a "summary" section: Isn't that the abstract?) Ness and I assembled our conclusions, caveats, and questions about The Cannon into an outline for the discussion section. We also talked a bit more about figures. She spent the day working on discussion and I worked a bit on the abstract.
In group meeting, we looked at Malz's first models of SDSS sky. Foreman-Mackey brought up the deep question: If we have a flexible model for the sky in SDSS fibers, how can we fit or constrain it without fitting out or distorting the true spectra of the astronomical objects that share the fibers? Great question, and completely analogous to the problem being solved by Wang in our model for Kepler pixels: How do we separate the signals caused by the spacecraft from those caused by exoplanets?
We are approaching Wang's problem by capitalizing on the causal or conditional independence properties of our generative model. But this is imperfect, since there are hyper-priors and hyper-hyper-priors that make everything causally related to everything else, in some sense. One example in the case of sky: Atomic and molecular physics in the atmosphere is the same atomic and molecular physics acting in stellar atmospheres and the interstellar medium in the spectra of astronomical sources. Another example: The line-spread function in the spectrograph is the same for sky lines and for galaxy emission and absorption lines. These kinds of commonalities make the "statistically independent" components in fact very similar.
Our main progress on The Cannon, paper 1, was to go through all the outstanding discussion points, caveats, realizations, and notes, and use them to build an outline for a Discussion section at the end of the paper. We also looked at final figure details, like colors (I am against them; I still read papers printed out on a black-and-white printer!), point sizes, transparency, and so on. We discussed how to understand the leave-one-out cross-validation, and why the leave-one-star-out cross-validation looks so much better than the leave-one-cluster-out cross-validation: In the latter case, when you leave out a whole cluster, you lose a significant footprint in the stellar label-space in the training data. The Cannon's training data set is a good example of something where performance improves a lot faster than square-root of N.
Melissa Ness arrived in NYC for a week of hacking on The Cannon, our project to transfer stellar parameter labels from well-understood stars to new stars using a data-driven model of infrared stellar spectra from APOGEE. We discussed nomenclature, notation, figures, and the paper outline. The hope is to get a submittable draft ready by Friday. I am optimistic. There are so many things we can do in this framework, the big issue is limiting scope for paper 1.
One big important point of the project is that this is not typical machine learning: We are not transforming spectra into parameter estimates, we are building a generative model of spectra that is parameterized by the stellar parameter labels. This permits us to use the noise properties of the spectra that we know well, generalize from high signal-to-noise training data to low signal-to-noise test data, and account for missing and bad data. The second point is essential: In problems like this, the training data are always much better than the test data!
I worked on my NSF proposal today. I am trying to figure out how the different threads we have on cosmology tie together: We are working on density-field modeling with Gaussian Processes, hierarchical probabilistic models for weak lensing, and probabilistic models for the point-spread function. We also have quasar target selection in the far past and approximate Bayesian computation (tm) in the possible near future. I tried to weave some combination of these into a project summary but am still confused about the best sell.
At group meeting, Hattori showed us an exoplanet discovery, made with his search for single transits! Actually, the object was a known single transit, but Hattori showed that it is in fact a double transit and has a period very different from its recorded value. So this counts as a discovery, in my book. We are nearly ready to fully launch Hattori's code "in the data center"; we just need to run it on a bunch more cases to complete our functional testing.
Also at group meeting, Sanderson discussed the Gaia Challenge meeting from the previous week. There are lots of simulated Gaia-like data sets available for testing methods and ideas for Gaia data analysis. This is exciting. We also discussed generalizing her structure-finding code to make it also a clustering algorithm on the stars.
Also at group meeting, Daniela Huppenkothen (NYU) showed us time-series and spectral data from the famous black-hole source GRS 1915, which has about a dozen different "states". She suggested that there might be lots of low-hanging fruit in supervised and unsupervised classification of these different states, using both time features and spectral features. The data are so awesome, they could launch a thousand data-science masters-student capstone projects!
Tsvi Piran (Racah) gave a lively talk on the likely influence of gamma-ray bursts on life on earth and other habitable worlds. He argued that perhaps we live so far out in the outskirts of the Milky Way because the GRB rate is higher closer to the center of the Galaxy, and GRBs hurt. The ozone layer, that is.
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?
At the end of the day, Malz came by the CDS space and we talked through first steps on a project to look at sky subtraction in spectroscopy. We had a great idea: If the sky residuals are caused by small line-shape changes, we can model the sky in each fiber with a linear combination of other sky fibers, including those same fibers shifted left and right by one pixel. This is like the auto-regression we do for variable stars—and they do on Wall St to model price changes in securities—but applied in the wavelength direction. It ought to permit the sky fitting to fit out convolution (or light deconvolution) as well as the brightness.
Group meeting included some very nice plots from Fadely showing that he can model the color-size distribution of sources in the SDSS data, potentially very strongly improving star–galaxy separation. We also talked about ABC (tm), or Bayesian inference when you can't write down a likelihood function, and also stellar centroiding.
At lunch, Goodman told the Data Science community about affine-invariant MCMC samplers. He did a good job advertising emcee and some new projects he is working on.
I spent time working through some inference problems in the future of cosmology, including how you use probabilistic redshift information, how you marginalize out beliefs about the density field and galaxy formation within that density field, and how you might get probabilistic information about the 2-pt function. I am confused about how much this all matters for different kinds of projects.
At lunch, Andy Haas (NYU) told us about searches for milli-charged particles at the LHC. He has a plan that would rule out a huge class of models.
I learned from Brant Robertson (Arizona), on twitter (tm) of all places, that the LSST level-2 data products will include probabilistic information about source redshifts. I spent some time working out how a "LSST customer" might use those data products. Most of the simple ideas one might have (weight by p(z) at each redshift, for example) are dead wrong and will wrong-ify your answers rather than make them more accurate. Now I am thinking: NSF proposal?