My last research day before heading to MPIA for the summer was taken up with many non-research things! However, I did have brief discussions with Lauren Anderson (Flatiron) about what is next for our collaboration, now that paper 1 is out!
At the Stars group meeting, John Brewer (Yale) and Matteo Cantiello (Flatiron) told us about the Kepler / K2 Science meeting, which happened last week. Brewer was particularly interested in the predictions that Ruth Murray-Clay made for chemical abundance differences between big and small planet hosts; it is too early to tell how well these match on to the results Brewer is finding for chemical differences between stars hosting different kinds of exoplanet architectures.
Other highlights included really cool supernova light curves, with amazing details, Granulation or flicker estimates of delta-nu and nu-max, and a clear bimodality in planetary radii between super-earths and mini-neptunes. There was much discussion in group meeting of this latter result, both what it might mean, and what predictions it might generate.
Highlights for Cantiello included results on the inflation of short-period planets by heating by their host stars. And, intriguingly, a possible asteroseismic measurement of stellar inclinations. That is, you might be able to tell the projection of a star's spin angular momentum vector projected onto the line of sight. If you could (and if some results about aligned spin vectors in star-forming regions hold up) this could lead to a new kind of tagging for stars that are co-eval!
In the morning, researchers from across the Flatiron Institute gathered for a discussion of statistical inference, which is a theme that cuts across the different departments. Justin Alsing (Flatiron) led the discussion, asking for advice on his project to model global ozone over the last few decades. He has data that spans latitude, altitude, and time, and the ozone levels can be affected by many things other than long-term degradation by pollutants. So he wants to build a non-linear, data-driven model of confounders but still come to strong conclusions about the long-term trends. There was discussion of many relevant methods, including large linear models (regularized strongly), independent components analysis, latent variable models, neural networks, and so on. It was a wide-ranging and valuable discussion. The CCB at Flatiron has some valuable mathematics expertise, which could be important to all the Flatiron departments.
OMG much of my research time today was spent trying to figure out everything that is wrong with Section 7 (uncertainties in both x and y) of the Hogg, Bovy, and Lang paper on fitting a line. Warning to users: Don't use Section 7 until we update! The problems appeared early (see the GitHub issues on this Chapter), but came to a head when Dan Foreman-Mackey (UW) wrote this blog post. Oddly I disagree with Foreman-Mackey's solution, and I don't have consensus with Jo Bovy (Toronto) yet. It has something to do with how we take the limit to very large variance in our prior. But I must update the paper asap!
I had a long set of conversations with Boris Leistedt (NYU) about various matters cosmological. The most exciting idea we discussed comes from thinking about good ideas that Andrew Pontzen (UCL) and I discussed a few weeks ago: If you can cancel some kinds of variance in estimators by performing matched simulations with opposite initial conditions, might there be other families of matched simulations that can be performed to minimize other kinds of estimator variances?
For example, Leistedt wants to make a set of simulations that are good for estimating the covariance of a power-spectrum estimator in a real experiment. How do we make a set of simulations that get this covariance (which is the variance of a power spectrum, which is itself a variance) with minimum variance on that covariance (of that variance)? Right now people just make tons of simulations, with random initial conditions. You simply must be able to do better than pure random here. If we can do this well, we might be able to zero out terms in the variance (of the variance of the variance) and dramatically reduce simulation compute time. Time to hit the books!
Stars group meeting ended up being all about the Milky Way Bar. Jo Bovy (Toronto), many years ago, made a prediction about the velocity distribution as a function of position if the velocity substructure seen locally (in the Solar Neighborhood) is produced (in part) by a bar at the Galactic Center. The very first plate of spectra from APOGEE-South happens to have been taken in a region that critically tests this model. And he finds evidence for the predicted velocity structure! He finds that the best-fit bar is a fast bar (whatever that means—something about the rotation period). This is a cool result, and also a great use of the brand-new APOGEE-S data.
Bovy was followed by Sarah Pearson (Columbia) who showed the effects of a bar on the Pal-5 stream and showed that some aspects of its morphology could be explained by a fast bar. We weren't able to fully check whether both Bovy and Pearson want the exact same bar, but there might be a consistent story emerging.
The research highlight of the day was Marla Geha (Yale) dropping in to Flatiron to chat about MCMC sampling. She is working through the tutorial that Foreman-Mackey (UW) and I are putting together and she is doing the exercises.
I'm impressed! She gave lots of valuable feedback for our first draft.
I spent time working through the last bits of a paper by Dun Wang (NYU) about image modeling for time-domain astrophysics. I asked him to send it to our co-authors.
The rest of the day was spent in discussions of Bayesian inference with the Flatiron Astronomical Data Group reading group. We are doing elementary exercises in data analysis and yet we are not finding it easy to discuss and understand, especially some of the details and conceptual arguments. In other words: No matter how much experience you have with data analysis, there are always things to learn!
I helped Justin Alsing (Flatiron) and Maggie Lieu (ESA) search for HST data relevant to their project for training a model to find cosmic rays and asteroids. They started to decide that HST's cosmic-ray identification methods that they are already using might be good enough to just rely upon, which drops their requirements down to asteroids. That's good! But it's hard to make a good training set.
Jia Liu (Columbia) swung by to discuss the possibility of finding things at exo-L1 or exo-L2 (or the other Lagrange points). Some of the Lagrange points are unstable, so anything we find would be clear signs of alien technology. We looked at the relevant literature; we may be fully scooped, but I think there are probably things to do still. One thing we discussed is the observability; it is somehow going to depend on the relative density of the planet and star!
A research highlight today was the first meeting of our Bayesian Data Analysis, 3ed reading group. It lasted a lot longer than an hour! We ended up going off into a tangent on the Fully Marginalized Likelihood vs cross-validation and Bayesian equivalents. We came up with some possible research projects there! The rest of the meeting was Bayesian basics. We decided on some problems we would do in Chapter 2. I hate to admit that the idea of having a problem set to do makes me nervous!
In the afternoon, Lauren Anderson (Flatiron) and I discussed our project to separate red-clump stars from red-giant-branch stars in the spectral domain. We have two approaches: The first is unsupervised: Can we see two spectral populations where the RC and RGB overlap? The second is supervised: Can we predict relevant asteroseismic parameters ina training set using the spectra?
At the Stars group meeting, I proposed a new approach for asteroseismology, that could work for TESS. My approach depends on the modes being (effectively) coherent, which is only true for short survey durations, where “short” can still mean years. Also, Mike Blanton (NYU) gave us an update on the APOGEE-S spectrograph, being commissioned now at LCO in Chile. Everything is nominal, which bodes very well for SDSS-IV and is great for AS-4. David Weinberg (OSU) showed up and told us about chemical-abundance constraints on a combination of yields and gas-recycling fractions.
In the afternoon I missed Cosmology group meeting, because of an intense discussion about marginalization (in the context of cryo-EM) with Leslie Greengard (Flatiron) and Marina Spivak (Flatiron). In the conversation, Charlie Epstein (Penn) came up with a very simple argument that is highly relevant. Imagine you have many observations of the function f(x), but for each one your x value has had noise applied. If you take as your estimate of the true f(x) the empirical mean of your observations, the bias you get will be (for small scatter in x) proportional to the variance in x times the second derivative of f. That's a useful and intuitive argument for why you have to marginalize.
I spent the day at Renaissance Technologies, where I gave an academic seminar. Renaissance is a hedge fund that created the wealth of the Simons Foundation among many other Foundations. I have many old friends there; there are many PhD astrophysicists there, including two (Kundić and Metzger) I overlapped with back when I was a graduate student at Caltech. I learned a huge amount while I was there, about how they handle data, how they decide what data to keep and why, how they manage and update strategies, and what kinds of markets they work in. Just like in astrophysics, the most interesting signals are at low signal-to-noise in the data! Appropriately, I spoke about finding exoplanets in the Kepler data. There are many connections between data-driven astrophysics and contemporary finance.
Today we decided that the newly-christened Astronomical Data Group at Flatiron will start a reading group in methods. Partially because of the words of David Blei (Columbia) a few weeks ago, we decided to start with BDA3, part 1. We will do two chapters a week, and also meet twice a week to discuss them. I haven't done this in a long time, but we realized that it will help our research to do more basic reading.
This week, Maggie Lieu (ESA) is visiting Justin Alsing (Flatiron) to work (in part) on Euclid imaging analysis. We spent some time discussing how we might build a training set for cosmic rays, asteroids, and other time-variable phenomena in imaging, in order to train some kind of model. We discussed the complications of making a ground-truth data set out of existing imaging. Next up: Look at what's in the HST Archive.
I worked for Hans-Walter Rix (MPIA) this weekend: I worked through parts of the After Sloan 4 proposal to the Sloan Foundation, especially the parts about surveying the Milky Way densely with infrared spectra of stars. I also had long conversations with Rix about our research plans for the summer. We have projects to do, and a Gaia Sprint to run!
First thing, I met with Schiminovich (Columbia), Mohammed (Columbia), and Dun Wang (NYU) to discuss our GALEX imaging projects. We decided that it is time for us to produce titles, abstracts, outlines, and lists of figures for our next two papers. We also realized that we need to produce pretty-picture maps of the plane survey data, and compare it to Planck and GLIMPSE and other related projects.
I had a great lunch meeting with Brian McFee (NYU) to catch up on his research (on music!) and ask his advice on various time-domain projects I have in mind. He has new systems to recognize chords in music, and he claims higher performance than previous work. We discussed time-series methods, including auto-encoders and HMMs. As my loyal reader knows, I much prefer methods that deal with the data probabilistically; that is, not methods that always require complete data without missing information, and so on. McFee had various thoughts on how we might adapt methods that expect complete data for tasks that are given incomplete data, like tasks that involve Kepler light curves.
At Stars group meeting, Matteo Cantiello (Flatiron) had us install MESA and then gave us a tutorial on aspects of post-main-sequence evolution of stars. There were many amazing and useful things, and he cleared up some misconceptions I had about energy production and luminosity during the main-sequence and red-giant phases of stellar evolution. He showed some hope (because of convective-region structure, which in turn depends on opacity, which in turn depends on chemical abundances) that we might be able to measure some aspects of chemical abundances with asteroseismology in certain stellar types.
In the Cosmology group meeting, we discussed many topics, but once again I got fired up about automated methods or exhaustive methods of searching for (and analyzing) estimators, both for making measurements in cosmology, and for looking for anomalies in a controlled way (controlled in the multiple-hypothesis sense).
One target is the neutrino mass, which is in the large-scale structure, but subtly.
In the space between meetings, Daniela Huppenkothen (NYU) and I worked with Chris Ick (NYU) to get him started building a mean model of Solar flares, and looking at the power spectrum of the flares and their mean models. The idea is to head towards quantitative testing of quasi-periodic oscillation models.
One great research moment today was Stephen Feeney (Flatiron) walking into my office to ask me about the Lutz–Kelker correction. This is a correction applied to parallax measurements to account for the point that there are far, far more stars at lower parallaxes (larger distances) than there are at smaller parallaxes. Because of (what I think of as being) Jacobian factors, the effect is stronger in parallax than it is in distance. The LK correction corrects for what—in luminosity space—is sometimes called Eddington bias (and often wrongly called Malmquist bias). Feeney's question was: Should he be applying this LK correction in his huge graphical model for the distance ladder? And, implicitly, should the supernova cosmology teams have applied it in their papers?
The short answer is: No. It is almost never appropriate to apply the LK correction to a parallax. The correction converts a likelihood description (the likelihood mode, the data) into a posterior description (the posterior mode) under an improper prior. Leaving aside all the issues with the wrongness of the prior, this correction is bad to make because in any inference using parallaxes, you want the likelihood information from the parallax-measuring experiment. If you use the LK-corrected parallax in your inference, you are multiplying in the LK prior and whatever prior you are using in your own inference, which is inconsistent, and wrong!
I suspect that if we follow this line of argument down, we will discover mistakes in the distance-ladder Hubble-constant projects! For this reason, I insisted that we start writing a short note about this.
Historical note: I have a paper with Ed Turner (Princeton) from the late 90s that I now consider totally wrong, about the flux-measurement equivalent of the Lutz-Kelker correction. It is wrong in part because it uses wrong terminology about likelihood and prior. It is wrong in part because there is literally a typo that makes one of the equations wrong. And it is wrong in part because it (effectively) suggests making a correction that one should (almost) never make!
Well of course Adrian Price-Whelan (Princeton) had lots of comments on the paper, so Lauren Anderson (Flatiron) and I spent the day working on them. So close now!
I had lunch with Bruce Knuteson (Kn-X). We talked about many things but including the knowledge exchange that Kn-X runs: The idea is to make it possible to buy and sell correct information, even from untrusted or anonymous sources. The idea is that the purchase only goes through if the information turns out to be true (or true-equivalent, like useful). It has lots of implications for news, but also for science, in principle. He asked me how we get knowledge from others in astronomy? My answer: Twitter (tm)!
Late in the day, Dan Foreman-Mackey (UW) and I had a long discussion about many topics, but especially possible events or workshops we might run next academic year at the Flatiron Institute. One is about likelihood-free or ABC or implicit inference. Many people in CCA and CCB are interested in these subjects, and Foreman-Mackey is thinking about expanding in this direction. Another is about extreme-precision radial velocity measurements, where models of confusing stellar motions and better methods in the pipelines might both have big impacts. Another is about photometry methods for the TESS satellite, which launches next year. We also discussed the issue that it is important, when we organize any workshop, to make it possible to discover all the talent out there that we don't already know about: That talent we don't know about will increase workshop diversity, and increase the amount we ourselves learn.
First thing, Ruth Angus (Columbia) and I discussed an old, abandoned project of mine to find exoplanets by looking at timing residuals (as it were) on high-quality (like nearly coherent) oscillating stars. It is an old idea, best executed so far (to my knowledge; am I missing anything?) by Simon Murphy (Sydney). I have ideas for improvements; they involve modeling the phase shift as a continuous function, not binning and averaging phase shifts (which is the standard operating procedure). It uses results from the Bayesian time-series world to build a likelihood function (or maybe a pseudo-likelihood function). One of the things I like about my approach is that it could be used on pulsar timing too.
For the rest of the day, Lauren Anderson (Flatiron) and I did a full-day paper sprint on her Gaia TGAS color-magnitude diagram and parallax de-noising paper. We finished! We decided to give Price-Whelan a weekend to give it a careful once-over and submit on Monday.