Bayesian basics; red clump

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?


cryo-electron-microscopy biases

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.


reading the basics

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.


summer plans

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!


music and stars

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.


post-main-sequence stellar evolution

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.


don't apply the Lutz-Kelker correction!

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!


buying and selling correct information

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.


oscillation-timing exoplanet discovery

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.



It was a low-research day. But I did learn a lot about the Simons Foundation, in a set of meetings that introduce new employees to the activities and vision of the Foundation.


variational inference

Today was a great day of group meetings! At the stars group meeting, Stephen Feeney (Flatiron) showed us the Student t distribution, and showed how it can be used in a likelihood function (and with one additional parameter) to capture un-modeled outliers. Semyeong Oh (Princeton) updated us on the pair of stars she has found with identical space velocities but very different chemical abundances. And Joel Zinn (OSU) told us about new approaches to determining stellar parameters from light curves. This is something we discuss a lot at Camp Hogg,
so it is nice to see some progress!

We had the great idea to invite David Blei (Columbia) and Rajesh Ranganath (Princeton) to the Cosmology group meeting today. It was great! After long introductions around the (full) room, we gave the floor to Blei, who chose to tell us about the current landscape of variational methods for inference in large models with large data. His group has been doing lots there. The discussion he led also ranged over a great, wide range of things, including fundamental Bayesian basics, problem structure, and methods for deciding which range of inference methodologies might apply to your specific problem. The discussion was lively, and the whole event was another reminder that getting methodologists and astronomers into the same room is often game-changing. We have identified several projects to discuss more in depth for a possible collaboration.

[With this post, this blog just passed 211.5 posts. I realize that a fractional power of two is not that impressive, but it is going to be a long time to 212 and I'll be lucky to ever publish post number 213!]


interdisciplinary inference meetings

Justin Alsing (Flatiron) organized an interdisciplinary meeting at Flatiron across astrophysics, biology, and computing, to discuss topics of mutual interest in inference or inverse problems. Most of the meeting was spent with us going around the room describing what kinds of problems we work on so as to find commonalities. Some interesting ideas: The neuroscientists said that not only do they have data analysis problems, they also want to understand how brains analyze data! Are there relationships there? Many people in the room from both biology and astronomy are in the “likelihood-free” regime: Lots of simulations, lots of data, no way to compare! That will become a theme, I predict. Many came to learn new techniques, and many came to learn what others are doing, so that suggests a format, going forward, in which we do a mix of tutorials, problem statements, and demonstrations of results. We kicked it off with Lauren Anderson (Flatiron) describing parallaxes and photometric parallaxes. [If you are in the NYC area and want to join us for future meetings, drop me a line.]


measuring the velocity of a star

Yesterday and today I wrote code. This is a much rarer activity than I would like! I wrote code to test different methods for measuring the centroid of an absorption line in a stellar spectrum, with applications to extreme precision radial-velocity experiments. After some crazy starts and stops, I was able to strongly confirm my strong expectation: Cross-correlation with a realistic template is far better for measuring radial velocities than cross-correlation with a bad template (especially a binary mask). I am working out the full complement of experiments I want to do. I am convinced that there is a (very boring) paper to be written.


what is math? interpolation of imaging

The research highlight of the day was a long call with Dustin Lang (Toronto) to discuss about interpolation, centroiding, and (crazily) lexicographic ordering. The latter is part of a project I want to do to understand how to search in a controlled way for useful statistics or informative anomalies in cosmological data. He found it amusing that my request of mathematicians for a lexicographic ordering of statistical operations was met with the reaction “that's not math, that's philosophy”.

On centroiding and interpolation: It looks like Lang is finding (perhaps not surprisingly) that standard interpolators (the much-used approximations to sinc-interpolation) in astronomy very slightly distort the point-spread function in imaging, and that distortion is a function of sub-pixel shift. He is working on making better interpolators, but both he and I are concerned about reinventing wheels. Some of the things he is worried about will affect spectroscopy as well as imaging, and, since EPRV projects are trying to do things at the 1/1000 pixel level, it might really, really matter.