Kepler issues

At breakfast, I went through with Barclay and Quintana (Ames) my list of all the effects that lead to variability in Kepler light-curves. These include intrinsic stellar variability, stellar variability from other stars that overlap the target, stellar variability transferred to the target by electronics issues. They include stellar proper motion, parallax, and aberration. They include variations in spacecraft temperature, pointing, and roll angle. And so on. The list is long! I am trying to make sure we understand what our pixel-level model covers and what it doesn't. I am spending a lot of my writing time on our data-driven pixel-level model getting the assumptions, capabilities, and limitations clearly specified.

ABC, IMF, and habitability

While Foreman-Mackey and Barclay set off on a tangent to measure (or limit) exoplanet masses using n-body models of exoplanet systems observed by Kepler, I had a great phone call with Schaefer (CMU), Cisewski (CMU), Weller (CMU), and Lang about using Approximate Bayesian Computation (ABC) to ask questions about the universality of the high-mass initial mass function (IMF) in stellar clusters observed in the PHAT survey. The idea behind ABC is to do a kind of rejection sampling from the prior to make an approximation to posterior sampling in problems where it is possible to generate data sets from the model (and priors) but impractical or impossible to write down a likelihood function.

The reason we got this conversation started is that way back when we were writing Weisz et al on IMF inference, we realized that some of the ideas about how high-mass stars might form in molecular clouds (and thereby affect the formation of other less-massive stars) could be written down as a data-generating process but not as a computable likelihood function. That is, we had a perfect example for ABC. We didn't do anything about it from there, but maybe a project will start up on this. I think there might be quite a few places in astrophysics where we can generate data with a mechanistic model (a simulation or a semi-analytic model) but we don't have an explicit likelihood anywhere.

At the end of the day, Sarah Ballard (UW) gave a great Physics Colloquium on habitable exoplanets and asteroseismology, and how these two fields are related. They are related because you only know the properties of the exoplanet as well as you can understand the properties of the star, and asteroseismology rocks the latter. She mentioned anthropics momentarily, which reminded me that we should be thinking about this: The anthropic argument in exoplanet research is easier to formulate and think about than it is in cosmology, but figuring it out on the easier problem might help with the harder one.

pixel-level model

In the morning, to steady our thoughts, Foreman-Mackey, Barclay, and I wrote on the blackboard our model for the Kepler pixel-level data. This is the data-driven model we wrote up in the white paper. The idea is to fit pixels with other pixels, but taking as "other" pixels only those that are far enough away that they can't be being affected by the same star. These other pixels will share in spacecraft issues (like temperature and pointing issues) but not share in stellar variability or exoplanet transit effects, because different stars are independently variable. A key idea of our model, which Foreman-Mackey mocked up for our white paper, is that we avoid over-fitting the pixels by using a train-and-test framework, in which we "learn" the fit coefficients using data not near (in time) to the pixel value we are trying to predict (or de-trend).

In the evening, I started writing up this model and our results. We are all ready to write paper zero on this.

papers we are going to write (really)

In the morning, Barclay and I decided to divide and conquer: He would write up the scope for a limb-darkening paper, and I would write up a plan for a re-calibration of the Kepler data (using Foreman-Mackey's regression model built for the whitepaper). We both then failed to complete our tasks (there's always tomorrow!). In the afternoon, I discussed large-scale structure measurements with Walsh and Tinker, who are looking at extensions to the halo-occupation model. One extension is to reconsider dependences for halo occupation on other halo parameters (other than mass). Another is to look at more large-scale-structure observables.

limb darkening

Tom Barclay (Ames) found himself in New York this week and we discussed our dormant project to measure stellar limb darkening using exoplanet transits. I love this project, because it is a way to image a star without high angular resolution imaging! We discussed applications for such measurements and (for the millionth time) the scope of our possible first paper. We also discussed many other things, including "what's next for Kepler?", and MCMC troubles, and searches for long-period planets. We also had a telecon about search with Bekki Dawson (Berkeley) and other exoSAMSI-ites. Late in the day, Hou reminded me that I owe him comments on his paper on nested sampling!

Hubble Constant

In an almost zero-research day, Wendy Freedman (OCIW) gave a great and inspiring talk about measuring the Hubble Constant with local measurements of Cepheid stars and supernovae. She demonstrated the great value of moving to infrared observations and argued convincingly that systematic uncertainties in the measurements are now down around the few-percent level. Of course the interesting thing is that these local measurements consistently get Hubble Constants a tiny bit higher (Universe a tiny bit smaller or younger) than the cosmic-microwave-background-based inferences. Freedman argued strongly that this tension should be pursued and tested, because (a) it provides a fundamental, independent test of the cosmological model, and (b) it could conceivably point to new physics. I agree.

fastness! and delivery!

The hypothesis-combination trick mentioned yesterday did indeed work, speeding up Foreman-Mackey's exoplanet search code by a factor of about 30 and keeping the same result, which is that we can detect Earth-like exoplanets on year-ish orbits around at least some Sun-like stars in the Kepler data. Now are there any? This speed-up, combined with the four orders of magnitude Foreman-Mackey got this weekend makes for a total speed up of 10^5.5, all in one crazy week. And then at lunch, Mike O'Neil (NYU) told us that given the form of our Gaussian Process kernel, he could probably get us another substantial speed-up using something called a "fast Gaussian transform". If this turns out to be true (we have to do some math to check), our exoplanet search could get down to less than a minute per star (which would be dandy).

In other overwhelming-force news, Fadely delivered psf-model fits to thousands of stars in HST WFC3 IR-channel data, showing that we can do a very good job of modeling the pixel-level data in preparation for flat-field determination. And Hou delivered a complete manuscript draft on his diffusive nested ensemble sampler. So it was a great day of hard work by my team paying off handsomely.

exoplanet search, large galaxies

I worked on large-galaxy photometry with Patel for part of the day. She is dealing with all our problem cases; we have good photometry for almost any large, isolated galaxy, but something of a mess for some of the cases of overlapping or merging galaxies. Not surprising, but challenging. I am also working on how to present the results: What we find is that with simple, (fairly) rigid galaxy models we get excellent photometry. How to explain that, when the models are too rigid to be "good fits" to the data? It has to do with the fact that you don't have to have a good model to make a good photometric measurement, and the fact that simple models are "interpretable".

In the afternoon, we had a breakthrough in which we realized that Foreman-Mackey's exoplanet search (which he sped up by a factor of 10⁴ on the weekend with sparse linear algebra and code tricks) can be sped up by another large factor by separating it into single-transit hypothesis tests and then hypothesis tests that link the single transits into periodic sets of transits. He may try to implement that tomorrow.

halo occupation, Earth analogs

I spent some time with Kilian Walsh (NYU) discussing halo occupation (putting galaxies into dark-matter halos). With Jeremy Tinker (NYU) he is looking at whether enriching the halo parameters (currently only mass and concentration) with environment information will improve halo-occupation models. As per usual, I asked for plots that show how well they are doing without the environment.

In the afternoon, Foreman-Mackey delivered results of a (very limited) search for Earth-like exoplanets in the light-curve of a bright Kepler G dwarf star, using his Gaussian-process likelihood function. In the limited search, he was able to re-find an injected Earth-like transit with a 300-day period. That's extremely promising. It is not clear whether things will get a lot worse when we do a fuller search or go to fainter stars.

out sick

did nothing

Tri-State Astronomy

I spent the research part of my day at the Tri-State Astronomy meeting, beautifully organized by Geha (Yale) and Maller (CUNY) and others. I won't do it justice; there were five great review talks and lots of great posters (and one-minute poster summaries). Alyson Brooks (Rutgers), in her review talk, beautifully summarized the issues with CDM at small scales, and discussed the idea that baryonic processes might explain all of these. My take on her bottom line (that baryons might explain everything) is that it would be a disappointment if we can't see the predicted properties of the dark matter at small scales! But she did point towards isolated dwarf galaxies (that is, very low luminosity galaxies that are not satellites of any more luminous galaxy) as critical tests of the ideas; isolated dwarfs should differ from satellite dwarfs if CDM is going to stay okay at small scales. She also implicitly made many predictions about outflows from small galaxies at intermediate redshifts. And she gave a few shout-outs to Zolotov, who has been deeply involved in these baryon issues since leaving NYU.

inferring spectra, optimizing search

Vy Tran (TAMU) showed up and we discussed inference of spectral energy distributions of high-redshift galaxies given only photometry (no spectroscopy). She showed us some nice results, but Fadely and I think we could actually infer spectral properties at wavelength resolution higher than that implied by the broad-band (or medium-band) photometry. So we more-or-less launched a collaboration.

On the way to lunch, Fadely, Foreman-Mackey, and I had an epiphany: Foreman-Mackey has been trying to set the hyperparameters of a Gaussian Process to optimize our ability to search for and find exoplanets. This has been befuddling because it is so frequentist (or not even frequentist you might say). The issue is that what you want to optimize (hyperparameter-wise) depends on the details of how you are going to decide what is an exoplanet (that is, on your threshold choices). We realized on the way to lunch that we probably should be choosing the hyperparameters to maximize the area under the ROC curve. Foreman-Mackey launched on this in the afternoon. Cool if it works; novel definitely.

search and hyperparameters

In a last-minute clutch play on a low-research day, Foreman-Mackey showed me that our ability to detect exoplanet transits in the lightcurves of stochastically varying stars depends in a non-trivial way on the hyperparameters of the Gaussian Process we use to model the unocculted star. We are hoping we can tune to the most-sensitive-for-search hyperparameters before searching, and only switch back to being agnostic about the hyperparameters at the post-search characterization stage.

marginalized likelihood, goose egg

Having written some stuff that I wasn't happy with a few months ago, thought about it, forgot about it, remembered it, mentioned it on the blog here and there, and then dusted it off today, I got close to being ready to make an argument about when you should and shouldn't compute the marginalized likelihood, even if you are a committed probabilistic reasoner. The fundamental idea is that you shouldn't do model selection based on marginalized likelihoods; these are very challenging integrals but only approximations (and often bad ones) to the integrals you would really want to do to inform a model choice. I guess one way to put it is: Don't spend a huge amount of computer time computing something that is a worse approximation to what you want than something else that might be much easier to compute! I sent my argument for review to Brewer, my guru in all things Bayes. I want to say things that are useful and uncontroversial, so I need to be careful, because on these matters I tend to be like a bull in a china shop.

Late in the day I talked to a NYU Data Science class about possible research projects they could do with the Kepler data. As I was talking about how we search for exoplanets in the data (and how likely it is that the data contain many undiscovered planets), one of the faculty in charge of the class (Mike O'Neil) asked me how many exoplanets we (meaning CampHogg) have found in the data so far. I had to admit that the answer is zero. That's just embarrassing. I need to ride the team hard tomorrow.

exoplanets, exoplanets, exoplanets

I gave the CCPP Brown Bag talk today, about Kepler data and exoplanets. I was going to talk about calibration, flat-field, and our white paper, but I ended up talking about very flexible models, for intrinsic stellar variability and spacecraft-induced variability in the lightcurves. People were shocked that some of our models have hundreds of thousands of parameters. I didn't let them in on the secret that, in some sense, the Gaussian Processes we use have infinite numbers of parameters!

Tim Morton (Caltech) dropped by to talk about various things exoplanet. He has a very nice system for computing and propagating probabilities for various exoplanet and non-exoplanet (false-positive) scenarios, given Kepler data. He produces most of what you need in order to do efficient follow-up and population studies, given uncertain or noisy exoplanet identifications. In other news, today was Angus's last day here at NYU. She has been visiting for a month from Oxford, and started some projects with us on search, using Gaussian Processes under the hood. They told us it couldn't be done (too slow) but we are doing it.