divide by your selection function, or multiply by it?

With Kate Storey-Fisher (San Sebastián), Abby Williams (Caltech) is working on a paper about large-angular-scale power, or anisotropy, in the distribution of quasars. It is a great subject; we need to estimate this power in the context of a very non-trivial all-sky selection function. The tradition in cosmology is to divide the data by this selection function. But of course you shouldn't manipulate your data. Instead, you could multiply your model by the selection function. You can guess which one I prefer! In fact you can do either, as long as you weight the data in the right way in the fit. I promised to write up a few words and equations about this for Williams.

building trust in emulators

I started writing in a possible grant proposal (that would be in collaboration with others) about the trustworthiness of machine-learning emulators. Emulators are systems that learn the input–output relationship of a computationally expensive simulation and produce (or speed the computation of) new simulation outputs, reducing total computational requirements for a given number of simulations. These are so important now that the ESA Euclid and Simons Observatory data-analysis plans crucially involve emulation.

The issue is: How do we trust that the emulators are giving good outputs? There is no obvious way to test them, except by comparing to held-out training data. But in large-scale structure contexts, no amount of held-out data can test the enormous input data space. I don't know how we will ever trust such systems (and damn do we need to!), but I have some ideas about how to improve the situation. One involves enforcing physics symmetries on the emulators. Another involves running adversarial attacks on them.

Dr Kate Storey-Fisher

Kate Storey-Fisher (NYU) defended her PhD here at NYU today. She killed it! She talked about emulating cosmological simulations (at the level of statistics, not maps), making invariant scalars that encode the shapes and dynamics of dark-matter halos, and her awesome 1.2 million all-sky quasar catalog from ESA Gaia and NASA WISE. It was all things my loyal reader knows lots about but I loved it. It has been an honor and a privilege to work with KSF these years, and I will miss her very very much.

doing cosmology differently

Today Chirag Modi (Flatiron) gave a really great lunchtime talk about new technologies in cosmology and inference or measurement of cosmological parameters. He beautifully summarized how cosmology is done now (or traditionally): Make summary statistics of the observables, make a theory of the summary statistics, make up a surrogate likelihood function for use in inference, measure covariance matrices to use in the latter, and go. He's trying to obviate all of these things by using the simulations directly to make the measurements. He has nice results in forward modeling of the galaxy field, and in simulation-based inferences. Many interesting things came up in his talk, including the idea that I have discussed over the years with Kate Storey-Fisher (NYU) of enumerating all possible cosmological statistics! So much interesting stuff in the future of large-scale structure.

halo mass assembly

On Fridays, Kate Storey-Fisher (NYU) organizes a small meeting to discuss her projects on dark-matter halos using equivariant scalar objects constructed from n-body simulation outputs. Today we included Yongseok Jo (Flatiron), who has worked on building tools to paint galaxies onto dark-matter-only n-body simulations. We discussed joint projects, and conceptual issues about mass-assembly histories. In particular, I am interested in how we can predict formation histories of dark-matter halos from the galaxy contents alone, or infer the dark matter distribution in phase space from the stellar distribution in phase space. I love these projects, because they combine growth of structure, gravitational dynamics, galaxy formation, and machine learning.

the symmetries of the observed universe are different from the symmetries of the latent universe

Kate Storey-Fisher and I spent a long time today talking about how to build a project that is about cosmological observables, built from the concepts in her projects on applying coordinate-free geometric forms to theoretical objects in cosmology. The idea could be: Find geometric scalars that exist in the theoretical (or latent) universe, find geometric scalars that exist in any observational survey of the observable universe, and learn the relationships between these; construct cosmological tests and tests of the dark-matter model. The big issue (from my perspective) is that the symmetries that apply to the 6-dimensional phase space of the Universe are different from the symmetries that apply to the observed 3-dimensional redshift-and-angle-space of the (galaxy or quasar, say) observations. Some might say that there are no symmetries in this observational space, since there are window functions and selection functions, but this is not correct: Coordinate symmetries still exist there, it is just that these other functions must also be tracked, in the same space. Anyway, it's a nice research program to figure all this out.

regularities of dark-matter halos

There is a regular dynamics meeting (maybe Galactic dynamics meeting?) at Flatiron. I went today and I learned a lot, from Ivana Escala (Princeton) and Danny Horta-Darrington (Flatiron). I briefly presented Kate Storey-Fisher's project of describing dark-matter halos with coordinate-free nonlinear geometric scalars, which isn't really a dynamics project but it could be, because these scalars could be part of a canonical transformation of the dark sector. Anyway, the crowd had interesting things to say. In particular, the idea came up that the subspace in which the dark-matter halos live (subspace of the space of these scalars) is likely to be very compact (or low-dimensional, or both) and that the susbspace probably depends on the dark-matter model. That's a great idea, and suggests that maybe we can construct new tests of gravity.

what to say for Jim Peebles

I have been honored by an invitation to speak at a meeting in honor of Jim Peebles (Princeton) and his 2019 Nobel Prize in Physics. I spent the day working on things I want to say at this event. Obviously I have to be very critical of the Nobel Prize and all prizes! Haha. But I want to talk about large-scale structure and also the problem that we only ever get to observe one Universe. What does that mean for inductive reasoning and epistemology?

spherical-harmonic transforms of point sets

On the weekend I computed the spherical-harmonic transform of Kate Storey-Fisher's quasar sample made from ESA Gaia data. I also computed the spherical-harmonic transform of the random catalog we use to map the selection function. The two transforms are extremely similar in their complex amplitudes! Since the random catalog is made assuming perfect homogeneity and isotropy, this similarity directly translates into a measurement of the isotropy of the Universe.

jackknife practice and intuitions

Last week I gave a colloquium at MPIA in which I advocated the use of jackknife and bootstrap resampling to obtain empirical uncertainty estimates in a complex data analysis. Today I actually implemented jackknife in my project on cosmic homogeneity (and isotropy). I jackknifed by sky position: I split the sky into 12 nearly-equal regions for 12-fold leave-one-out. I have intuitions about when it is a good idea to jackknife on a quantity (like sky position) and when it is a good idea to jackknife on a quantity that is completely random, but I don't know exactly where my intuition comes from. In general it must be the case that jackknifing on different things answers different questions about your noise.

start a paper on homogeneity

After making (yesterday) all the plots that demonstrate the uniformity and large-scale homogeneity of Kate Storey-Fisher's Gaia quasar catalog (which she is writing up now), I decided (tentatively) to write a paper on cosmic homogeneity with these data: When a catalog shows beautiful homogeneity, that is both a statement about the catalog and a statement about the Universe. I wrote a title and abstract and some figure captions today.

the fractal dimension of the Universe is 3

Back around 2004 I promised myself I would never compute a fractal dimension ever again! But I did today, using Kate Storey-Fisher's (NYU) new quasar catalog from the ESA Gaia data. And it turns out that it is 3. Good! Actual measurement with uncertainty coming soon.

new paper scope

We had a great meeting today with Kate Storey-Fisher (NYU), Hans-Walter Rix (MPIA), Christina Eilers (MIT), and me to discuss KSF's progress on the ESA Gaia quasar sample. We looked at her large-scale structure results and her jackknifes and discussed paper scope. Options range from a quasar-catalog paper to a selection-function paper to a full cosmological parameter-estimation paper. Of course we decided to do all three! But importantly we decided that this week we would focus on writing a quasar-catalog paper. That's good, and achievable.

jackknife the sky?

On the weekend, Kate Storey-Fisher (NYU) and I implemented jackknife uncertainty estimation for KSF's cosmology-with-Gaia-quasars project. We jackknifed by cutting the sky into RA slices. This is standard practice but I don't love it! It assumes that you know that your main source of error is calibration or sample consistency over the sky. It might be something way more insidious. In principle I guess you should jackknife over many things, and also randomly.

do we have the baryon acoustic feature?

Today I posted this tweet (below), which I think explains what happened today! I also gave a talk at MPIA Galaxy Coffee, with Adrian Price-Whelan (Flatiron), about the appearance of stellar parameters in the ESA Gaia XP spectral coefficients.

Seen on @katestoreyfish’s monitor rn. Is that a BARYON ACOUSTIC FEATURE in the @ESAGaia DR3 quasar sample?? #GaiaFete pic.twitter.com/0W0PPJd8H8

— David W Hogg (@davidwhogg) July 28, 2022

quasars and stellar density

Kate Storey-Fisher (NYU) has made really nice random catalogs that look very very similar, in sky coordinates, to the quasars we have. However, there is obviously more exclusion of quasars from the Galactic plane region than we can explain with any reasonable model of how dust is affecting things. It's the stellar density of course: ESA Gaia selection is very sensitive to stellar density, especially (as now) when you are using the XP spectra. Today she included the stellar density in the random-catalog regression and boom: Excellent random! Our model is not mechanistic, it is effective and data-driven.

non-separable and generative random catalogs

Standard practice in large-scale structure is to make large-scale structure and cross-correlation measurements using a catalog of tracers (quasars in our case now) with random catalogs taking the role of tracking the selection function. In most cases this random catalog is made by sampling from a model for the angular selection function and, separately, for each object, sampling from a model for the radial selection function (redshift distribution in our case now). But of course the redshift distribution depends, in detail, on the angular selection function (because, for example, some of the angular selection is set by dust extinction). Kate Storey-Fisher (NYU) and I discussed now to capture these issues in the random we are building for the ESA Gaia quasar sample we are using. One idea is to give the randoms quasar-like luminosities and building the random catalog using our causal ideas about how things make it into the catalog

reverse-engineering the quasar sample

Kate Storey-Fisher (NYU) (with some consulting by me and others) has been trying to model the selection function (in the form of an accurate random catalog) for the ESA Gaia DR3 quasar sample (or a cleaned-up version of it). We currently believe that the selection function should depend most on the Gaia scan history, the local stellar crowding, and the interstellar dust. We are finding that scan history is a very subtle (maybe ignorable) effect, and that dust is big. But when we apply the dust correction, the random-catalog features don't look quite like the features in the real data. Today KSF showed (anti-) correlations between the observed quasar density and the stellar density on the sky. Will correcting for this fix our issues? I sure hope so.

so much Gaia; #renameJWST

I spent the day working on ESA Gaia data, parallel to Kate Storey-Fisher (NYU). She was working on the quasar catalog and the correlation with the CMB convergence maps; I was working on estimating stellar luminosities from low-resolution spectral coefficients. We are too much in the thick of it to report how it's going yet. But stellar luminosities are hard to predict from spectra!

Late in the day I sent this letter to NASA:

I served on the US Astronomy and Astrophysics Advisory Committee (AAAC) for several years; I served on the NASA Spitzer Space Telescope Oversight Committee for many years; I served on the NASA Extragalactic Database User Committee for several years; and my research has been funded by NASA for my entire career (since I was a PhD student in the 1990s). I currently do research with HST, Kepler, TESS, 2MASS, WISE, and WMAP data, and now I'm getting ready for JWST and SPHEREx.

I am writing to say that I think it would serve NASA's interests, and the interests of NASA science especially, to rename JWST. There have been plenty of discussions of the name; it is clear that many scientists (and especially those who are part of the LBGT community or who have concerns for the LBGT community) feel disrespected by the name. I also personally think that the evidence is clear that some of the career activities of James Webb did direct harm to patriotic Americans who were gay.

I want to emphasize, however, that I think the important argument about the name goes beyond the question of any individual historical facts: The LBGT communities are of great importance to all of us. These voices must be heard, and the legitimate concerns must be addressed.

Because NASA is a forward-looking agency, and working towards a more equitable, better world, especially for people working in science and engineering in the US, I think it is time that the spacecraft be renamed. I think this could be done easily and without any trouble; many spacecraft have either officially or effectively changed names at or around first light, two examples that come immediately to mind are WMAP and Spitzer.

Gaia quasar redshift distributions

Today I worked with Kate Storey-Fisher on the ESA Gaia quasar sample. We looked at the redshift distribution as a function of magnitude and as a function of color cuts or selection. Right now we are getting an odd angular correlation function for the sample, which we think is because our random catalog (or completeness model) is wrong in important but subtle ways. Interestingly, there are probably terms coming from both the dust map (extinction) and from the Gaia internal completeness (scanning law) and maybe both contribute enough to change the answer? But it sure looks like dust dominates.