worst of all possible worlds

The Milky Way potential is time-dependent, filled with orbiting, massive substructure, and has no useful symmetries. The stars orbiting have not had time to fully mix in phase space. Is inference—of the dynamics from a snapshot of the kinematics—still possible in this worst of all possible worlds? I think it is and I gave some hints about it today in the last of my workshop-like seminars.

[Going on vacation now for almost a month.]


ransac streams

As if Lang and I weren't distracted enough, we revived an old idea of finding Milky Way substructure (think streams) by a ransac-related approach. Use pairs of stars to generate hypotheses, test those hypotheses with the other stars. We revived this only after coming up with plans for finishing our unfinished papers, but still it was typical distraction from the critical path!


Bayesian black-hole masses, cold structures

A vigorous morning of debate with Tremaine got us to the point that our work on orbital roulette is pointed towards the Galactic Center. Our Bayesian approach permits us to use data of varying quality, subject to heterogeneous and unknown selection functions, and with missing dimensions (think projected positions and radial velocities). This will permit us to analyze simultaneously and comparatively all the available data sets, and resolve issues in the literature. Bovy is well tasked for the break.

I gave the second of my workshop-like talks about inferring Milky Way dynamics from kinematic data; today I talked about cold structures in phase space and their information content.


extreme tidal disruption, moving groups

In the limit that everything in the stellar halo is the result of tidal disruption of a satellite, the phase space will contain lots of structure, but subject to important constraints, because tidal stripping mixes or stretches one (predictable) dimension more than the others. Bovy and I discussed this along with many other ideas for finding and using phase-space structure.

Bovy also made some plots of the observational properties of moving groups of stars in Hipparcos. He may have some phenomenology that rules out some hypotheses for the origin of this structure.


extreme deconvolution, mixed angles

I gave the first of three workshop-like seminars at NYU this week. This one was on reconstructing dynamical models from kinematic measurements in the limits that the potential is integrable and the angles are mixed (the system has evolved for a very long time without resonances).

Bovy handed me a new version of his document on building the underlying, deconvolved distribution which, when given errors, generates the data in a sample, even when the errors are different and large for every point. He tentatively titled it extreme deconvolution



Lang and I spent a long time discussing Tremaine's objection to the Bayesian program for showing that a set of angles (say) are drawn from the flat (uniform) distribution between 0 and 2 pi. If the N-dimensional probability distribution for N angles phi is just the product of N flat distributions, then every N-dimensional point is equally likely, whether it corresponds to spread-out phases or concentrated phases. Lang and I came up with some clever things to say about this, but we don't yet have an answer that will satisfy Tremaine. At some level, the problem comes down to the problem that a frequentist can ask are the data consistent with the flat hypothesis? whereas the Bayesian needs to ask is the flat hypothesis better than X? where X is a well-specified alternative.


stellar populations, image modeling

Bovy, Lang, and I wrote down a complete model and objective function for our image modeling / astrometric catalog / multiwavelength counterparts project. In principle, the model and objective function is all the science; optimization is just engineering, but in practice that is never trivial for problems as hard as this one. We also reminded ourselves why the best way to do catalog matching is through synthetic image reconstruction.

Scott Trager (Kapteyn) gave our group meeting talk on stellar populations in old galaxies. When I last worked in this area, the theoretical modeling limited any conclusions. Since then, the already great data have become even better, but Trager surprised me by showing that the models have also enormously improved, in part thanks to him. It might be time to dive back in.


astrometry and image modeling

Lang is in town. Bovy, Lang, and I discussed image modeling, in preparation for Bovy's shot at multi-wavelength simultaneous modeling for the construction of astrometric measurements or an astrometric catalog. We argued about what freedom to give the point-spread function: Use the survey- or observation-provided point-spread function, fit the provided point-spread function, or learn the point-spread function from the data. I lean towards the latter, despite the fact that it involves reinventing the wheel, but I lean that way because otherwise we have to write specialized modules, one for each input data set, to deal with the point-spread function analysis available.

Lang and I also discussed getting the main Astrometry.net paper done and submitted.


radial velocities

In my tiny amount of research time today, Blanton and I discussed the possibility of taking a billion radial velocities to match Gaia's transverse measurements. This would be an enormous project, but not expensive on the scale of space missions.


Spitzer telemetry, angular momentum, and scheduling

I am at the Oversight Committee meeting for the Spitzer Science Center, which is, by the rules, not research. However, I learned a lot about scheduling and telemetry and pointing. The latter is done with reaction wheels. In low-Earth orbit, you can use a combination of reaction wheels and magnetic torques, and therefore control the reaction-wheel revolutions and speeds. But Spitzer is on an Earth-trailing orbit, very far away; it is not in a magnetic field that is large enough. This means that the reaction wheels are doing lots of revolutions, and they are known empirically to comprise one of the systems most likely to fail during the Telescope's latter years. The Earth-trailing orbit is also a challenge for data telemetry, because it relies on sending data bursts to enormous radio antennas in the Deep Space Network (and even this can only be done at certain satellite Earth-angles).


type Ia supernovae

Carles Badenes (Princeton) gave a great astro seminar about the remnants of type Ia supernovae. He can type ancient supernovae by observing their remnants, and in some cases his type determinations can be tested by observing light echos (now, hundreds of years after the original explosion).


halo paper, MCMC insanity

Started reading and commenting on Zolotov's paper on observations of a simulated galaxy. It shows that kinematics is not necessarily a good tracer of origin (that is, accreted versus in-situ formation for stars).

Suffering from insanity, I wrote a demo that uses Markov Chain Monte Carlo to fit a model composed of a mixture of k Gaussians to a set of one-dimensional data with proper Poisson likelihood. This is insane, because the Expectation-Maximization algorithm solves this problem already, and it is simple and comprehensible and far faster than MCMC. But I want us to be able to marginalize over parameters, so I need a sampling around the best fit. I don't think I have any other choice.


k-means, MML, mixtures

When I crashed Bovy's office today, he was working on a minimum message length application for the k-means data clustering algorithm. Because k-means is not usually thought of as a data model, it is a little strange to apply MML, but we are interested in comparing PCA to k-means and assessing scaling and other properties from the point of view of data compression or data summary. We also discussed our usual basket of topics, but notably implementing an MCMC-optimized mixture of gaussians model, which would have some (inferential, but not speed) advantages over EM.


Spitzer geometry

Wu, Schiminovich, and I met to discuss the progress of the S5 data reduction, which involves the assembly and unified reduction of a large number of galaxy spectra in the mid-infrared. We discussed progress and to-do items, but spent a bit of time understanding the geometry of the focal plane and spectral apertures, so that we could make informative figures and diagrams showing the relationship between the spectroscopy and our imaging data.


one star, one delta function

After the breakthroughs of the weekend, Bovy and I worked out the case for one single star (measure x, v, infer omega) for the one-dimensional simple harmonic oscillator, where we assume that the distribution function in action space is a delta function. It turns out to be identical to what we had before, but it will be different when we have N stars.