yet more derivatives

I spent the day working out derivatives of my diffraction imaging model with respect to parameters. The crazy thing is that there is a sum over components in the density model (for the molecule) and then a sum over photons within the image (or instance) and then a sum over orientation-angle samples, and finally a sum over images (or instances). And various of these sums have logs and exps inside them. So it is a mess! I wrote them out with a pen on paper, and then typed them up in a nascent paper. The short-term plan is to get to stochastic gradient.

photon pile-up

At Blanton–Hogg group meeting, Daniela Huppenkothen brought up photon pile-up in x-ray and gamma-ray detectors. The issue is that if two photons arrive at the same time, or in the same electronics-restricted time window, they will appear as one photon, but of higher energy. It is an issue for Chandra and for Fermi, among other assets. This pile-up leads to a distortion of the spectrum (and point-spread function, and so on) of very bright sources. We discussed how one might model this, given that it is easy to simulate but hard to describe with a likelihood function. We also came up with a ridiculously simple idea for testing cosmic-ray detection in time-series imaging, which really, really needs to e done.

In the afternoon, I did text writing and problem (exercise) writing in my MCMC tutorial. Stay on target. #AcWriYear

high-energy astrophysics; inference without likelihoods

[Lull in posting because of vacation in Quebec. Slept one (exceedingly cold) night in an actual, real-life igloo!]

At lunchtime in the NYU Center for Data Science there was a great talk by Daniela Huppenkothen about x-ray and gamma-ray astrophysics, for non-astronomers. She talked about imaging, spectroscopy, and time series, with a focus on the latter. She did a great job explaining the differences between astrophysics and other data-science domains. At the end there were good questions from (among others) neural scientist Bijan Peseran, who (comparing perhaps to his own domain) was interested in non-trivial time correlations among photon events. After all, neurons are all about non-trivial time correlations in spike trains.

Earlier in the day, Foreman-Mackey and I spoke about K2 projects and exoplanet population projects. The plan is to try some likelihood-free inference; we spent some time talking about technical details. In likelihood-free inference (ABC) one performs repeated simulations of the data; there are fundamental parameters, and then there are (usually) also random-number draws. We might want to sample separately in these, in some Gibbs-like way. Thanks to Brewer for getting us thinking along these lines.