A Novel Bayesian Model to Fit Spectrophotometric Data of Hubble and Spitzer Space Telescopes by Mo Akhshik

Events PyMCon2020
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Talk Abstract

Understanding how the most massive galaxies rapidly formed and quenched when Universe was only ~3 billion years old is one of the major challenges of extragalactic astronomy. In this talk, I will discuss how to improve our understanding of massive galaxy formation by combining the spectro-photometric observations of the Hubble and Spitzer Space Telescopes for strong gravitationally lensed galaxies. In particular, a multi-level regression model is built that can fit all multi-wavelength data for a range of instruments within a hierarchical Bayesian framework to constrain the properties of the stellar populations. The details of how this model is implemented using PyMC3, as well as the estimates of the posteriors of all parameters of interest and nuisance parameters will be highlighted.
Mo Akhshik Twitter @MoAkhshik GitHub makhshik

Talk

Mo Akhshik

Mo is a grad student of (astro)physics by day, a matheux and a Bayesian enthusiast all along. Broadly interested in cosmology and probability too.

This is a PyMCon 2020 talk

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Thanks for the talk! Great to see how PyMC3 is used modeling spectrophotometric data.
Looking at the model code it seems there are a fair among of dimshuffle and tensordot within a for loop - I wonder if there is a way to better vectorized those and replace some of those with tt.einsum

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Thanks @junpenglao! That’s a great suggestion and I will definitely look into it. In fact, I didn’t know that theano supports einsum-like operations and that’s why I tried to use dimshuffle and tensordot instead. One of the biggest bottlenecks in the code is also related to one of these dimshuffle and the broadcasting that it brings…

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@makhshik: Since so many aspects of your stellar pop model are linear, I was wondering if there might be some components that could be marginalized in closed form. Is this something you’ve considered (even as an approximation) to possibly speed up the inference?

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That’s a great point, @dfm! I considered it briefly, but I didn’t really work on it. One possible way is to try to marginalize w, which is somehow quantifying dust/metallicity uncertainty, and it’s not the parameter that we are primarily interested in. I think, given the generic prior of w and the linear nature of the problem as you mentioned, I should be able to integrate it out in a closed form.

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Thank you very much for the presentation. And very novel! It is hard to find stellar population synthesis following a Bayesian paradigm.

I have to read the paper and check your library to understand how it works but I was eager to ask: How do you explore the SSP grid ? Do you interpolate among the 12 SSP across each metallicity-age cell grid or do you always assign a weight even if it zero?

Thanks

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