The following is an advert for a Masters project for students on the MSc in Statistics course at Imperial College London.

A simulator model is a computer program, which takes a vector of parameters as input and produces a stochastic output. The likelihood function is defined implicitly and in general is computationally intractable. Simulation-based inference (SBI) methods refer to methods for Bayesian inference for such models.

SBI is becoming very popular in Astrophysics because (i) it can handle complex data-generating mechanisms and (ii) it is fast. However, some challenges associated with SBI include (i) scaling to high-dimensional parameter spaces and (ii) that the posterior approximations can be overconfident.

This project will look at using SBI to infer the spectra (energy distribution) of stars and other high-energy astronomical sources. The spectrum may be used to learn about properties of the source such as its chemical composition, temperature and relative velocity. The energies of photons emitted by the astronomical source are recorded by the telescope’s detector via a number of complicated steps. Although it is possible to design a tractable model of the process of data collection, the process is so intricate that the resulting likelihood is very expensive to compute. SBI might vastly speed-up inference. Some questions the project could seek to address are (i) can SBI be used to infer high-quality approximate posteriors for spectral parameters? (ii) how sensitive to data compression is the approximate posterior inferred using SBI? The student should have the opportunity to work with real data gathered by the Chandra X-ray Observatory, provided by the Harvard & Smithsonian Center for Astrophysics.