PhD Student

Fast Radio Bursts are one of the most mysterious objects in astrophysics. First found in observations by accident in 2007, they are observed as extraordinarily bright flashes of milli-second duration, most of them in far-away galaxies. We don’t know what they are, or what produces them. A steadily and rapidly growing data set of observations lends itself to data-driven discovery, especially of the extremely rapid changes in brightness within these objects, but statistical and machine learning methods to take advantage of these data sets are very sparse. Thus, this is a project that will enable discovery at the very edge of astrophysics research.

Simulation-based inference

“Simulation-based inference is the next evolution in statistics.”

- Kyle Cramner (Popularized statistical methods for the discovery of the Higgs boson). Retweet by Kevin Patrick Murphy (author of Machine Learning: A Probabilistic Perspective).

Fast Radio Bursts can be modeled as the superposition of several short peaks of intense light. Consider the task of inferring the number of peaks θo contributing to an observed light curve xo of a Fast Radio Burst. We design a computer program that maps the number of constituent peaks θ to a simulated light curve x using relevant physical theory. Our simulator computes x from θ, but the inverse mapping is unspecified and likely intractable. Simulation-based inference puts this problem in a probabilistic context. Although we cannot analytically evaluate it, we assume that the simulator is sampling from the conditional probability distribution p(x | θ). After specifying a prior p(θ), the inverse amounts to estimating the posterior p(θ | xo). The posterior gives us a prediction of the number of peaks which could have contributed to the observed Fast Radio Burst. Our goal is to estimate this posterior using simulation-based inference.

Project Description

We will develop a new simulation-based inference technique which employs Reversible Jump Markov-chain Monte Carlo, aka the Metropolis-Hastings-Green algorithm, to sample from a custom simulator that models fast radio bursts using a variable number of peaks. We will compare results to likelihood-based methods using belief propagation and nested sampling.

Applicants for the thesis should have developed programming skills in python using pytorch and understand how to implement supervised learning tasks. Knowledge of hierarchical models and  sampling using Markov-chain Monte Carlo is also desired.

Links

https://link.springer.com/article/10.1007/s00159-019-0116-6
https://www.pnas.org/doi/10.1073/pnas.1912789117
https://www.stat.umn.edu/geyer/f05/8931/bmhg.pdf 

Ben Miller

Masters Thesis Projects