Spectral Subsampling for Large-Scale Bayesian Inference - Theory and Applications

Rapid technological developments have made it possible to generate huge amounts of data.

In social science, large databases have opened up new fields like computational social science, and digitalization of text has paved the way for the digital humanities.

The bottleneck is the lack of statistical methods for analyzing data at large scale, making applied scientists unable to exploit the full potential of the data.Recently, it has been show that theoretically sound data subsampling algorithms can be used to give inference based on all the data at only a small fraction of the computational cost.

Our recent subsampling Markov Chain Monte Carlo (MCMC) algorithms for large-scale Bayesian inference are state-of-the-art in the field.

However, all proposed subsampling algorithms assume independent data and are therefore not applicable for time series and spatial data. We have recently proposed a way to enable subsampling MCMC for high-frequency time series data.

This project aims to further develop this method and its theoretical underpinning, to extend it to spatial problems and beyond, and to test it in challenging applications in finance, neuroscience and transportation.The project is part of a long established research collaboration between Prof Mattias Villani´s group in Stockholm and Prof Robert Kohn´s group in Sydney.

The work involves algorithmic development, deriving mathematical properties of the methods and testing the methods in complex high-profile scientific problems.