Seminar| Institute of Mathematical Sciences
Time: Monday, September 28th, 2026,10:00-11:00
Location: IMS RS408
Speaker: Matias Quiroz, University of Technology Sydney
Abstract: Modern time series can be extraordinarily long, making fully Bayesian inference computationally demanding and, in some cases, impossible on a single machine. This makes the use of multiple machines attractive. Unlike independent data, however, time series cannot simply be divided into subsets and analysed in parallel, since observations are dependent across time.
In this talk, I will present a spectral divide-and-conquer approach to scalable Bayesian inference for stationary time series. The key idea is to move from the time domain to the frequency domain, where the Whittle likelihood provides an approximate representation in terms of asymptotically independent frequency components. This makes it possible to adapt divide-and-conquer Markov chain Monte Carlo methods originally developed for independent data. To handle very long series, we combine these methods with a distributed fast Fourier transform implemented within a modern cluster-computing framework.
I will discuss theoretical results establishing the accuracy of the resulting posterior approximation, together with empirical results illustrating its performance across a range of time-series settings. In particular, the method provides accurate approximations to the full-data Whittle posterior and outperforms a recent state-of-the-art time-domain divide-and-conquer approach, especially for highly persistent processes. I will also discuss applications to large-scale time-series data.
This is joint work with Zixuan Wang (University of Technology Sydney), Feng Li (Peking University), Mattias Villani (Stockholm University), and Robert Kohn (University of New South Wales).
About the speaker: Matias Quiroz is a Senior Lecturer in the School of Mathematical and Physical Sciences at the University of Technology Sydney, a position held since 2023, and an Honorary Fellow at the Human Technology Institute. He also serves as an Associate Editor of Computational Statistics and Data Analysis and Econometrics and Statistics.