Branch National Speaker Series by NSW Branch: The Hawkes Process in Focus: Theory, Applications, and Neural Network Approaches

The Statistical Society of Australia's branches have come together to launch the National Branch Lecture Series, bringing you insightful talks from experts across the country. Each month, a different branch will host a webinar, showcasing diverse topics in statistics and data science. We’re excited to invite you to this month’s session, hosted by the NSW Branch.

The NSW branch has two speakers: Feng Chen presenting an introduction to the Hawkes process and its applications and Jason Lambe presenting Neural Networks for Parameter Estimation of the Discretely Observed Hawkes Process.

Feng Chen's Talk: An introduction to the Hawkes process and its applications

The Hawkes process is a powerful point process model for analysing event sequence data. In this talk, we present a concise overview of the model, its main variants, and associated inference methods, along with applications in fields such as seismology, social media, finance, and epidemiology. We will also discuss the inference challenges that arise when the sample path is observed only at discrete time points, and outline some of our approaches to addressing these challenges.

Bio: Feng Chen

Feng is an Associate Professor in Statistics at the School of Mathematics and Statistics. His research interest is in the broad area of developing statistical methods to model real-life phenomena and make inferences with a focus on Hawkes processes.

Jason Lambe's talk:  Neural Networks for Parameter Estimation of the Discretely Observed Hawkes Process

When the sample path of a Hawkes process is observed discretely, such that only the total event counts in disjoint time intervals are known, the likelihood function becomes intractable. To overcome the challenge of likelihood-based inference in this setting, we propose to use a likelihood-free approach to parameter estimation, where simulated data is used to train a fully connected neural network (NN) to estimate the parameters of the Hawkes process from a summary statistic of the count data. A naive imputation estimate of the parameters forms the basis of our summary statistic, which is fast to generate and requires minimal expert knowledge to design. The resulting NN estimator is comparable to the best extant approximate likelihood estimators in terms of mean-squared error but requires significantly less computational time. We also propose to use a bootstrap procedure for bias correction and variance estimation. The proposed estimation procedure is applied to weekly count data for two infectious diseases, with a time-varying background rate used to capture seasonal fluctuations in infection risk.

Bio: Jason Lambe

Jason is a second year PhD student under the supervision of Feng Chen, Tom Stindl, and Jeffrey Kwan. His research focus is on parameter estimation of discretely observed Hawkes processes.