Change Point Detection and Mean-Field Dynamics of Variable Productivity Hawkes Processes

TL;DR

This paper develops a Bayesian change point detection method for Hawkes processes with time-varying productivity, revealing how information about change points localizes and saturates, and demonstrates its application to disease incidence data.

Contribution

It introduces a novel Bayesian change point detection approach for Hawkes processes with variable productivity, including analytical insights and practical implementation.

Findings

Identified a decline in disease productivity aligned with vaccine rollout.

Derived closed-form mean-field relaxation for exponential kernels.

Demonstrated the method on pneumococcal disease incidence data.

Abstract

Many self-exciting systems change because endogenous amplification, as opposed to exogenous forcing, varies. We study a Hawkes process with fixed background rate and kernel, but piecewise time-varying productivity. For exponential kernels we derive closed-form mean-field relaxation after a change and a deterministic surrogate for post-change Fisher information, revealing a boundary layer in which change time information localises and saturates, while post-change level information grows linearly beyond a short transient. These results motivate a Bayesian change point procedure that stabilizes inference on finite windows. We illustrate the method on invasive pneumococcal disease incidence in The Gambia, identifying a decline in productivity aligned with pneumococcal conjugate vaccine rollout.