Bayesian inference for aggregated Hawkes processes

TL;DR

This paper introduces a Bayesian estimation method for Hawkes processes that works effectively with aggregated data, enabling analysis of complex self-exciting phenomena in various fields.

Contribution

It develops a Bayesian inference framework for Hawkes processes applicable to aggregated data, ensuring parameter identifiability and broadening practical applicability.

Findings

Method accurately estimates parameters from simulated aggregated data.

Parameters are identifiable under general conditions.

Applied to real-world conflict data with aggregated observations.

Abstract

The Hawkes process, a self-exciting point process, has a wide range of applications in modeling earthquakes, social networks and stock markets. The established estimation process requires that researchers have access to the exact time stamps and spatial information. However, available data are often rounded or aggregated. We develop a Bayesian estimation procedure for the parameters of a Hawkes process based on aggregated data. Our approach is developed for temporal, spatio-temporal, and mutually exciting Hawkes processes where data are available over discrete time periods and regions. We show theoretically that the parameters of the Hawkes process are identifiable from aggregated data under general specifications. We demonstrate the method on simulated data under various model specifications in the presence of one or more interacting processes, and under varying coarseness of data aggregation. Finally, we examine the internal and cross-excitation effects of airstrikes and insurgent violence events from February 2007 to June 2008, with some data aggregated by day.