# Coarse-Grained Hawkes Processes

## TL;DR

This paper introduces a new model for analyzing event data when only aggregated counts are available, improving accuracy and efficiency.

## Contribution

The novel coarse-grained Hawkes process model captures statistical features of aggregated event data effectively.

## Key findings

- The model accurately captures second-order statistics of bin-count data with large bin sizes.
- The proposed inference method performs as well or better than existing techniques in simulations.
- The approach maintains computational efficiency during parameter estimation.

## Abstract

When analyzing real-world event data, it is often the case that bin-count processes are observed instead of precise event time-stamps along a continuous timeline, owing to practical limitations in measurement accuracy. In this work, we propose a modeling framework for aggregated event data generated by multivariate Hawkes processes. The introduced model, termed the coarse-grained Hawkes process, effectively captures the second-order statistical characteristics of the bin-count representation of the Hawkes process, particularly when the bin size is large relative to the typical support of the excitation kernel. Building upon this model, we develop a method for inferring the underlying Hawkes process from bin-count observations, and demonstrate through simulation studies that the proposed approach performs comparably to, or even surpasses, existing techniques, while maintaining computational efficiency in parameter estimation.