Modelling superspreading dynamics and circadian rhythms in online discussion boards using Hawkes processes

TL;DR

This paper introduces a novel Hawkes process-based model for online discussion cascades that captures superspreading and circadian rhythms, validated on Reddit data, providing insights into discussion dynamics and moderation.

Contribution

The paper develops a flexible Hawkes process model for online discussions, incorporating superspreading and circadian effects, with a Bayesian inference framework for model fitting and validation.

Findings

Discussions follow circadian rhythms with peak activity in the morning.

Approximately 58-62% of posts generate no replies.

The model accurately captures heavy-tailed reply distributions.

Abstract

Online boards offer a platform for sharing and discussing content, where discussion emerges as a cascade of comments in response to a post. Branching point process models offer a practical approach to modelling these cascades; however, existing models do not account for apparent features of empirical data. We address this gap by illustrating the flexibility of Hawkes processes to model data arising from this context as well as outlining the computational tools needed to service this class of models. For example, the distribution of replies within discussions tends to have a heavy tail. As such, a small number of posts and comments may generate many replies, while most generate few or none, similar to `superspreading' in epidemics. Here, we propose a novel model for online discussion, motivated by a dataset arising from discussions on the r/ireland subreddit, that accommodates such phenomena and develop a framework for Bayesian inference that considers in- and out-of-sample tests for goodness-of-fit. This analysis shows that discussions within this community follow a circadian rhythm and are subject to moderate superspreading dynamics. For example, we estimate that the expected discussion size is approximately four for initial posts between 04:00 and 12:00 but approximately 2.5 from 15:00 to 02:00. We also estimate that 58% to 62% of posts fail to generate any discussion, with 95% posterior probability. Thus, we demonstrate that our framework offers a general approach to modelling discussion on online boards.