10 research outputs found
A hierarchical model of non-homogeneous Poisson processes for Twitter retweets
We present a hierarchical model of nonhomogeneous Poisson processes (NHPP) for information diffusion on online social media, in particular Twitter retweets. The retweets of each original tweet are modelled by a NHPP, for which the intensity function is a product of time-decaying components and another component that depends on the follower count of the original tweet author. The latter allows us to explain or predict the ultimate retweet count by a network centrality-related covariate. The inference algorithm enables the Bayes factor to be computed, to facilitate model selection. Finally, the model is applied to the retweet datasets of two hashtags. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplemen
Fluctuations for mean-field interacting age-dependent Hawkes processes
The propagation of chaos and associated law of large numbers for mean-field
interacting age-dependent Hawkes processes (when the number of processes n goes
to +) being granted by the study performed in (Chevallier, 2015), the
aim of the present paper is to prove the resulting functional central limit
theorem. It involves the study of a measure-valued process describing the
fluctuations (at scale n --1/2) of the empirical measure of the ages around its
limit value. This fluctuation process is proved to converge towards a limit
process characterized by a limit system of stochastic differential equations
driven by a Gaussian noise instead of Poisson (which occurs for the law of
large numbers limit)