Stochastics of News Article Propagation: Joint Modeling of Counts and Reliability Composition in Event-Driven News Cascades
We study the news cascade triggered by a single high-impact event as a pair of coupled stochastic processes: the daily article count $N(t)$ and the reliable-vs-unreliable composition $\pi_{\mathrm{pos}}(t)$. Using the 2017 Las Vegas shooting as a primary case study (CC-News + NewsGuard, 91 days, 2,702 articles), we fit and compare four counting-process models for $N(t)$ and four distributional models for $\pi_{\mathrm{pos}}(t)$ on a common likelihood scale. For counts, a hybrid Inhomogeneous-Poisson plus Hawkes model wins decisively on AIC, BIC, and log-likelihood, as the IHP accounts for the initial exogenous shock, while the Hawkes accounts for the subsequent self-excitation. A profile-likelihood sweep of the Hawkes decay rate collapses the optimal Hawkes kernel to an AR(1) one-step lag $\lambda(t)=\mu+nN(t-1)$. This Markovian structure on the counts directly motivates the Part-B reliability models: we treat the reliability label as a first-order Markov chain on a binary state space and test homogeneous, regime-switching, and mean-field parameterizations against a bivariate Hawkes baseline model using a shared conditional binomial likelihood. The results show that the bivariate Hawkes model and the non-homogeneous Markov models are nearly indistinguishable on fit, as they exhaust the signal and start fitting to the noise. A brief replication on the 2017 Hurricane Harvey data shows that the same methodology applies but produces different results due to Hurricane Harvey's gradual endogenous build-up.