{"ID":2825692,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.20068","arxiv_id":"2512.20068","title":"Change Point Detection and Mean-Field Dynamics of Variable Productivity Hawkes Processes","abstract":"Many self-exciting systems change because endogenous amplification, as opposed to exogenous forcing, varies. We study a Hawkes process with fixed background rate and kernel, but piecewise time-varying productivity. For exponential kernels we derive closed-form mean-field relaxation after a change and a deterministic surrogate for post-change Fisher information, revealing a boundary layer in which change time information localises and saturates, while post-change level information grows linearly beyond a short transient. These results motivate a Bayesian change point procedure that stabilizes inference on finite windows. We illustrate the method on invasive pneumococcal disease incidence in The Gambia, identifying a decline in productivity aligned with pneumococcal conjugate vaccine rollout.","short_abstract":"Many self-exciting systems change because endogenous amplification, as opposed to exogenous forcing, varies. We study a Hawkes process with fixed background rate and kernel, but piecewise time-varying productivity. For exponential kernels we derive closed-form mean-field relaxation after a change and a deterministic su...","url_abs":"https://arxiv.org/abs/2512.20068","url_pdf":"https://arxiv.org/pdf/2512.20068v2","authors":"[\"Conor Kresin\",\"Boris Baeumer\",\"Sophie Phillips\"]","published":"2025-12-23T05:43:55Z","proceeding":"stat.OT","tasks":"[\"stat.OT\",\"math.ST\"]","methods":"[]","has_code":false}