Change Point Detection and Mean-Field Dynamics of Variable Productivity Hawkes Processes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917171425181696 |
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| author | Kresin, Conor Baeumer, Boris Phillips, Sophie |
| author_facet | Kresin, Conor Baeumer, Boris Phillips, Sophie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20068 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Change Point Detection and Mean-Field Dynamics of Variable Productivity Hawkes Processes Kresin, Conor Baeumer, Boris Phillips, Sophie Other Statistics Statistics Theory 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. |
| title | Change Point Detection and Mean-Field Dynamics of Variable Productivity Hawkes Processes |
| topic | Other Statistics Statistics Theory |
| url | https://arxiv.org/abs/2512.20068 |