Bayesian Estimation of Multivariate Hawkes Processes with Inhibition and Sparsity
Abstract
Hawkes processes are point processes that model data where events occur in clusters through the self-exciting property of the intensity function. We consider a multivariate setting where multiple dimensions can influence each other with intensity function to allow for excitation and inhibition, both within and across dimensions. We discuss how such a model can be implemented and highlight challenges in the estimation procedure induced by a potentially negative intensity function. Furthermore, we introduce a new, stronger condition for stability that encompasses current approaches established in the literature. Finally, we examine the total number of offsprings to reparametrise the model and subsequently use Normal and sparsity-inducing priors in a Bayesian estimation procedure on simulated data.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2022
- DOI:
- 10.48550/arXiv.2201.05009
- arXiv:
- arXiv:2201.05009
- Bibcode:
- 2022arXiv220105009D
- Keywords:
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- Statistics - Applications;
- Statistics - Methodology
- E-Print:
- 26 pages, 3 figures