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Raiha Browning on Bayesian nonparametric approach for discrete-time Hawkes processes

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Flexible estimation of discrete-time Hawkes processes 

Hawkes processes are a self-exciting stochastic process to describe phenomena for which past events increase the probability of future events occurring. Most standard models of Hawkes processes rely on a parametric form for the self-exciting term of the intensity function, referred to as the triggering kernel, which describes the influence of past events. This is insufficient to capture the true excitation pattern for complex data. This work presents a flexible approach for modelling a discrete-time variant of the traditional Hawkes process. We develop a Bayesian nonparametric approach based on random histogram priors to model the triggering kernel for discrete-time Hawkes processes, allowing for significantly more flexibility than a parametric form. To estimate the histogram function, a clustering algorithm based on the Chinese restaurant process is proposed. The proposed model exploits the branching structure of the Hawkes process, which describes the parent and offspring relationship between the events in the process through time.

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