Bayesian inference for Hawkes processes

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Abstract

The Hawkes process is a practically and theoretically important class
of point processes, but parameter-estimation for such a process can pose
various problems. In this paper we explore and compare two approaches
to Bayesian inference. The first approach is based on the so-called conditional
intensity function, while the second approach is based on an underlying
clustering and branching structure in the Hawkes process. For
practical use, MCMC (Markov chain Monte Carlo) methods are employed.
The two approaches are compared numerically using three examples of the
Hawkes process.
Original languageEnglish
PublisherDepartment of Mathematical Sciences, Aalborg University
Number of pages21
Publication statusPublished - Feb 2011
SeriesResearch Report Series
NumberR-2011-03
ISSN1399-2503

Keywords

  • Bayesian inference
  • cluster process
  • Hawkes process
  • Markov chain Monte Carlo
  • missing data
  • point process

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