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EM Algorithm

In: The Elements of Hawkes Processes

Author

Listed:
  • Patrick J. Laub

    (University of Melbourne, Faculty of Business and Economics)

  • Young Lee

    (Harvard University, Faculty of Arts and Sciences)

  • Thomas Taimre

    (The University of Queensland, School of Mathematics and Physics)

Abstract

The challenging part of fitting Hawkes processes to arrival data is that we do not know whether some particular observation t i represents an immigrant or a birth in the immigration–birth interpretation from Sect. 3.3 . If we were in an alternate universe where we knew both the arrival times and also the ‘family tree’ of the arrivals (see Fig. 4.2 a for an example), then inferring the parameters of the Hawkes process turns out to be relatively easy. Indeed, this is a classic situation for which the expectation–maximisation (EM) algorithm should be used.

Suggested Citation

  • Patrick J. Laub & Young Lee & Thomas Taimre, 2021. "EM Algorithm," Springer Books, in: The Elements of Hawkes Processes, chapter 0, pages 45-56, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-84639-8_6
    DOI: 10.1007/978-3-030-84639-8_6
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