EM Algorithm

Patrick J. Laub, Young Lee and Thomas Taimre
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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

Chapter Chapter 6 in The Elements of Hawkes Processes, 2021, pp 45-56 from Springer

Abstract: 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.

Date: 2021
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DOI: 10.1007/978-3-030-84639-8_6

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