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Bayesian Inference for Hawkes Processes

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  • Jakob Gulddahl Rasmussen

    (Aalborg University)

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.

Suggested Citation

  • Jakob Gulddahl Rasmussen, 2013. "Bayesian Inference for Hawkes Processes," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 623-642, September.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:3:d:10.1007_s11009-011-9272-5
    DOI: 10.1007/s11009-011-9272-5
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    References listed on IDEAS

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    1. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    2. Mohler, G. O. & Short, M. B. & Brantingham, P. J. & Schoenberg, F. P. & Tita, G. E., 2011. "Self-Exciting Point Process Modeling of Crime," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 100-108.
    3. Jesper Møller & Jakob G. Rasmussen, 2006. "Approximate Simulation of Hawkes Processes," Methodology and Computing in Applied Probability, Springer, vol. 8(1), pages 53-64, March.
    4. Veen, Alejandro & Schoenberg, Frederic P., 2008. "Estimation of SpaceTime Branching Process Models in Seismology Using an EMType Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 614-624, June.
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    Cited by:

    1. Donatien Hainaut & Griselda Deelstra, 2019. "A Bivariate Mutually-Excited Switching Jump Diffusion (BMESJD) for Asset Prices," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1337-1375, December.
    2. Xiaoting Li & Christian Genest & Jonathan Jalbert, 2021. "A self‐exciting marked point process model for drought analysis," Environmetrics, John Wiley & Sons, Ltd., vol. 32(8), December.
    3. Francesco Serafini & Finn Lindgren & Mark Naylor, 2023. "Approximation of Bayesian Hawkes process with inlabru," Environmetrics, John Wiley & Sons, Ltd., vol. 34(5), August.
    4. Vipul Aggarwal & Elina H. Hwang & Yong Tan, 2021. "Learning to Be Creative: A Mutually Exciting Spatiotemporal Point Process Model for Idea Generation in Open Innovation," Information Systems Research, INFORMS, vol. 32(4), pages 1214-1235, December.
    5. Cavaliere, Giuseppe & Lu, Ye & Rahbek, Anders & Stærk-Østergaard, Jacob, 2023. "Bootstrap inference for Hawkes and general point processes," Journal of Econometrics, Elsevier, vol. 235(1), pages 133-165.
    6. Philip A. White & Alan E. Gelfand, 2021. "Generalized Evolutionary Point Processes: Model Specifications and Model Comparison," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 1001-1021, September.
    7. Hainaut, Donatien & Deelstra, Griselda, 2018. "A Bivariate Mutually-Excited Switching Jump Diffusion (BMESJD) for asset prices," LIDAM Discussion Papers ISBA 2018011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Andreia Monteiro & Raquel Menezes & Maria Eduarda Silva, 2021. "Modelling informative time points: an evolutionary process approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 364-382, June.
    9. Liu, Chenguang, 2020. "Statistical inference for a partially observed interacting system of Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5636-5694.
    10. Santitissadeekorn, Naratip & Lloyd, David J.B. & Short, Martin B. & Delahaies, Sylvain, 2020. "Approximate filtering of conditional intensity process for Poisson count data: Application to urban crime," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).

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