Point processes on directed linear networks

Research output: Book/ReportReportResearch

Abstract

In this paper we consider point processes specified on directed linear networks, i.e. linear networks with associated directions. We adapt the so-called conditional intensity function used for specifying point processes on the time line to the setting of directed linear networks. For models specified by such a conditional intensity function, we derive an explicit expression for the likelihood function, specify two simulation algorithms (the inverse method and Ogata's modified thinning algorithm), and consider methods for model checking through the use of residuals. We also extend the results and methods to the case of a marked point process on a directed linear network. Furthermore, we consider specific classes of point process models on directed linear networks (Poisson processes, Hawkes processes, non-linear Hawkes processes, self-correcting processes, and marked Hawkes processes), all adapted from well-known models in the temporal setting. Finally, we apply the results and methods to analyse simulated and neurological data.
Original languageEnglish
PublisherCSGB, Institut for Matematik, Aarhus Universitet
Number of pages25
Publication statusPublished - 2018
SeriesCSGB Research Report
Number11
Volume2018

Fingerprint

Point Process
Intensity Function
Marked Point Process
Inverse Method
Nonlinear Process
Thinning
Likelihood Function
Poisson process
Process Model
Model Checking
Line
Model
Simulation

Cite this

Rasmussen, J. G., & Christensen, H. S. (2018). Point processes on directed linear networks. CSGB, Institut for Matematik, Aarhus Universitet. CSGB Research Report, No. 11, Vol.. 2018
Rasmussen, Jakob Gulddahl ; Christensen, Heidi Søgaard. / Point processes on directed linear networks. CSGB, Institut for Matematik, Aarhus Universitet, 2018. 25 p. (CSGB Research Report; No. 11, Vol. 2018).
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Rasmussen, JG & Christensen, HS 2018, Point processes on directed linear networks. CSGB Research Report, no. 11, vol. 2018, CSGB, Institut for Matematik, Aarhus Universitet.

Point processes on directed linear networks. / Rasmussen, Jakob Gulddahl; Christensen, Heidi Søgaard.

CSGB, Institut for Matematik, Aarhus Universitet, 2018. 25 p.

Research output: Book/ReportReportResearch

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AU - Rasmussen, Jakob Gulddahl

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PY - 2018

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N2 - In this paper we consider point processes specified on directed linear networks, i.e. linear networks with associated directions. We adapt the so-called conditional intensity function used for specifying point processes on the time line to the setting of directed linear networks. For models specified by such a conditional intensity function, we derive an explicit expression for the likelihood function, specify two simulation algorithms (the inverse method and Ogata's modified thinning algorithm), and consider methods for model checking through the use of residuals. We also extend the results and methods to the case of a marked point process on a directed linear network. Furthermore, we consider specific classes of point process models on directed linear networks (Poisson processes, Hawkes processes, non-linear Hawkes processes, self-correcting processes, and marked Hawkes processes), all adapted from well-known models in the temporal setting. Finally, we apply the results and methods to analyse simulated and neurological data.

AB - In this paper we consider point processes specified on directed linear networks, i.e. linear networks with associated directions. We adapt the so-called conditional intensity function used for specifying point processes on the time line to the setting of directed linear networks. For models specified by such a conditional intensity function, we derive an explicit expression for the likelihood function, specify two simulation algorithms (the inverse method and Ogata's modified thinning algorithm), and consider methods for model checking through the use of residuals. We also extend the results and methods to the case of a marked point process on a directed linear network. Furthermore, we consider specific classes of point process models on directed linear networks (Poisson processes, Hawkes processes, non-linear Hawkes processes, self-correcting processes, and marked Hawkes processes), all adapted from well-known models in the temporal setting. Finally, we apply the results and methods to analyse simulated and neurological data.

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Rasmussen JG, Christensen HS. Point processes on directed linear networks. CSGB, Institut for Matematik, Aarhus Universitet, 2018. 25 p. (CSGB Research Report; No. 11, Vol. 2018).