TY - JOUR
T1 - Point Processes on Directed Linear Networks
AU - Rasmussen, Jakob Gulddahl
AU - Christensen, Heidi Søgaard
PY - 2021
Y1 - 2021
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.
KW - Conditional intensity
KW - Dendrite network
KW - Directed acyclic linear network
KW - Hawkes process
KW - Self-correcting process
UR - http://www.scopus.com/inward/record.url?scp=85081971346&partnerID=8YFLogxK
U2 - 10.1007/s11009-020-09777-y
DO - 10.1007/s11009-020-09777-y
M3 - Journal article
SN - 1387-5841
VL - 23
SP - 647
EP - 667
JO - Methodology and Computing in Applied Probability
JF - Methodology and Computing in Applied Probability
IS - 2
ER -