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A Spline Function Method for Modelling and Generating a Nonhomogeneous Poisson Process

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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A Spline Function Method for Modelling and Generating a Nonhomogeneous Poisson Process. / Morgan, Lucy; Nelson, Barry; Titman, Andrew et al.
In: Journal of Simulation, Vol. 18, No. 4, 03.07.2024, p. 557-568.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Morgan, L, Nelson, B, Titman, A & Worthington, D 2024, 'A Spline Function Method for Modelling and Generating a Nonhomogeneous Poisson Process', Journal of Simulation, vol. 18, no. 4, pp. 557-568. https://doi.org/10.1080/17477778.2023.2224928

APA

Morgan, L., Nelson, B., Titman, A., & Worthington, D. (2024). A Spline Function Method for Modelling and Generating a Nonhomogeneous Poisson Process. Journal of Simulation, 18(4), 557-568. https://doi.org/10.1080/17477778.2023.2224928

Vancouver

Morgan L, Nelson B, Titman A, Worthington D. A Spline Function Method for Modelling and Generating a Nonhomogeneous Poisson Process. Journal of Simulation. 2024 Jul 3;18(4):557-568. Epub 2023 Jun 19. doi: 10.1080/17477778.2023.2224928

Author

Morgan, Lucy ; Nelson, Barry ; Titman, Andrew et al. / A Spline Function Method for Modelling and Generating a Nonhomogeneous Poisson Process. In: Journal of Simulation. 2024 ; Vol. 18, No. 4. pp. 557-568.

Bibtex

@article{509db414e32a46a48f5ea3dd30d042b5,
title = "A Spline Function Method for Modelling and Generating a Nonhomogeneous Poisson Process",
abstract = "This paper presents a spline-based input modelling method for inferring the rate function of a nonhomogeneous Poisson process (NHPP) given arrival-time observations and a simple method for generating arrivals from the resulting rate function. Splines are a natural choice for modelling rate functions as they are smooth by construction, and highly flexible. Although flexibility is an advantage in terms of reducing the bias with respect to the true rate function, it can lead to overfitting. Our method is therefore based on maximising the penalised NHPP log-likelihood, where the penalty is a measure of rapid changes in the spline-based representation. A controlled empirical comparison of the spline-based method against two recently developed input modelling techniques is presented considering the recovery of the rate function, the propagation of input modelling error, and the performance of methods given data that are under or over-dispersed in comparison to a Poisson process.",
keywords = "Input Modelling, Input uncertainty, Poisson processes, Spline functions",
author = "Lucy Morgan and Barry Nelson and Andrew Titman and David Worthington",
year = "2024",
month = jul,
day = "3",
doi = "10.1080/17477778.2023.2224928",
language = "English",
volume = "18",
pages = "557--568",
journal = "Journal of Simulation",
issn = "1747-7778",
publisher = "Palgrave Macmillan Ltd.",
number = "4",

}

RIS

TY - JOUR

T1 - A Spline Function Method for Modelling and Generating a Nonhomogeneous Poisson Process

AU - Morgan, Lucy

AU - Nelson, Barry

AU - Titman, Andrew

AU - Worthington, David

PY - 2024/7/3

Y1 - 2024/7/3

N2 - This paper presents a spline-based input modelling method for inferring the rate function of a nonhomogeneous Poisson process (NHPP) given arrival-time observations and a simple method for generating arrivals from the resulting rate function. Splines are a natural choice for modelling rate functions as they are smooth by construction, and highly flexible. Although flexibility is an advantage in terms of reducing the bias with respect to the true rate function, it can lead to overfitting. Our method is therefore based on maximising the penalised NHPP log-likelihood, where the penalty is a measure of rapid changes in the spline-based representation. A controlled empirical comparison of the spline-based method against two recently developed input modelling techniques is presented considering the recovery of the rate function, the propagation of input modelling error, and the performance of methods given data that are under or over-dispersed in comparison to a Poisson process.

AB - This paper presents a spline-based input modelling method for inferring the rate function of a nonhomogeneous Poisson process (NHPP) given arrival-time observations and a simple method for generating arrivals from the resulting rate function. Splines are a natural choice for modelling rate functions as they are smooth by construction, and highly flexible. Although flexibility is an advantage in terms of reducing the bias with respect to the true rate function, it can lead to overfitting. Our method is therefore based on maximising the penalised NHPP log-likelihood, where the penalty is a measure of rapid changes in the spline-based representation. A controlled empirical comparison of the spline-based method against two recently developed input modelling techniques is presented considering the recovery of the rate function, the propagation of input modelling error, and the performance of methods given data that are under or over-dispersed in comparison to a Poisson process.

KW - Input Modelling

KW - Input uncertainty

KW - Poisson processes

KW - Spline functions

U2 - 10.1080/17477778.2023.2224928

DO - 10.1080/17477778.2023.2224928

M3 - Journal article

VL - 18

SP - 557

EP - 568

JO - Journal of Simulation

JF - Journal of Simulation

SN - 1747-7778

IS - 4

ER -