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

Morgan, Lucy and Nelson, Barry and Titman, Andrew and Worthington, David (2023) A Spline Function Method for Modelling and Generating a Nonhomogeneous Poisson Process. Journal of Simulation. ISSN 1747-7778

[thumbnail of JoS_SplinesSubmission_LM_070422 (002)]
Text (JoS_SplinesSubmission_LM_070422 (002))
JoS_SplinesSubmission_LM_070422_002_.pdf - Accepted Version
Available under License Creative Commons Attribution.

Download (692kB)

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.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Simulation
Uncontrolled Keywords:
Research Output Funding/no_not_funded
Subjects:
?? input modellinginput uncertaintypoisson processesspline functionsno - not fundednomodelling and simulationmanagement science and operations researchinformation systems and managementsoftware ??
ID Code:
199557
Deposited By:
Deposited On:
27 Jul 2023 14:25
Refereed?:
Yes
Published?:
Published
Last Modified:
16 Jul 2024 11:28