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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 557-568 |
| Number of pages | 12 |
| Journal | Journal of Simulation |
| Volume | 18 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2024 |
Funding
We gratefully acknowledge the support of the EPSRC funded EP/L015692/1 STOR-i Centre for Doctoral Training, NSF Grant CMMI-1537060 and GOALI sponsor Simio LLC. A preliminary version of this paper was published in the Proceedings of the 2019 Winter Simulation Conference as morgan2019splines. The authors report that there are no competing interests to declare
Keywords
- Input Modelling
- Input uncertainty
- Poisson processes
- Spline functions
ASJC Scopus subject areas
- Software
- Modeling and Simulation
- Management Science and Operations Research
- Industrial and Manufacturing Engineering