The Ease of Fitting but Futility of Testing a Nonstationary Poisson Processes from One Sample Path

Barry L. Nelson; Lawrence M. Leemis

doi:10.1109/WSC48552.2020.9383930

The Ease of Fitting but Futility of Testing a Nonstationary Poisson Processes from One Sample Path

Barry L. Nelson, Lawrence M. Leemis

Industrial Engineering and Management Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Scopus citations

Abstract

The nonstationary Poisson process (NSPP) is a workhorse tool for modeling and simulating arrival processes with time-dependent rates. In many applications only a single sequence of arrival times are observed. While one sample path is sufficient for estimating the arrival rate or integrated rate function of the process - as we illustrate in this paper - we show that testing for Poissonness, in the general case, is futile. In other words, when only a single sequence of arrival data are observed then one can fit an NSPP to it, but the choice of NSPP can only be justified by an understanding of the underlying process physics, or a leap of faith, not by testing the data. This result suggests the need for sensitivity analysis when such a model is used to generate arrivals in a simulation.

Original language	English (US)
Title of host publication	Proceedings of the 2020 Winter Simulation Conference, WSC 2020
Editors	K.-H. Bae, B. Feng, S. Kim, S. Lazarova-Molnar, Z. Zheng, T. Roeder, R. Thiesing
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	266-276
Number of pages	11
ISBN (Electronic)	9781728194998
DOIs	https://doi.org/10.1109/WSC48552.2020.9383930
State	Published - Dec 14 2020
Event	2020 Winter Simulation Conference, WSC 2020 - Orlando, United States Duration: Dec 14 2020 → Dec 18 2020

Publication series

Name	Proceedings - Winter Simulation Conference
Volume	2020-December
ISSN (Print)	0891-7736

Conference

Conference	2020 Winter Simulation Conference, WSC 2020
Country/Territory	United States
City	Orlando
Period	12/14/20 → 12/18/20

Funding

Nelson’s work is partially supported by National Science Foundation Grant Number DMS-1854562. The authors thank Shane Henderson for comments on an early draft.

ASJC Scopus subject areas

Software
Modeling and Simulation
Computer Science Applications

Access to Document

10.1109/WSC48552.2020.9383930

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Nelson, B. L., & Leemis, L. M. (2020). The Ease of Fitting but Futility of Testing a Nonstationary Poisson Processes from One Sample Path. In K.-H. Bae, B. Feng, S. Kim, S. Lazarova-Molnar, Z. Zheng, T. Roeder, & R. Thiesing (Eds.), Proceedings of the 2020 Winter Simulation Conference, WSC 2020 (pp. 266-276). Article 9383930 (Proceedings - Winter Simulation Conference; Vol. 2020-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/WSC48552.2020.9383930

Nelson, Barry L. ; Leemis, Lawrence M. / The Ease of Fitting but Futility of Testing a Nonstationary Poisson Processes from One Sample Path. Proceedings of the 2020 Winter Simulation Conference, WSC 2020. editor / K.-H. Bae ; B. Feng ; S. Kim ; S. Lazarova-Molnar ; Z. Zheng ; T. Roeder ; R. Thiesing. Institute of Electrical and Electronics Engineers Inc., 2020. pp. 266-276 (Proceedings - Winter Simulation Conference).

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abstract = "The nonstationary Poisson process (NSPP) is a workhorse tool for modeling and simulating arrival processes with time-dependent rates. In many applications only a single sequence of arrival times are observed. While one sample path is sufficient for estimating the arrival rate or integrated rate function of the process - as we illustrate in this paper - we show that testing for Poissonness, in the general case, is futile. In other words, when only a single sequence of arrival data are observed then one can fit an NSPP to it, but the choice of NSPP can only be justified by an understanding of the underlying process physics, or a leap of faith, not by testing the data. This result suggests the need for sensitivity analysis when such a model is used to generate arrivals in a simulation.",

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Nelson, BL & Leemis, LM 2020, The Ease of Fitting but Futility of Testing a Nonstationary Poisson Processes from One Sample Path. in K-H Bae, B Feng, S Kim, S Lazarova-Molnar, Z Zheng, T Roeder & R Thiesing (eds), Proceedings of the 2020 Winter Simulation Conference, WSC 2020., 9383930, Proceedings - Winter Simulation Conference, vol. 2020-December, Institute of Electrical and Electronics Engineers Inc., pp. 266-276, 2020 Winter Simulation Conference, WSC 2020, Orlando, United States, 12/14/20. https://doi.org/10.1109/WSC48552.2020.9383930

The Ease of Fitting but Futility of Testing a Nonstationary Poisson Processes from One Sample Path. / Nelson, Barry L.; Leemis, Lawrence M.
Proceedings of the 2020 Winter Simulation Conference, WSC 2020. ed. / K.-H. Bae; B. Feng; S. Kim; S. Lazarova-Molnar; Z. Zheng; T. Roeder; R. Thiesing. Institute of Electrical and Electronics Engineers Inc., 2020. p. 266-276 9383930 (Proceedings - Winter Simulation Conference; Vol. 2020-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Leemis, Lawrence M.

PY - 2020/12/14

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N2 - The nonstationary Poisson process (NSPP) is a workhorse tool for modeling and simulating arrival processes with time-dependent rates. In many applications only a single sequence of arrival times are observed. While one sample path is sufficient for estimating the arrival rate or integrated rate function of the process - as we illustrate in this paper - we show that testing for Poissonness, in the general case, is futile. In other words, when only a single sequence of arrival data are observed then one can fit an NSPP to it, but the choice of NSPP can only be justified by an understanding of the underlying process physics, or a leap of faith, not by testing the data. This result suggests the need for sensitivity analysis when such a model is used to generate arrivals in a simulation.

AB - The nonstationary Poisson process (NSPP) is a workhorse tool for modeling and simulating arrival processes with time-dependent rates. In many applications only a single sequence of arrival times are observed. While one sample path is sufficient for estimating the arrival rate or integrated rate function of the process - as we illustrate in this paper - we show that testing for Poissonness, in the general case, is futile. In other words, when only a single sequence of arrival data are observed then one can fit an NSPP to it, but the choice of NSPP can only be justified by an understanding of the underlying process physics, or a leap of faith, not by testing the data. This result suggests the need for sensitivity analysis when such a model is used to generate arrivals in a simulation.

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Nelson BL, Leemis LM. The Ease of Fitting but Futility of Testing a Nonstationary Poisson Processes from One Sample Path. In Bae KH, Feng B, Kim S, Lazarova-Molnar S, Zheng Z, Roeder T, Thiesing R, editors, Proceedings of the 2020 Winter Simulation Conference, WSC 2020. Institute of Electrical and Electronics Engineers Inc. 2020. p. 266-276. 9383930. (Proceedings - Winter Simulation Conference). doi: 10.1109/WSC48552.2020.9383930

The Ease of Fitting but Futility of Testing a Nonstationary Poisson Processes from One Sample Path

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