Maximum likelihood estimation by monte carlo simulation: Toward data-driven stochastic modeling

Yijie Peng; Michael C. Fu; Bernd Heidergott; Henry Lam

doi:10.1287/opre.2019.1978

Maximum likelihood estimation by monte carlo simulation: Toward data-driven stochastic modeling

Yijie Peng^*, Michael C. Fu, Bernd Heidergott, Henry Lam

^*Corresponding author for this work

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Abstract

We propose a gradient-based simulated maximum likelihood estimation to estimate unknown parameters in a stochastic model without assuming that the likelihood function of the observations is available in closed form. A key element is to develop Monte Carlo-based estimators for the density and its derivatives for the output process, using only knowledge about the dynamics of the model. We present the theory of these estimators and demonstrate how our approach can handle various types of model structures. We also support our findings and illustrate the merits of our approach with numerical results.

Original language	English
Pages (from-to)	1896-1912
Number of pages	17
Journal	Operations Research
Volume	68
Issue number	6
Early online date	26 Oct 2020
DOIs	https://doi.org/10.1287/opre.2019.1978
Publication status	Published - Dec 2020

Funding

Funding: This work was supported by the National Natural Science Foundation of China [Grants 71901003, 71571048, 71720107003, 71690232, 71790615, and 9184630], the Air Force of Scientific Research [Grant FA9550-15-10050], and the National Science Foundation [Grants CMMI-1362303, CMMI-1434419, CMMI-1542020, CAREER CMMI-1834710, and IIS-1849280].

Funders	Funder number
National Science Foundation	CMMI-1362303, IIS-1849280, CMMI-1834710, CMMI-1542020, CMMI-1434419
National Science Foundation
Air Force Office of Scientific Research	FA9550-15-10050
Air Force Office of Scientific Research
National Natural Science Foundation of China	71720107003, 71790615, 9184630, 71901003, 71571048, 71690232
National Natural Science Foundation of China

Keywords

Generalized likelihood ratio method
Gradient-based MLE
Sensitivity analysis
Simulation

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10.1287/opre.2019.1978

opre.2019.1978_Maximum likelihood estimation by monte carlo simulationFinal published version, 1.23 MBLicence: Article 25fa Dutch Copyright Act

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abstract = "We propose a gradient-based simulated maximum likelihood estimation to estimate unknown parameters in a stochastic model without assuming that the likelihood function of the observations is available in closed form. A key element is to develop Monte Carlo-based estimators for the density and its derivatives for the output process, using only knowledge about the dynamics of the model. We present the theory of these estimators and demonstrate how our approach can handle various types of model structures. We also support our findings and illustrate the merits of our approach with numerical results.",

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author = "Yijie Peng and Fu, \{Michael C.\} and Bernd Heidergott and Henry Lam",

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doi = "10.1287/opre.2019.1978",

language = "English",

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AU - Lam, Henry

PY - 2020/12

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AB - We propose a gradient-based simulated maximum likelihood estimation to estimate unknown parameters in a stochastic model without assuming that the likelihood function of the observations is available in closed form. A key element is to develop Monte Carlo-based estimators for the density and its derivatives for the output process, using only knowledge about the dynamics of the model. We present the theory of these estimators and demonstrate how our approach can handle various types of model structures. We also support our findings and illustrate the merits of our approach with numerical results.

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KW - Sensitivity analysis

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Maximum likelihood estimation by monte carlo simulation: Toward data-driven stochastic modeling

Abstract

Funding

Keywords

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