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Estimation of unknown parameters using partially observed data

Eunji Lim (Department of Decision Sciences and Marketing, School of Business, Adelphi University, Garden City, New York, USA)

Journal of Modelling in Management

ISSN: 1746-5664

Article publication date: 14 September 2020

Issue publication date: 25 May 2021




This paper considers the complex stochastic systems such as supply chains, whose dynamics are controlled by an unknown parameter such as the arrival or service rates. The purpose of this paper is to provide a simulation-based estimator of the unknown parameter when only partially observed data on the underlying system is available.


The proposed method treats the unknown parameter as a random variable and estimates the parameter by computing the conditional expectation of the random variable given the partially observed data. This study then express the conditional expectation as a weighted sum of reverse conditional probabilities using Bayes’ rule. The reverse conditional probabilities are estimated using simulation.


The simulation studies indicate that the proposed estimator converges to the true value of the conditional expectation as the computer time allocated to the simulation increases. The proposed estimator is computed within a few seconds in all of the numerical examples, which demonstrates its time efficiency.


Most of the existing methods for estimating an unknown parameter require a significant amount of simulation, causing long computation delays. The proposed method requires a single simulation run for each candidate of the unknown parameter. Thus, it is designed to carry a significantly reduced computational burden. This feature will enable managers to use the proposed method when making real-time decisions.



The author wishes to express her thanks to the referees and associate editor for their suggestions and comments, which served to significantly improve the quality of the paper.


Lim, E. (2021), "Estimation of unknown parameters using partially observed data", Journal of Modelling in Management, Vol. 16 No. 2, pp. 651-667.



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