Virtual Library of Simulation Experiments:

Multi Fidelity Simulation Test Problems

Calibration/Tuning Test Problems

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Park (1991) Function 2

Description:

Dimensions: 4

This function is used as an illustrative example in several papers outlining methods for calibrating models from computer codes of differing accuracies, and tuning computer codes to data. For the purpose of tuning, Cox et al. (2001) add a small noise term to the response to simulate the collection of experimental data.

Input Domain:

The function is evaluated on the hypercube x_i ∈ [0, 1), for all i = 1, 2, 3, 4.

Modifications and Alternative Forms:

For the purpose of multi-fidelity simulation, Xiong et al. (2013) use the following function for the lower fidelity code:

Code:

References:

Cox, D. D., Park, J. S., & Singer, C. E. (2001). A statistical method for tuning a computer code to a data base. Computational statistics & data analysis, 37(1), 77-92.

Park, J.S. (1991). Tuning complex computer codes to data and optimal designs. Unpublished Ph.D. Thesis, University of Illlinois, Champaign-Urbana.

Xiong, S., Qian, P. Z., & Wu, C. J. (2013). Sequential design and analysis of high-accuracy and low-accuracy computer codes. Technometrics, 55(1), 37-46.

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For questions or comments, please email Derek Bingham at: dbingham@stat.sfu.ca.