Virtual Library of Simulation Experiments:

Emulation/Prediction Test Problems

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Han et al. (2009) Function

Description:

Dimensions: 2

This function has one quantitative and one qualitative input variable. The plot above shows the function for all three possible values of the qualitative z-variable.

Zhou et al. (2011) and Han et al. (2009) use this function for three different scenarios, each time using a different b-vector (b₀₁, b₀₂, b₀₃, b₁₁, b₁₂, b₁₃, b₂₁, b₂₂, b₂₃). For each scenario, the elements of the b-vector are drawn from Normal distributions with a standard deviation of 0.01 and the following expected values:
(1, 0, -1, 6, 4, 5, -6, -6, -6),
(1, 0, -1, 0, 6, 5, 2, -6, -6) and
(1, 0, -1, 6, 6, 6, -6, -6, -6).
The above plot is given for the first vector in the list.

Input Domain:

The quantitative variable x is in [0, 1], and the qualitative variable z takes on one of the three possible values in {1, 2, 3}.

Code:

References:

Han, G., Santner, T. J., Notz, W. I., & Bartel, D. L. (2009). Prediction for computer experiments having quantitative and qualitative input variables. Technometrics, 51(3). 51, 278-288.

Zhou, Q., Qian, P. Z., & Zhou, S. (2011). A simple approach to emulation for computer models with qualitative and quantitative factors. Technometrics, 53(3).

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