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Abstract:
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This paper discusses percentile estimation in a computer experiments setting. We consider the case with multiple inputs and a single output. We assume that the inputs have some known distribution and wish to estimate the p-th percentile of the induced distribution of the output. We propose a sequential procedure based on an expected improvement criterion that will perform efficiently within a fixed budget. The algorithm is a two-step procedure. At stage n, training data are used to first estimate the p-th percentile of the output, say Yp,n, and then estimate the input variable settings that would produce Yp,n. The expected improvement criterion is used to select the next point to add to the training data to improve our estimate of the p-th percentile. We observe the computer code at this point, and iterate to stage n+1. Our procedure is based on previous work by Ranjan, P. et al. (2006).
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