Robust Parameter Design With Computer Experiments Using Orthonormal Polynomials

Tan, Matthias Hwai Yong

doi:10.1080/00401706.2014.969446

Cited by 13 publications

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“…Note: Using a Bayesian approach to the analysis of the I/O data from simulation, Tan (2014a) first fits a Kriging model to the I/O data, then approximates this Kriging model through a so-called orthonormal polynomial (which is more complicated than the polynomial models that we discussed in Sect. 2.1), and finally uses this polynomial for "functional analysis of variance" or FANOVA (we discussed FANOVA in Sect.…”

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Design and Analysis of Simulation Experiments

Kleijnen

2015

International Series in Operations Research &Amp; Management Science

215

138

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This chapter is organized as follows. Section 5.1 introduces Kriging, which is also called Gaussian process (GP) or spatial correlation modeling. Section 5.2 details so-called ordinary Kriging (OK), including the basic Kriging assumptions and formulas assuming deterministic simulation. Section 5.3 discusses parametric bootstrapping and conditional simulation for estimating the variance of the OK predictor. Section 5.4 discusses universal Kriging (UK) in deterministic simulation. Section 5.5 surveys designs for selecting the input combinations that gives input/output data to which Kriging metamodels can be fitted; this section focuses on Latin hypercube sampling (LHS) and customized sequential designs. Section 5.6 presents stochastic Kriging (SK) for random simulations. Section 5.7 discusses bootstrapping with acceptance/rejection for obtaining Kriging predictors that are monotonic functions of their inputs. Section 5.8 discusses sensitivity analysis of Kriging models through functional analysis of variance (FANOVA) using Sobol's indexes. Section 5.9 discusses risk analysis (RA) or uncertainty analysis (UA). Section 5.10 discusses several remaining issues. Section 5.11 summarizes the major conclusions of this chapter, and suggests topics for future research. The chapter ends with Solutions of exercises, and a long list of references.

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