9 Computer experiments

TLDR: This chapter presents and compares two statistical approaches to computer experiments and introduces randomness by modeling the function, f, as a realization of a Gaussian process.

Abstract: Publisher Summary This chapter presents and compares two statistical approaches to computer experiments. The second approach does so by taking random input points. Randomness is required to generate probability or confidence intervals. The first approach introduces randomness by modeling the function, f, as a realization of a Gaussian process. Deterministic computer simulations of physical phenomena are becoming widely used in science and engineering. Some of the most widely used computer models arise in the design of the semiconductors used in the computers themselves. There are two main statistical approaches to computer experiments, one based on Bayesian statistics and a frequentist one based on sampling techniques. A Bayesian approach to modeling simulator output can be based on a spatial model adapted from the geo-statistical Kriging model. This approach treats the bias or systematic departure of the response surface from a linear model as the realization of a stationary random function. This model has exact predictions at the observed responses and predicts with increasing error variance as the prediction point moves away from all the design points.