Bayesian cubic spline in computer experiments

Abstract

Cubic splines are commonly used in numerical analysis. It has also become popular in the analysis of computer experiments, thanks to its adoption by the software JMP 8.0.2 2010. In this chapter, a Bayesian version of the cubic spline method is proposed, in which the random function that represents prior uncertainty about y is taken to be a specific stationary Gaussian process and y is the output of the computer experiment. A Markov chain Monte Carlo (MCMC) procedure is developed for updating the prior given the observed y values. Simulation examples and a real data application are given to show that the proposed Bayesian method performs better than the frequentist cubic spline method and the standard method based on the Gaussian correlation function.