Morris, Max D.; Mitchell, Toby J.; Ylvisaker, Donald Bayesian design and analysis of computer experiments: Use of derivatives in surface prediction. (English) Zbl 0785.62025 Technometrics 35, No. 3, 243-255 (1993). Summary: This article is concerned with the problem of predicting a deterministic response function \(y_ 0\) over a multidimensional domain \(T\), given values of \(y_ 0\) and all of its first derivatives at a set of design sites (points) in \(T\). The intended application is to computer experiments in which \(y_ 0\) is an output from a computer model of a physical system and each point in \(T\) represents a particular configuration of the input parameters. It is assumed that the first derivatives are already available (e.g., from a sensitivity analysis) or can be produced by the code that implements the model. A Bayesian approach in which the random function that represents prior uncertainty about \(y_ 0\) is taken to be a stationary Gaussian stochastic process is used. The calculations needed to update the prior given observations of \(y_ 0\) and its first derivatives at the design sites are given and are illustrated in a small example.The issue of experimental design is also discussed, in particular the criterion of maximizing the reduction in entropy, which leads to a kind of \(D\)-optimality. It is shown that, for certain classes of correlation functions in which the intersite correlations are very weak, \(D\)-optimal designs necessarily maximize the minimum distance between design sites. A simulated annealing algorithm is described for constructing such maximin distance designs. An example is given based on a demonstration model of eight inputs and one output, in which predictions based on a maximin design, a Latin hypercube design, and two compromise designs are evaluated and compared. Cited in 71 Documents MSC: 62F15 Bayesian inference 62K05 Optimal statistical designs 65C20 Probabilistic models, generic numerical methods in probability and statistics 62P99 Applications of statistics 65C99 Probabilistic methods, stochastic differential equations Keywords:\(D\)-optimality; Bayesian prediction; interpolation; sensitivity analysis; predicting a deterministic response function; multidimensional domain; computer experiments; stationary Gaussian stochastic process; reduction in entropy; correlation functions; simulated annealing; maximin distance designs; Latin hypercube design PDFBibTeX XMLCite \textit{M. D. Morris} et al., Technometrics 35, No. 3, 243--255 (1993; Zbl 0785.62025) Full Text: DOI Link