The spatial correlation function approach to response surface estimation
The spatial correlation function approach to response surface estimation
复制标题
响应面估计的空间相关函数方法
DOI：
10.1145/167293.167638
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
M. Morris
中科院分区：
文献类型：
--
作者：
T. Mitchell;M. Morris
这是一篇说明性文件，讨论了在模拟实验中使用的传统响应面法的替代方法，其中目标是将输出变量(响应)表示为几个输入变量的函数。该方法是贝叶斯的，因为关于真实响应函数y的不确定性由在输入参数空间中的感兴趣区域X上定义的随机函数Y来表示。如果Y是高斯的，则存在简单的公式来更新y的给定观测值y(x{sup 1})、y(x{sup 2})、{hor_省略}、Y(x{sup n})，这些公式可以在输入参数的不同设置(x{sup i}{epsilon}X)下从n次模拟运行中获得。Y(X)的后验均值被视为x的函数，用作估计的响应函数{cflx y}。该方法主要通过选择的空间相关函数(SCF)来驱动，该空间相关函数定义了输入参数空间中任意两点的响应之间的先验相关性。一旦选择了SCF，该方法自然是自适应的--随着更多的模拟运行，{cflx y}变得更加微妙和复杂，不需要干预来向参数模型添加项。虽然这篇论文的大部分焦点更多地集中在确定性模拟上，我们在这方面已经有了大部分经验，但我们将展示如何进行修改以处理``随机``响应。文中还讨论了一些例子，以说明本文的观点和结果的性质。
This is an expository paper which discusses an alternative to conventional response surface methodology for use in simulation experiments where the objective is to express an output variable (response) as a function of several input variables. The method is Bayesian in the sense that uncertainty about the true response function y is expressed by the random function Y, defined on the region of interest X in the space of the input parameters. If Y is Gaussian, straightforward formulas exist for updating y given observations of y(x{sup 1}),y(x{sup 2}),{hor_ellipsis},Y(x{sup n}), which are available from n simulation runs at different settings (x{sup i}{epsilon}X)of the input parameters. The posterior mean of Y(x), viewed as a function of x, serves as the estimated response function {cflx y}. The method is driven primarily by means of a chosen spatial correlation function (SCF), which defines the prior correlation between the responses at any two points in the space of the input parameters. Once the SCF is chosen, the method is naturally adaptive -- {cflx y} becomes more subtle and complex as more simulation runs are made, with no intervention required to add terms to a parametric model. Although much of the focus of this paper ismore » on deterministic simulations, where we have had most of our experience, we shall show how modifications can be made to handle ``random`` responses. Some examples are discussed to illustrate the ideas and the nature of the results.« less