Signal aliasing in Gaussian random fields for experiments with qualitative factors
Signal aliasing in Gaussian random fields for experiments with qualitative factors
复制标题
用于定性因素实验的高斯随机场中的信号混叠
作者：
Ming;Shao;Ching
信号混叠是使用部分因子设计的必然结果。与具有固定因子效应的线性模型不同，对于在一些贝叶斯设计和计算机实验文献中提倡的高斯随机场模型，信号混叠问题没有得到类似的关注。在本文中，这个问题是解决实验的定性因素。高斯随机场中的信号可以由从协方差函数识别的随机效应来表征。信号的混叠严重程度由两个关键要素决定：（i）混叠模式，仅取决于所选设计;（ii）效应优先级，与随机效应的方差相关，并取决于模型参数。我们首先应用这个框架来研究正则部分因子设计的信号混叠问题。对于一般的析因设计，包括不规则的，我们提出了一个混叠严重性指数来量化信号混叠的严重性。我们还观察到，混叠的严重性指数是高度相关的预测方差。
Signal aliasing is an inevitable consequence of using fractional factorial designs. Unlike linear models with fixed factorial effects, for Gaussian random field models advocated in some Bayesian design and computer experiment literature, the issue of signal aliasing has not received comparable attention. In the present article, this issue is tackled for experiments with qualitative factors. The signals in a Gaussian random field can be characterized by the random effects identified from the covariance function. The aliasing severity of the signals is determined by two key elements: (i) the aliasing pattern, which depends only on the chosen design, and (ii) the effect priority, which is related to the variances of the random effects and depends on the model parameters. We first apply this framework to study the signal-aliasing problem for regular fractional factorial designs. For general factorial designs including nonregular ones, we propose an aliasing severity index to quantify the severity of signal aliasing. We also observe that the aliasing severity index is highly correlated with the prediction variance.