Shi J Q, Wang B, Murray-Smith R, Titterington D M
School of Mathematics and Statistics, University of Newcastle, Newcastle Upon Tyne NE1 7RU, UK.
Biometrics. 2007 Sep;63(3):714-23. doi: 10.1111/j.1541-0420.2007.00758.x.
A Gaussian process functional regression model is proposed for the analysis of batch data. Covariance structure and mean structure are considered simultaneously, with the covariance structure modeled by a Gaussian process regression model and the mean structure modeled by a functional regression model. The model allows the inclusion of covariates in both the covariance structure and the mean structure. It models the nonlinear relationship between a functional output variable and a set of functional and nonfunctional covariates. Several applications and simulation studies are reported and show that the method provides very good results for curve fitting and prediction.
提出了一种高斯过程函数回归模型用于批量数据的分析。同时考虑协方差结构和均值结构，协方差结构由高斯过程回归模型建模，均值结构由函数回归模型建模。该模型允许在协方差结构和均值结构中都包含协变量。它对函数输出变量与一组函数和非函数协变量之间的非线性关系进行建模。报告了几个应用和模拟研究，结果表明该方法在曲线拟合和预测方面提供了非常好的结果。
