基于非信息超先验的Bayesian Kriging元建模算法

Bayesian meta-modeling for Kriging utilizing noninformative hyper prior

计算机试验引入近似建模的思想,使其广泛地用于复杂物理系统。针对计算机试验中的近似建模问题,基于Jeffreys非信息超先验为Kriging模型的相关参数赋予了多层先验约束,提出了一种有效的Bayesian元建模方法,并且利用期望最大化算法对相关参数进行数值求解。新方法在本质上属于惩罚似然方法,但是它不含有任何需要调整或者估计的参数。将之与国际上已有的几种方法进行了比较,实验结果显示新方法不仅能够取得较高的元建模精度,而且能够大大降低计算复杂度。

Computer experiments introduce the fundamental idea of building a metamodel of its simulation model,which has widely used for complex physical systems.The paper proposes a novel Bayesian meta-modeling approach for computer experiments.It imposes a hierarchical prior on the correlation parameters in Kriging based on Jeffreys＇ noninformative hyper prior,and is solved by the expectation-maximization（EM） algorithm.Though the new approach is essentially a penalized likelihood method,it does not involve any parameters to be adjusted or estimated.Compared with several other methods in literature,experimental results show that the new approach not only yields state-of-the-art performance,but also has much low computational cost.