Simultaneous Outlier Detection and Prediction for Kriging with True Identification
提出一种新的克里金方法，通过引入正态-伽马先验同时检测异常值并进行预测，避免了马尔可夫链蒙特卡洛的昂贵计算，并证明了异常值检测的真实识别性质和预测的信息一致性。
Kriging with interpolation is widely used in various noise-free areas, such as computer experiments. However, owing to its Gaussian assumption, it is susceptible to outliers, which affects statistical inference, and the resulting conclusions could be misleading. Little work has explored outlier detection for kriging. Therefore, we propose a novel kriging method for simultaneous outlier detection and prediction by introducing a normal-gamma prior, which results in an unbounded penalty on the biases to distinguish outliers from normal data points. We develop a simple and efficient method, avoiding the expensive computation of the Markov chain Monte Carlo algorithm, to simultaneously detect outliers and make a prediction. We establish the true identification property for outlier detection and the consistency of the estimated hyperparameters in kriging under the increasing domain framework as if the number and locations of the outliers were known in advance. Under appropriate regularity conditions, we demonstrate information consistency for prediction in the presence of outliers. Numerical studies and real data examples show that the proposed method generally provides robust analyses in the presence of outliers.