报告题目：An Optimal Composite Likelihood Estimation and Prediction for Large-scale Gaussian Process Models
报告摘要：Large-scale Gaussian process (GP) models are becoming increasingly important and popularly used in the context of geostatistics, machine learning, simulation optimization, etc. However, the standard methods of GP models, the maximum likelihood estimation and the best linear unbiased predictor, are designed to run in a single computer whose computational power is often limited even for a computer in a super-computing center. Therefore, approximate alternatives that can use the power of multiple computers are in an increasing demand, such as the composite likelihood methods. However, those alternative methods in the literature offer limited options for practitioners, because most methods care more about computational efficiency than the statistical efficiency. In fact, there is lack of methods in the literature that can provide accurate solutions to parameter estimation and model prediction of large-scale GP applications for practitioners who can use a super-computing center. Therefore, we develop an optimal composite likelihood method in this paper that tries to minimize information loss in parameter estimation and prediction of large-scale GP models. We prove that the proposed composite likelihood prediction, called the best linear unbiased block predictor, has the minimum prediction variance under some conditions. Numerical examples show that both the composite parameter estimation and prediction method we proposed exhibit more accurate performance than their traditional counterparts under various cases.