具有局部特征和非嵌套试验设计的多保真度计算机模型的贝叶斯分析：应用于WRF模型
Bayesian analysis of multifidelity computer models with local features and non-nested experimental designs: Application to the WRF model
摘要：
我们提出了一个多保真度贝叶斯模拟器的天气研究和预报（WRF）模型的分析时，可用的模拟不产生分层嵌套的试验设计的基础上。拟议的程序，称为增强贝叶斯树协同克里金，扩展了协同克里金的范围在两个主要方面。我们在多保真度设置中引入了一个二叉树分区潜在过程，以考虑模型输出在不同保真度水平下的非平稳和潜在不连续性。此外，我们引入了一个有效的插补机制，它允许实际实施的协同克里金时，试验设计是非层次嵌套的半共轭先验的规格。我们的插补策略允许设计一个高效的RJ-MCMC实现，涉及到塌陷块和直接模拟条件分布。我们开发的蒙特卡罗递归仿真器，它提供了一个蒙特卡罗代理的模型输出的完整预测分布在每个保真度水平，在计算上可行的方式。我们的方法的性能表现在一个基准的例子，并与现有的方法进行比较。所提出的方法是用于分析的大尺度气候模拟应用程序，其中涉及WRF模式。
英文摘要：
We propose a multi-fidelity Bayesian emulator for the analysis of the Weather Research and Forecasting (WRF) model when the available simulations are not generated based on hierarchically nested experimental design. The proposed procedure, called Augmented Bayesian Treed Co-Kriging, extends the scope of co-kriging in two major ways. We introduce a binary treed partition latent process in the multifidelity setting to account for non-stationary and potential discontinuities in the model outputs at different fidelity levels. Moreover, we introduce an efficient imputation mechanism which allows the practical implementation of co-kriging when the experimental design is non-hierarchically nested by enabling the specification of semi-conjugate priors. Our imputation strategy allows the design of an efficient RJ-MCMC implementation that involves collapsed blocks and direct simulation from conditional distributions. We develop the Monte Carlo recursive emulator which provides a Monte Carlo proxy for the full predictive distribution of the model output at each fidelity level, in a computationally feasible manner. The performance of our method is demonstrated on a benchmark example, and compared against existing methods. The proposed method is used for the analysis of a large-scale climate modeling application which involves the WRF model.
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