Abstract

Motivated by a multi-fidelity Weather Research and Forecasting (WRF) climate model application where the available simulations are not generated based on hierarchically nested experimental design, we develop a new co-kriging procedure called Augmented Bayesian Treed Co-Kriging. The proposed procedure 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 benchmark examples and used for the analysis of a large-scale climate modeling application which involves the WRF model. Supplementary materials are available online.

摘要

受多保真天气研究和预报（WRF）气候模型应用的启发，在这种应用中，不会基于分层嵌套的实验设计生成可用的模拟，因此，我们开发了一种新的联合克里金程序，称为增强贝叶斯树联合克里金法。拟议的程序以两种主要方式扩展了协同克里格的范围。我们在多保真度设置中引入了二叉树分区潜伏过程，以解决模型输出中不同保真度级别的非平稳和潜在不连续性。此外，我们引入了一种有效的归因机制，该机制可以通过启用半共轭先验的规范来在非分层嵌套实验设计时实际实施共克里金法。我们的归因策略允许设计一种有效的RJ-MCMC实现，该实现涉及折叠的块和根据条件分布的直接仿真。我们开发了Monte Carlo递归仿真器，它以计算上可行的方式为每个保真度级别的模型输出提供了完整的预测分布的Monte Carlo代理。我们的方法的性能在基准示例上得到了证明，并用于分析涉及WRF模型的大规模气候建模应用程序。 补充材料可在线获得。