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 nonstationary 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 nonhierarchically nested by enabling the specification of semiconjugate priors. Our imputation strategy allows the design of an efficient reversible jump Markov chain Monte Carlo 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.

摘要

受多保真天气研究和预测 (WRF) 气候模型应用程序的启发，其中可用的模拟不是基于分层嵌套实验设计生成的，我们开发了一种新的联合克里金法程序，称为增强贝叶斯树联合克里金法。提议的程序以两种主要方式扩展了联合克里金法的范围。我们在多保真度设置中引入了一个二叉树分区潜在过程，以解决不同保真度级别的模型输出中的非平稳和潜在不连续性。此外，我们引入了一种有效的插补机制，当实验设计是非分层嵌套时，通过启用半共轭先验的规范，该机制允许实际实施共同克里金法。我们的插补策略允许设计一种高效的可逆跳跃马尔可夫链蒙特卡罗实现，该实现涉及折叠块和条件分布的直接模拟。我们开发了蒙特卡罗递归仿真器，它以计算上可行的方式为每个保真度级别的模型输出的完整预测分布提供了蒙特卡罗代理。我们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。以一种计算上可行的方式。我们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。以一种计算上可行的方式。我们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。