General circulation models (GCMs) are essential tools for climate studies. Such climate models may have varying accuracy across the input domain, but no model is uniformly best. One can improve climate model prediction performance by integrating multiple models using input-dependent weights. Weight functions modeled using Bayesian Additive Regression Trees (BART) were recently shown to be useful in nuclear physics applications. However, a restriction of that approach was the piecewise constant weight functions. To smoothly integrate multiple climate models, we propose a new tree-based model, Random Path BART (RPBART), that incorporates random path assignments in BART to produce smooth weight functions and smooth predictions, all in a matrix-free formulation. RPBART requires a more complex prior specification, for which we introduce a semivariogram to guide hyperparameter selection. This approach is easy to interpret, computationally cheap, and avoids expensive cross-validation. Finally, we propose a posterior projection technique to enable detailed analysis of the fitted weight functions. This allows us to identify a sparse set of climate models that recovers the underlying system within a given spatial region as well as quantifying model discrepancy given the available model set. Our method is demonstrated on an ensemble of 8 GCMs modeling average monthly surface temperature.

翻译：大气环流模型（GCMs）是气候研究的重要工具。此类气候模型在不同输入域可能具有不同的精度，但没有模型能在所有情况下保持最优。通过采用输入依赖的权重对多个模型进行集成，可以提升气候模型的预测性能。近期研究表明，基于贝叶斯可加回归树（BART）构建的权重函数在核物理应用中具有良好效果。然而，该方法存在权重函数为分段常数的局限性。为实现多气候模型的平滑集成，本文提出一种新型树模型——随机路径贝叶斯回归树（RPBART）。该模型通过在BART中引入随机路径分配机制，生成平滑的权重函数与预测结果，且完全采用无矩阵化表述。RPBART需要更复杂的先验设定，为此我们引入半变异函数以指导超参数选择。该方法具有解释性强、计算成本低、无需昂贵交叉验证的优势。最后，我们提出后验投影技术以实现对拟合权重函数的精细分析。通过该技术，我们能够在给定空间区域内识别出能还原底层系统的稀疏气候模型集合，并基于现有模型集量化模型差异。本方法在8个模拟月均地表温度的大气环流模型集成中得到了验证。