In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and integrate their outcomes. In this paper, we operate within the Bayesian paradigm, relying on Gaussian processes as our models. These models generate predictive probability density functions (pdfs), and the objective is to integrate them systematically, employing both linear and log-linear pooling. We introduce novel approaches for log-linear pooling, determining input-dependent weights for the predictive pdfs of the Gaussian processes. The aggregation of the pdfs is realized through Monte Carlo sampling, drawing samples of weights from their posterior. The performance of these methods, as well as those based on linear pooling, is demonstrated using a synthetic dataset.

翻译：在科学与工程领域，我们常基于模型对目标变量进行精确预测。鉴于这些模型是对现实的近似，通常需要将多种模型应用于同一数据并整合其预测结果。本文在贝叶斯范式下，以高斯过程作为模型框架。这些模型生成预测概率密度函数（PDF），而目标则是通过线性池化与对数线性池化方法对其进行系统性整合。我们提出对数线性池化的新方法，为高斯过程的预测PDF确定与输入相关的权重。通过蒙特卡洛采样从权重后验分布中抽取样本实现PDF的聚合。基于合成数据集，验证了该方法及线性池化方法的性能表现。