We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference, and (ii) it allows the incorporation of expert knowledge through rule-based systems. The blending of those two different frameworks can be particularly beneficial for various domains (e.g., engineering), where even though the significance of uncertainty quantification motivates a Bayesian approach, there is no simple way to incorporate researcher intuition into the model. We validate our models by applying them to synthetic applications: a simple linear regression problem and two more complex structures based on partial differential equations, and we illustrate their use through two cases derived from real data. Finally, we review the advantages of our methodology, which include the simplicity of the implementation, the uncertainty reduction due to the added information and, in some occasions, the derivation of better point predictions, and we outline limitations, mainly from the computational complexity perspective, such as the difficulty in choosing an appropriate algorithm and the added computational burden.

我们引入了一种新的基于规则的方法来处理回归问题。新方法包含来自两个框架的元素：（i）它使用贝叶斯推理提供有关感兴趣参数的不确定性的信息，以及（ii）它允许通过基于规则的系统整合专家知识。这两种不同框架的混合对于各个领域（例如工程）可能特别有益，尽管不确定性量化的重要性激发了贝叶斯方法，但没有简单的方法将研究人员的直觉纳入模型。我们通过将模型应用于综合应用来验证我们的模型：一个简单的线性回归问题和两个基于偏微分方程的更复杂的结构，我们通过从真实数据得出的两个案例来说明它们的用途。