Mathematical models of the real world are simplified representations of complex systems. A caveat to using mathematical models is that predicted causal effects and conditional independences may not be robust under model extensions, limiting applicability of such models. In this work, we consider conditions under which qualitative model predictions are preserved when two models are combined. Under mild assumptions, we show how to use the technique of causal ordering to efficiently assess the robustness of qualitative model predictions. We also characterize a large class of model extensions that preserve qualitative model predictions. For dynamical systems at equilibrium, we demonstrate how novel insights help to select appropriate model extensions and to reason about the presence of feedback loops. We illustrate our ideas with a viral infection model with immune responses.
翻译:现实世界的数学模型是复杂系统的简化表现。 使用数学模型的告诫是,在模型扩展中,预测的因果关系和有条件的独立性可能不够强大,限制了此类模型的适用性。 在这项工作中,我们考虑在两种模型合并时,在哪些条件下保留定性模型预测。在温和假设下,我们展示了如何使用因果排序技术来有效评估定性模型预测的可靠性。我们还定性了一大类模型扩展性,以保持定性模型预测。对于平衡的动态系统,我们展示了新颖的洞察力如何帮助选择适当的模型扩展和关于反馈循环存在的理由。我们用免疫反应的病毒感染模型来说明我们的想法。