Model-based Bayesian evidence combination leads to models with multiple parameteric modules. In this setting the effects of model misspecification in one of the modules may in some cases be ameliorated by cutting the flow of information from the misspecified module. Semi-Modular Inference (SMI) is a framework allowing partial cuts which modulate but do not completely cut the flow of information between modules. We show that SMI is part of a family of inference procedures which implement partial cuts. It has been shown that additive losses determine an optimal, valid and order-coherent belief update. The losses which arise in Cut models and SMI are not additive. However, like the prequential score function, they have a kind of prequential additivity which we define. We show that prequential additivity is sufficient to determine the optimal valid and order-coherent belief update and that this belief update coincides with the belief update in each of our SMI schemes.
翻译:基于模型的贝叶斯证据组合导致多个参数模块的模型。 在设置模型在其中模块中的错误区分效应时,通过切断来自错误指定模块的信息流,在某些情况下可以改善其中某个模块的模型错误区分效应。半模块推论(SMI)是一个允许部分削减的框架,这种部分削减可以调节模块之间的信息流动,但并不完全切断模块之间的信息流动。我们表明,SMI是实施部分削减的一组推断程序的一部分。已经证明,添加剂损失决定了最佳、有效和顺序一致的信仰更新。在切除模型和SMI中产生的损失不是添加剂。然而,与预量化分函数一样,它们具有一种我们定义的预累积性。我们表明,预先添加性足以确定最佳有效和顺序一致的信念更新,而这种更新与我们每个SMI计划中的信念更新相吻合。