论文标题
在半模块化推理中引起的临时加性损失功能的有效信念更新
Valid belief updates for prequentially additive loss functions arising in Semi-Modular Inference
论文作者
论文摘要
基于模型的贝叶斯证据组合会导致具有多个参数模块的模型。在此设置中，模型错误指定在其中一个模块中的效果可能在某些情况下可以通过从误指定的模块中切除信息流来改善。半模块化推理（SMI）是一个框架，允许部分切割，但不能完全切割模块之间的信息流。我们表明，SMI是实施部分削减的推理程序家族的一部分。已经表明，加性损失决定了最佳，有效和订购的信念更新。切割模型和SMI中出现的损失不是加性的。但是，像孕前分数函数一样，它们具有我们定义的一种临时添加性。我们表明，孕作性添加性足以确定最佳的有效和订购信念更新，并且此信念更新与我们每个SMI计划中的信念更新一致。
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.
