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Title: Bayesian inference in models made of modules Authors:  Pierre Jacob - Harvard University (United States) [presenting]
Chris Holmes - University of Oxford (United Kingdom)
Christian Robert - Universite Paris-Dauphine (France)
Lawrence Murray - University of Oxford (United Kingdom)
George Nicholson - University of Oxford (United Kingdom)
Abstract: Statisticians are faced with integrating heterogeneous data modalities relevant for an inference or decision problem. It is convenient to use a graphical model to represent the statistical dependencies, via a set of connected ``modules'', each relating to a specific data modality, and drawing on specific domain expertise in their development. Each module can involve parametric, semi-parametric or non-parametric components. In principle, given data, the conventional statistical update then allows for coherent uncertainty quantification and information propagation through and across the modules. However, misspecification of any module can contaminate the update of others. In various settings, particularly when certain modules are trusted more than others, practitioners have preferred to avoid learning with the full (joint) model in favor of ``cut distributions''. We will describe why these modular approaches might be preferable to the full model in misspecified settings, and propose criteria to choose between modular and full-model approaches. The question is intertwined with computational difficulties associated with the cut distribution.