Bayesian Semi-Modular Inference: theory and methods for inference in multi-modular settings under model misspecification

Thesis

One of the strengths of Bayesian analysis lies in its ability to incorporate all relevant data into the analysis and address all uncertainties in the model simultaneously. Evidence combination is a core aspect of statistical inference, and the Bayesian approach is particularly well-suited for this task. However, as model structures become larger and more intricate, it becomes increasingly challenging for Bayesians to attempt to model the true data-generating mechanism. Bayesian statistical inference loses predictive optimality when generative models are misspecified.

The increasing complexity of modern applications in statistics has led to an increased interest in multi-modular models. Unfortunately, these models are susceptible to model contamination, as the risk of misspecification in each module accumulates as modules are added. The Cut Posterior and Modularized Inference surged as an approach to address model misspecification by eliminating feedback from suspect modules. Unfortunately the understanding of such methods and available algorithms for them were limited until recently.

This dissertation provides three major contributions to the growing field of Modular Bayesian Inference. First, we introduce a generalized inferential framework that bridges the gap between standard Bayesian inference and the Cut posterior by proposing an overarching methodology that we call Semi-Modular Inference (SMI). Second, we develop novel algorithms for the computation of the Semi-Modular Posterior, enabling the use of Modularized Inference in large scale applications with thousands of model parameters and multiple cuts. Third, we provide evidence of the benefits of Semi-Modular Inference through several real-world applications, where we outperform both the Cut and Bayes posteriors by efficiently tuning the influence of modules using the Semi-Modular Posterior.

Authors: Carmona, CU

• DOI: 10.5287/ora-w4yrdepbx
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Bayesian methods; Semi-Modular Inference; statistics; variational inference; model misspecification; cut posterior; spatial statistics; Gaussian processes