Mitigating Model Misspecification with Variational Bayesian Inference - Krissaane, Ines (2024)
Learning dynamical systems from data is an important modelling problem in which one approximates the underlying equations of motion governing the evolution of some system. The conventional approach involves utilising a dynamical model, often derived from expert knowledge to accurately replicate the real-world data. This system often involves the inference of interpretable parameters so that model predictions align with observed data. When a chosen model fails to adequately represent the entire unknown dynamic, the ability to extract meaningful information from a fitted model can be challenging. This thesis investigates strategies addressing dynamical model misspecification within the framework of Bayesian inference. We delve into the limitations of standard Bayesian inference methods, specifically for parameter estimation, uncertainty quantification, and prediction accuracy. In our pursuit of a robust inferential approach, we assess the effectiveness of various contemporary methods such as generalised variational methods for dynamic modelling. Additionally, we introduce novel strategies to address model discrepancy, employing both Gaussian Processes and Approximate Bayesian Computation methods. This research aims to advance our understanding of Bayesian inference under model misspecification and offers practical guidance on constructing robust inferential approaches for more accurate and reliable results in continuous-time dynamic process.