We are pleased to announce the public defense of the doctoral thesis by Omar Fabian González, entitled “Bayesian Computational Inference in High-Dimensional Systems”. The dissertation has been conducted under the supervision of Professor Joaquín Míguez Arenas.
The defense took place on Wednesday, April 8th at 11:00 AM, in the Aula de Grados (Adoración de Miguel), at Universidad Carlos III de Madrid.
The thesis addresses fundamental challenges in stochastic filtering, a key area of applied probability concerned with estimating hidden stochastic processes from noisy observations. This framework is central to a wide range of applications, including communications, target tracking, image processing, artificial intelligence, finance, and physics. In particular, the work focuses on two major limitations of modern filtering methods: the curse of dimensionality and model misspecification.
A first major contribution of the dissertation is a novel theoretical analysis of nested importance sampling methods in high-dimensional settings. The results show that, under suitable conditions, approximation errors scale only polynomially with the dimension of nuisance variables, contrasting with the exponential degradation predicted by classical theory. Notably, the analysis identifies regimes in which the error remains uniformly bounded even as the dimensionality grows. These findings provide new insights into the scalability of importance sampling techniques and their role in more advanced inference algorithms.
The second part of the thesis investigates the problem of model misspecification through the lens of nudging techniques. The work establishes a formal interpretation of nudging as a modification of the transition dynamics in state-space models, demonstrating that it can lead to models with improved marginal likelihood. This provides a rigorous theoretical justification for its effectiveness in practice. In addition, the thesis introduces an operator-theoretic framework for Bayesian filtering, offering a unified perspective on stability and robustness and clarifying how modeling errors propagate over time.
Overall, this dissertation advances the theoretical foundations of Bayesian filtering while enhancing its practical reliability in complex, high-dimensional scenarios.