Sequential Bayesian inference in complex and realistic dynamical systems

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This PhD position will be at the interesting overlap between computational statistics, Bayesian analysis, statistical signal processing, and machine learning, motivated by applications that aim to improve human life and environment. The successful applicant will be supervised by Dr. Victor Elvira. Several international collaborations with scientists in France and USA are also expected. Many problems in different scientific domains can be described through statistical models that relate the sequential observed data to a hidden process through some unobserved parameters. In the Bayesian framework, the probabilistic estimation of the unknowns is represented by the posterior distribution of these parameters. However in most of the realistic models, the posterior is intractable and must be approximated. For instance, Importance Sampling (IS)- based algorithms are Monte Carlo methods that have shown a satisfactory performance in many problems of Bayesian inference, including the sequential setting. In this thesis, we will develop novel methods for Bayesian inference in complexsystems (high-dimensional, large amount of data, non-linear non-Gaussian relations, with model misspecification, etc). More specifically, we will propose novel efficient computational methods to deal with these complex models in order to overcome current limitations of more traditional Monte Carlo techniques in such a challenging context. We will also explorethe application of these methods to structural equation models which have recently gained a lot of interest in machine learning and statistics. Many practical applications can be benefited from the development of these methodologies, including problems in climatology, biological systems, or ecology, among many others.