Sequential Bayesian inference in complex and realistic dynamical systems

This PhD position will be at the interesting overlap between statistical signal processing, statistics, 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. 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 IS-based methods for Bayesian inference in complex systems (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. Many applications can be benefited from the development of these methodologies, including inferential problems in climatology, biological systems, or ecology, among many others.


Candidate profile:

Essential:
– A Bachelor’s degree in Engineering, Statistics, Mathematics, Computer Science, Physics or similar (a First Class or good Upper Second Class Honours degree, or the equivalent from an overseas university);
– Programming ability in high-level scientific development language, e.g., MATLAB, Python, R;
– Experience in Bayesian modeling or Monte Carlo methods.
– Strong verbal and written communication skills in English;
– High motivation, curiosity, and proactivity.


Desirable:
– Mathematical maturity with emphasis on estimation and inference;
– Experience in optimization methods;
– A Master’s degree with prior publications in leading signal processing, machine learning, or statistics venues.