This thesis develops a Bayesian learning framework for autoregressive models with exogenous variables, and the proposed approach optimally selects a conjugate prior for unknown parameters, infers the model structure, and tracks parameter variations through a data-driven optimized forgetting algorithm.

A multi-step decision policy design under quadratic loss, is formulated via feasible square-root optimization and implemented in a receding-horizon setting. The policy exploits a fully probabilistic design that provides consistent and principled risk handling. The resulting framework offers a theoretically complete and analytical solution to a challenging decision-making problem and is applicable to a broad class of related problems.

Experiments on real-world data demonstrate that the proposed portfolio optimization strategy consistently outperforms the uniform portfolio benchmark under relevant and reasonable conditions, validating the effectiveness of the approach.

Speaker: Tomáš Procházka

The seminar will be held on Monday, March 9, 2026 at 14:00 in Room 474.