Σεμινάριο: "Bayesian nonparametrics & Random dynamical systems"

ΚΥΚΛΟΣ ΣΕΜΙΝΑΡΙΩΝ ΣΤΑΤΙΣΤΙΚΗΣ 2023-2024

Ομιλητής: Konstantinos Kaloudis, Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean

Bayesian nonparametrics & Random dynamical systems

ΑΙΘΟΥΣΑ Τ105, ΚΤΙΡΙΟ ΤΡΟΙΑΣ

ΠΕΡΙΛΗΨΗ

The normality of the (dynamical) noise process is one of the most common assumptions in the Random dynamical systems literature. In this talk, we will present a unified methodological framework, under the Bayesian nonparametric modeling approach, useful for the approximation of dynamical invariants based on observed time-series data. Specifically, we will use the Dirichlet Process and Geometric Stick-Breaking Process random measures as priors over the noise density. The presented methods can also be used for reconstruction, prediction and noise reduction purposes, under the assumption of a known functional form of the data-generating process and a symmetric (non-gaussian) noise density. Finally, we will discuss a recent extension of our framework, based on the utilization of Bayesian Neural Networks.