Disertation

Ph.D.

Ústav aplikované matematiky, Fakulta dopravní ČVUT v Praze

Na Florenci 25, 110 00 Praha 1

2010

pan Váchová (ÚTIA - Management Výzkumného centra DAR)

Bayesian modelling, estimation theory

In the thesis, a new method called `partial forgetting' is developed. Its purpose is to solve the main drawbacks of most forgetting techniques. In comparison to most of them, it is defined in the Bayesian framework as a general method, theoretically independent of the underlaying parametric model and practically directly usable for a wide class of models. It is specified for one popular member of that class - the Gaussian (auto)regressive model with external disturbances. Though the mathematics related to it is nontrivial, the derivation was done almost analytically and only a minor need of numerical approximation of the digamma function appeared. By formulation of hypotheses about the multivariate parameter entries, the method allows to track them independently and to forget them with different rates. It possesses stabilizing property, which, in the Gaussian autoregressive model, helps to prevent the parameter covariance blow-up phenomenon, when the gain of the estimation algorithm grows without bounds for nonexciting signals.