Recursive estimation in the general linear model

Recursive linear estimation for general discrete-time descriptor systems

This paper considers the optimal linear estimates recursion problem for discrete-time linear systems in its more general formulation. The system is allowed to be in descriptor form, rectangular, time-variant, and with the dynamical and measurement noises correlated. We propose a new expression for the filter recursive equations which presents an interesting simple and symmetric structure. Conve...

Variational Bayesian Parameter Estimation Techniques for the General Linear Model

Variational Bayes (VB), variational maximum likelihood (VML), restricted maximum likelihood (ReML), and maximum likelihood (ML) are cornerstone parametric statistical estimation techniques in the analysis of functional neuroimaging data. However, the theoretical underpinnings of these model parameter estimation techniques are rarely covered in introductory statistical texts. Because of the wide...

Equivalence-motivated non-linear recursive estimation

Recursive non-linear Bayesian estimation is addressed using equivalence approach as motivating framework. Its specific form – tailored to a model class covering non-normal ARX (auto-regression with exogenous variables) models, models with discrete outputs and continuous-valued regression vectors and their dynamic mixtures – is presented. The resulting algorithms provide efficient solutions of d...

Linear Filtering and Recursive Credibility Estimation

Recursive credibility estimation is discussed from the viewpoint of linear filtering theory. A conjunction of geometric mterpretation and the innovation approach leads to general algorithms not developed before. Moreover, covariance characterizations considered by other researchers drop our elegantly as a result of geometric considerations. Examples are presented of Kalman type filters valid fo...

Comparing The ANN And Linear Regression In Estimation Of The Growth Model (The Case Of MENA)