The Department of Theoretical Methods gained its present form in 2002 after structural reorganization of the institute when the Laboratory of Theoretical Methods and the Laboratory of Neural Nets merged into a new department.
Scientific research in the department is aimed at development of theoretical methods in the area of mathematical statistics and applied mathematics.
Basic and applied research of the department is focused mainly on research in the field of the theory of probability, mathematical statistics, artificial neural nets and non-linear dynamics, with orientation towards problems of measurement and evaluation of measured data:
- basic reserach in the field of linear and non-linear regression models, mainly models with variance and covariance components;
- research of new estimating and testing procedures on parameters of the first and the second order in these models with complex covariance structure, including computational aspects and development of algorithms for the newly proposed methods and procedures;
- basic research in the area of testing procedures optimality, nonparametric methods and goodness-of-fit tests;
- research of probability distribution of estimators and test statistics for small-sized samples as well as for large sample sizes (i.e. from the asymptotical point of view) with emphasis on projection statistics, likelihood ratio tests and likelihood ratio principle;
- basic and applied research of estimators and testing procedures for non-linear models and models with non-linear structure of the covariance matrix with emphasis on time series models;
- research of statistical methods and algorithms for biomedical and technical applications, problems of measurement and metrology;
- basic research of methods based on the principle of maximum entropy (MaxEnt);
- design of flexible neural nets for time series prediction, non-linear adaptive filtration and classification of signals;
- self-organizing neural nets (Kohonen’s maps, so-called growing cell structures) and their generalizations for processing of time series;
- analysis of chaotic behaviour of complex biological systems – reduction of noise, modelling and prediction of non-linear time series by means of non-linear dynamics methods;
- studying of biotechnical feedback by means of EEG signal;
- applications of neural nets.