Contacts
Intranet
SK
Viktor Witkovský
National projects
| Theoretical properties and applications of special families of probability distributions | |
| Teoretické vlastnosti a aplikácie špeciálnych tried rozdelení pravdepodobnosti | |
| Program: | VEGA |
| Duration: | 1.1.2024 – 31.12.2027 |
| Project leader: | Doc. RNDr. Witkovský Viktor, CSc. |
| Annotation: | In the project, problems related to probability distributions and their applications in mathematical modeling will be studied. We will analyze some classes of distributions (distributions generated by partial summations, the Schröter family) and study properties of distributions belonging to these classes. Issues related to calibration regression models will be addressed. New methods for solving multivariate statistical problems will be developed. These methods will be based on the calculation of exact probability distributions using the inverse transformation of the characteristic function of the distribution of the output variable. Entropy, another property of probability distributions, plays an important role in detecting causality in time series. The primary area of application is theuse of the distribution of test statistics in hypothesis testing. The new results obtained during the solution of the project will also be applied to mathematical modeling in metrology, linguistics and actuarial mathematics. |
| Causal analysis of measured signals and time series | |
| Kauzálna analýza nameraných signálov a časových radov | |
| Program: | VEGA |
| Duration: | 1.1.2022 – 31.12.2025 |
| Project leader: | RNDr. Krakovská Anna, CSc. |
| Annotation: | The project is focused on the causal analysis of measured time series and signals. It builds on the previous results of the team, concerning the generalization of the Granger test and the design of new tests in the reconstructed state spaces. The aim of the project is the development of new methods for bivariate and multidimensional causal analysis. We will see the investigated time series and signals as one-dimensional manifestations of complex systems or subsystems. We will also extend the detection of causality to multivariate cases – dynamic networks with nodes characterized by time series. Such complex networks are common in the real world. Biomedical applications are among the best known. Brain activity, determined by multichannel electroencephalographic signals, is a crucial example. We want to help show that causality research is currently at a stage that allows for ambitious goals in the study of effective connectivity (i.e., directed interactions, not structural or functional links) in the brain. |
| MATHMER – Advanced mathematical and statistical methods for measurement and metrology | |
| Pokročilé matematické a štatistické metódy pre meranie a metrológiu | |
| Program: | SRDA |
| Duration: | 1.7.2022 – 31.12.2025 |
| Project leader: | Doc. RNDr. Witkovský Viktor, CSc. |
| Annotation: | Mathematical models and statistical methods for analysing measurement data, including the correct determination of measurement uncertainty, are key to expressing the reliability of measurements, which is a prerequisite for progress in science, industry, health, the environment and society in general. The aim of the project is to build on traditional metrological approaches and develop new alternative mathematical and statistical methods for modelling and analysing measurement data for technical and biomedical applications. The originality of the project lies in the application of modern mathematical methods for modelling and detecting dependence and causality, as well as statistical models, methods and algorithms for determining measurement uncertainty using advanced probabilistic and computational methods based on the use of the characteristic function approach (CFA). In contrast to traditional approximation and simulation methods, the proposed methods allow working with complex and at the same time accurate probabilistic measurement models and analytical methods. Particular emphasis is placed on stochastic methods for combining information from different independent sources, on modelling dependence and causality in dynamic processes, on accurate methods for determining the probability distribution of values that can be reasonably attributed to the measured quantity based on a combination of measurement results and expert knowledge, and on the development of methods for comparative calibration, including the probabilistic representation of measurement results with a calibrated instrument. An important part of the project is the development of advanced numerical methods and efficient algorithms for calculating complex probability distributions by combining and inverting characteristic functions. These methods are widely applicable in various fields of measurement and metrology. In this project they are applied to the calibration of temperature and pressure sensors. |