SAS
HRS4R
Viktor Witkovský
International projects
| Precision Neuromodulation for Chronic Pain: Integrating Functional MRI and Focused Ultrasound for Personalised Treatment | |
| Presná neuromodulácia chronickej bolesti: Integrácia funkčnej magnetickej rezonancie a fokusovaného ultrazvuku pre personalizovanú liečbu, skratka „NeuroPain“ | |
| Program: | ERANET |
| Duration: | 1.1.2026 - 31.8.2028 |
| Project leader: | Doc. RNDr. Witkovský Viktor, CSc. |
National projects
| Characteristic function-based goodness-of-fit test for fuzzy data with application to climate analysis | |
| Testy dobrej zhody založené na charakteristickej funkcii pre neurčité údaje s aplikáciou na analýzu klimatických dát | |
| Program: | SRDA |
| Duration: | 1.1.2026 - 31.8.2028 |
| Project leader: | Doc. RNDr. Witkovský Viktor, CSc. |
| Annotation: | Modern research faces growing data uncertainty from measurement errors, gaps, and subjective assessments. Traditional statistical methods, assuming precise data, often fail under such conditions. Fuzzy data, which capture vagueness and imprecision, offer a natural framework, yet robust statistical tools for them remain scarce. This interdisciplinary project — combining probability and mathematical statistics, applied mathematics, and measurement science — aims to develop a goodness-of-fit test based on characteristic functions for fuzzy and interval-valued data. This novel methodology addresses both theoretical and applied challenges, with a focus on climate analysis. Objectives include: (1) Developing theoretical and empirical characteristic functions for fuzzy data, defining distance measures, formulating the test, and deriving its statistical properties. (2) Designing and implementing efficient algorithms in R, MATLAB, or Python. (3) Evaluating performance through simulations and benchmarking against existing methods. (4) Applying the method to real climate datasets (e.g., temperature, rainfall) to demonstrate its relevance under uncertainty. The methodology leverages the uniqueness and computational benefits of characteristic functions, extended to fuzzy settings. The project innovatively integrates characteristic functions and fuzzy theory for hypothesis testing, providing a statistically rigorous yet practical approach to imprecise data analysis. Expected outcomes include: a new statistical test, open-source software, simulation and benchmark studies, case studies on climate data, and preparation of a publication in leading journal. This bilateral project brings together expertise in fuzzy theory (University of Montenegro) and measurement science (Institute of Measurement Science of the Slovak Academy of Sciences). |
| 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. |