Mathematical gnostics (or mathgnostics) is a methodology of data treatment based on the gnostic theory of individual uncertain data and small samples. It is a non-statistical alternative to both classical and robust statistics, suitable for application related to strongly uncertain data. Unlike mathematical statistics developed to be applied to “sufficiently large” samples, computer programs based on the gnostic theory of uncertain data enable the maximum information to be obtained from small samples of strongly uncertain data. The application field of this tool is thus even broader than that of statistics. There is a rich experience with successful applications of Gnostic programs in many fields of science and technology, many of them linked to sustainable living achievement:
- Environmental analysis of pollutants in water, air, in human organisms and of toxicity.
- Financial statement analysis, market predictions, marketing and economic objective rating.
- Objective diagnostic limits, decision making support and hypotheses testing in medicine.
- Quality assessment control in chemical industry and mechanical engineering.
- Survival models of parts of heavy trucks.
- Cleanroom control for production of highly integrated chips.
- Identification of acoustic signals.
- Image treatment.
- Analysis of aerosols.
- Archeological analysis.
Natural robustness and maximization of information enables not only traditional tasks to be solved, but also some new ones like tailored diagnostics of individual patients (estimation of reference values of medical parameters based on the patient's individuality), tailor-made prices in insurance based on reliable risk estimates. Generally speaking: the optimum data treatment includes managing the task of robust estimation of data-based bounds and risks of uncertain situations. This approach has resulted from the long-term scientific activity of the Institute of Information Theory and Automation of the Czechoslovak Academy of Sciences in Prague.
Within the 2-FUN project, mathgnostic models and data treatment software tools were developed, including:
- a non-statistical theory of individual uncertain data and small data samples,
- a collection of data treatment methods based on the theory,
- a package of programs to apply these methods.
2-FUN newsletter 8, newsletter 7 and newsletter 4