Mathematical Gnostics

The book describes the theoretical principles of nonstatistical methods of data analysis but without going deep into complex mathematics. The emphasis is laid on presentation of solved examples of real data either from authors' laboratories or from open literature. The examples cover wide range of applications such as quality assurance and quality control, critical analysis of experimental data, comparison of data samples from various sources, robust linear and nonlinear regression as well as various tasks from financial analysis. The examples are useful primarily for chemical engineers including analytical/quality laboratories in industry, designers of chemical and biological processes. Features: - Exclusive title on Mathematical Gnostics with multidisciplinary applications, and specific focus on chemical engineering. - Clarifies the role of data space metrics including the right way of aggregation of uncertain data. - Brings a new look on the data probability, information, entropy and thermodynamics of data uncertainty. - Enables design of probability distributions for all real data samples including smaller ones. - Includes data for examples with solutions with exercises in R or Python. The book is aimed for Senior Undergraduate Students, Researchers, and Professionals in Chemical/Process Engineering, Engineering Physics, Stats, Mathematics, Materials, Geotechnical, Civil Engineering, Mining, Sales, Marketing and Service, and Finance.

Pavel Kovanic (Born 1928) 1950-1955: Studied high voltage technology on the Technical University in Sverdlovsk (recently Ekaterinburg, Russia). 1956-1970: Researcher, head of a scientific department at the Nuclear Research Institute of the Czechoslovak Academy of Sciences. 1970-1995: Scientist at the Institute of the Automation and Theory of Information of the Czech Academy of Sciences. 1995-2018: As a retired scientist participated as a scientific consultant on several research projects including grants of European Union.

1. Introductory Kindergarten. 2. Axioms. 3. Introduction to Non-Standard Thought. 4. Quantification. 5. Estimation and Ideal Gnostic Cycle. 6. Geometry. 7. Aggregation. 8. Thermodynamics of Uncertain Data. 9. Kernel estimation. 10. Probability Distribution Functions. 11. Applications of Local Distributions. 12. On the Notion of Normality. 13. Applications of Global Distribution Functions. 14. Data Censoring. 15. Gnostic Thermodynamic Analysis of Data Uncertainty. 16. Robust Estimation of a Constant. 17. Measuring the Data Uncertainty. 18. Homo- or Heteroscedastic Data. 19. Gnostic Multidimensional Regression Models. 20. Data Filtering. 21. Decision Making in Mathematical Gnostics. 22. Comparisons. 23. Advanced Production Quality Control. 24. Robust Correlation. 25. General Relations.