Gnostic theory of uncertain data (mathematical gnostics) is one of non-statistical approaches of analyzing data which are subject to expermental errors or othe types of uncertainty. The method does not pose any a priori assumptions to the character of uncertainty and is based upon properties of each single datum. the results are thus valid even for small data samples.
Introduction to the gnostic theory can be found in the following publications (the last two are in Czech):
You can also read an abstract of the book P. Kovanic and M. B. Humber: The Economics of Information---Gnostic Methods for the Treatment of Uncertain Data.
I am developing Free OpenSource gnostic analyzer based on Octave. The first version is almost ready for distribution, it is only necessary to clarify a few details. What is missing is documentation and mainly explanation of the gnostic theory. the first version should thus come with a set of solved examples on which the gnostic algorithms will be explained.
This page also contains PDF files of presentation slides of my four lectures. the PDF files will automatically open in the prsentation mode. Do not view them directly through internet but rather save them to your disk. There are, unfortunately, no full texts to these presentations. Lecture Application of Gnostic Theory to Analysis of Particle Size Distribution was presented on the Czech-Finnish Aerosol Symposium and its extended abstract was published in:
Wagner Z., Zdimal V., Smolik J.: Application of Gnostic Theory to Analysis of Particle Size Distribution. Czech-Finnish Aerosol Symposium, Report Series in Aerosol Science, No 56, p. 164-168, Prague, Czech Republic, 23-26 May 2002.
Lecture Gnosticka teorie neurcitych dat (priklady aplikaci) was presented on 9th April 2003 in Czech at the Charles University.
Lecture Stanoveni distribuce velikosti castic v aerosolu s vyuzitim gnosticke teorie was presented (in Czech) on 30th April 2004 in the Institute of Chemical Process Fundamentals of the Academy of Sciences of the Czech Republic. After presenting the lecter a better algorithm for determination of parameters of local distribution function was developed. It was presented on international conference ChemStat 2004.
Lecture Robust estimation of particle size distribution in atmospheric aerosols by gnostic theory was given on the above mentioned conference. You can read its full text in the proceedings:
Wagner Z., Zdimal V., Smolik J.: International Chemometrics Meeting Chemstat 2004, Conference Proceedings, p. 76--84, Pardubice, Czech Republic, 30 August--02 September 2004. ISBN 80-239-3462-7.