Dear Friends, Thanks for the interest, Dr. Gorban has indeed been studying real-life processes in which instead of a fixed limit frequency we have limit frequencies fluctuating within an interval ��� his idea is that most real-life processes are like that. I am sending a copy of this message to Dr. Gorban. Vladik

 

From: SIPTA [mailto:sipta-bounces@idsia.ch] On Behalf Of Abrams, Marshall
Sent: Friday, January 26, 2018 12:26 PM
To: sipta@idsia.ch
Subject: [SIPTA] Books by Igor Gorban

 

I just discovered a couple of books by Igor Gorban on what he calls ���hyper-randomness��� and ���statistical stability���.  I haven���t read them yet���I placed an order for both books, but I thought I���d mention them on the SIPTA list while I���m thinking about it.  I think these books might be of interest to others interested in imprecise probability.  The books seem to come from a different domain of research, so I���m not sure that the IP community would be aware of them.  Gorban���s name doesn���t appear in the bibliography of Augustin et al.���s  Introduction to Imprecise Probabilities, for example.  I would be interested if someone has discussed Gorban���s work in connection with IP.  Here are the books:

 

The Statistical Stability Phenomenon

Igor I. Gorban

Springer 2017

 

Randomness and Hyper-Randomness

Igor I. Gorban

Springer 2018

 

These are translations of books by Gorban in Russian published a few years earlier, and he has some other related books in Russian that he���s published.  (Amazon has free electronic previews that include references to the other books, with transliterated Russian titles.)

 

What I understand from descriptions and previews is that Gorban argues that there are many phenomena in nature in which repeated physical trials of the same chance setup produce sequences of outcomes that do not tend to a limit, but instead stay within certain ranges.   This sounds a lot like some of the phenomena that Terrence Fine and his collaborators have discussed, modeled, etc.  Hyper-randomness is the term that Gorban uses for his approach ot modeling such phenomena.  I have no idea yet how hyper-randomness relates to Fine et al.���s work, or IP models more generally.

 

The first book is longer, includes several chapters on empirical examples of non-converging phenomena as well as a lot of mathematical material, I think.  It���s supposed to  ���be of particular interest to engineers and scientists in general who study the phenomenon of statistical stability and use statistical methods for high-precision measurements, prediction, and signal processing over long observation intervals.��� (from the Amazon description)    It ���may also be useful for high-level courses given to university students majoring in physics, engineering, and mathematics.  To understand the material, it is sufficient to be familiar with a standard university course on probability theory and mathematical statistics.��� (from the preface)

 

The second book is intended to be more introductory, and of ���interest to a wide readership: from university students on a first course majoring in physics, engineering, and mathematics to engineers, post-graduate students, and scientists carrying out research on the statistical laws of natural physical phenomena, developing and using statistical methods for high-precision measurement, prediction, and signal processing over broad observation intervals. To read the book, it is sufficient to be familiar with a standard first university course on mathematics.���  This book includes chapters on standard probability theory, random processes, and elementary statistics.

 

Marshall

 

 

Marshall Abrams, Associate Professor 

Department of Philosophy, University of Alabama at Birmingham

Email: mabrams@uab.edu; Phone: (205) 996-7483;  Fax: (205) 975-6610

Mail: HB 414A, 900 13th Street South, Birmingham, AL 35294-1260;  Office: HB 418

Website: http://members.logical.net/~marshall