Dear Marshall, Dear group,

Marshall wrote:

I just discovered a couple of books by Igor Gorban on what he calls “hyper-randomness” and “statistical stability”. […] 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. […] I would be interested if someone has discussed Gorban’s work in connection with IP.

Vladik Kreinovich alerted us here on this list in July last year of the first book's appearance. I do not know of anyone in the IP community having discussed them publicly.

I have access via my institute's library, I'll give the DOIs:

The Statistical Stability Phenomenon

http://dx.doi.org/10.1007/978-3-319-43585-5

Randomness and Hyper-Randomness

http://dx.doi.org/10.1007/978-3-319-60780-1

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.

Yes, there is certainly this connection. However, from skimming the books, it seems that Gorban has worked in relative isolation. He mentions Walley's 1991 book as an extra, uncited reference, but that seems to be it for the connection to our community.

My impression is that his experimental results may be very relevant for the IP community as arguments for the use of IP models, even in cases where lots of data is available. Given his relative isolation, my guess is that the modeling tools we have available would be quite useful in his endeavor. He appears to use mostly p-box type models for overcoming the limitations of classical probability theory (but don't cite me on this).

Best,

Erik

-- https://ac.erikquaeghebeur.name