Dear Marshall
Dear Group

A referee for our ISIPTA paper on imprecision and randomness, where we showed that precise randomness is a very small island in a sea of interesting phenomena, pointed to Gorban���s work. My study of his latest survey book allows me to concur with Erik���s assessment. There is a lot of interesting stuff there, but the phrase ���working in isolation��� is also relevant.

Every good wish, Gert

On 30 Jan 2018, 13:11 +0100, Erik Quaeghebeur <E.R.G.Quaeghebeur@tudelft.nl>, wrote:

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
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