
jslade


Total Posts: 1123 
Joined: Feb 2007 


Can anyone suggest a good review article/book/code samples on the subject? I don't really want to know about it, because I like concepts like probability and Bayes rule, but some people seem to find it interesting, and they have more money than me. 
"Learning, n. The kind of ignorance distinguishing the studious." 



polysena


Total Posts: 1057 
Joined: Nov 2007 


DempsterSchafer and the like belongs to a promising (in my view and from the viewpoint of my mathematical tastes) research area called "imprecise probability theory".. it is a quite deep field at the crossing of statistics, combinatorics, computer science, philosophy and formal logics, intelligence. In this respect it is varied as fascinating. I believe it also helps to understand what assumptions are implicitely made in "probability" theory. At least in my view. There is a society (SIPTA) which binds all these people. One great guy is P.Walley ( I can share the article on pm if you have no access) I quite like what they are doing to me it is fundamental. I always believed that it would be nice to be able (one day..) to use such approaches in general in finance (perhaps not in pricing, but then even.. ) in areas pertaining to credit surely.. but the techniques are complicated, no super "computational friendly yet" and for sure no manager would ever endorse that.. (I tried and failed). ISIPTA conferences.
Imprecise probability is understood in a very wide sense. It is used as a generic term to cover all mathematical models which measure chance or uncertainty without sharp numerical probabilities. It includes both qualitative (comparative probability, partial preference orderings, …) and quantitative modes (interval probabilities, belief functions, upper and lower previsions, …). Imprecise probability models are needed in inference problems where the relevant information is scarce, vague or conflicting, and in decision problems where preferences may also be incomplete.
The article by P Smet might be a good place to start with on top of that of P. Walley, http://iridia.ulb.ac.be/~psmets/WhatIsDS.pdf (presentation of the Dempster model)
or perhaps this http://www.sipta.org/isipta15/data/slides/Wheeler.pdf (you can search the SIPTA conference proceedings you will find various things) you might like this on Bayesianism http://decsai.ugr.es/~smc/isipta99/proc/047.html
Now JSlade if you do not want to know about it, I am not too sure how to advise you, it is a wide domain, but really fascinating... Hope this will make your appetite grow.. May I ask you in what respect your rich people are interested in that.. (if not public a pm answer would just make me happy...) truth is they might indeed have good taste..
Regards Poly

Свобода  это то, что у меня внутри.
(Ленинград и Кипелов  "Свобода") 


jslade


Total Posts: 1123 
Joined: Feb 2007 


Apparently people are beginning to use DS theory in building data fusion gizmos. Combining "sensor" data in interesting, well reasoned ways has all kinds of applications. The following paper is a weird use case, which isn't quite what I had in mind, but the Kalmanlike approach using DS looked particularly interesting. http://www.cs.cmu.edu/~whd/publications/7179.pdf
Thanks very much for the references. I particularly liked the one by Smets which stated at the outset: "I do not know what is DempsterShafer's model, except that it is a model that uses the mathematical object called 'belief function'." I'm hoping to have a better idea after digesting the lot of them.
I suppose it is interesting stuff; one wonders if it might be applied to quantum mechanics or something in a natural way. Unfortunately, I have to prioritize my interests to avoid the poor house. My hobby time is mostly symbolic dynamics at present. Though if a customer wants DS sensor fusion, I'm happy to think about that for a while. 
"Learning, n. The kind of ignorance distinguishing the studious." 



polysena


Total Posts: 1057 
Joined: Nov 2007 


Yes Data & Expertopinion elicitation & fusion is really one of the possible applications. Poly 
Свобода  это то, что у меня внутри.
(Ленинград и Кипелов  "Свобода") 


polysena


Total Posts: 1057 
Joined: Nov 2007 


Attached File: Blutner_beimGraben_2015.pdf
Slade, here a relatively "big picture" article with a related but slightly different focus around the research program on quantum preferences (will appeal to those with Physics background although it is truely about algebraic structures), if you search you will also see a footnote with DempsterSchafer. Perhaps this will inspire you more. Poly 
Свобода  это то, что у меня внутри.
(Ленинград и Кипелов  "Свобода") 



jslade


Total Posts: 1123 
Joined: Feb 2007 


Thanks Poly! I'm a little under the gun at the moment, but that looks real interesting. 
"Learning, n. The kind of ignorance distinguishing the studious." 


Rashomon


Total Posts: 172 
Joined: Mar 2011 


polysena, you're the first person I've come across who shared an interest in imprecise probability. (I used to get it from ippserv.rug.ac.be, which appears to be defunct.)
Learning about tempered distributions (via one of mj's books) changed my view about how to do this right. Schwartz's stroke of genius was to avoid hyperparameters altogether and derive things just from the assumption of smoothness.
As you say I think the impetus is problems in foundations of probability. In particular measure theory doesn't capture confidence (not CI's, but the difference between your noDutchbooks bet when you've just heard of it, versus when you're intermediate familiarity or expert in a matter).
A practical direction to take this, I think, would be to find a way of quantifying (as in paralleltransport) model differences, assumption differences, or differences in response rates. "Average of 85, with 70% NA's" and "average of 85, with 30% NA's" are not applestoapples.
EDIT: Somehow branding as modified Kelly criteria, would be how I would sell the research. 
"My hands are small, I know, but they're not yours, they are my own. And they're, not yours, they are my own." ~ Jewel 



deeds


Total Posts: 378 
Joined: Dec 2008 

 

deeds


Total Posts: 378 
Joined: Dec 2008 


EDIT: oops, accidentally posted twice 








