Talk:Imprecise probability

message: The reasons given for the removal of this subsection were: 1) it is incorrect; 2) "It is not part of the book"; 3) it is original research. (1) No indication or explanation of any error is given. (2) Does Wikipedia consist of advertisements for books? (3) It is trivial high school or undergraduate material in probability theory.
illywhacker; (talk) 09:32, 14 September 2009 (UTC)
replies: text: The reasons stated strongly argue in favour of deletion of the "Motivating example" entirely, and not just the alternative explanation! Let me address the concerns again, in detail. 1) Fhermans already hinted at the error quite accurately. A typical imprecise probability approach uses a set of probabilities compatible with the available information. For instance, the Frechet bounds are a fine example where you use the set of all probabilities that are compatible with marginals rather than arbitrarily assuming independence. 2) The "Motivating example" states "Walley considers the exercise of determining the probability that a tossed thumbtack lands pin-up. Three experimenters perform this exercise, as follows (adapted from Walley)" - however there is no precise citation to Walley at all - so the reason for deletion is indeed that the citation is plainly wrong, and moreover it is not part of any work on imprecise probability that anyone knows of (and definitely not of Walley's book, which I have read). 3) Logically, if the motivating example cannot be found in the literature, then it qualifies as original research on imprecise probability theory. Having said all this, I really would like to see a more serious discussion on imprecise probability theory in this article, including a historical overview to show that there is nothing new at all about this theory and that it is as old as probability theory itself (as evidenced in for instance George Boole's "An investigation on the laws of thought" from 1854, which contains *many* motivating examples). Mtroffaes (talk) 10:51, 22 September 2009 (UTC)
replies: text: IIRC, a very similar argument to the "Alternative explanation" is made by Edwin Thompson Jaynes in his book "Probability Theory: The Logic of Science" (chapter 18, 'The Ap-Distribution and Rule of Succession', section "Confirmation and Weight of Evidence"), as a motivation for assigning "probabilities of probablilities".  If Jaynes is indeed making the same argument, then that would suffice as a reference.  --Classicalecon (talk) 11:15, 23 September 2009 (UTC)
replies: text:  Imprecise probability theory is not about probabilities of probabilities, but about sets of probabilities. This is an important point to make and the current motivational example does not allow this. There are far better, attributable examples that also allow mention of criticism (which the alternative explanation is, in essence) commonly found in the literature. I know Edwin Thompson Jaynes has formulated criticism in his posthumously published book (easily rebuked IMHO), so that could be a source. Equaeghe (talk) 15:03, 23 September 2009 (UTC)
replies: text:  But sets are simply a special case of probability distributions, so probabilities of probabilities subsumes sets of probabilities! illywhacker; (talk) 09:21, 23 April 2010 (UTC)
replies: text:  I think I must misunderstand what you mean. How or in what way can you say that a function (probability distribution) is a set? Moreover, where in the probability theory literature (precise or imprecise) is this idea proposed/used? Equaeghe (talk) 14:26, 1 July 2010 (UTC)
replies: text:  I did not say a probability distribution was a set. I said a set was a special case of a probability distribution, one that takes on a constant value on the set and zero elsewhere. Thus, the set of probabilties [p, q] ⊂ [0, 1] is represented by the uniform distribution on [p, q]. illywhacker; (talk) 13:20, 1 October 2010 (UTC)
replies: text:  I understand where you are coming from, and this is indeed a common misunderstanding to newcomers of imprecise probability theory. If you read the literature, then (aside perhaps from some obscure research) the understanding is generally that imprecise probabilities are sets of probability measures, without any further hierarchical modelling. If you put a distribution on the set, you have a classical 2nd order probability model. You don't need any of the imprecise probability machinery to deal with this. Is it now clear? Mtroffaes (talk) 17:14, 16 March 2011 (UTC)
replies: text:  I do not as yet see the difference. A set can be represented by a probability distribution. After that, any difference can only be a question of the algebraic structure used. After all, a parametric model is a set of probability distributions. illywhacker; (talk) 14:20, 29 March 2011 (UTC)

text: Thanks. I added those citations simply to adhere to Wikipedia standard. Imprecise probability is nowadays a rather big topic (at least compared to what it was 30 years ago), so I think that this article can only be a summary of what is out there, with pointers to other articles with further details about particular theories. Dempster-Shafer theory is (at least as many of my colleagues see it) a special case within imprecise probability theory—I think this is clear from the current article—if not, feel free to improve it. However, it is obvious that this article cannot discuss any theory in very much detail: the danger is that it could quickly degrade into a completely unreadable mess. Mtroffaes (talk) 13:23, 12 July 2010 (UTC)
thread_title: Justification for undo of removal of subsection "Alternative explanation without imprecise probabilities"

message: I would suggest adding a sets of probability functions bullet to the mathematical models as it doesn't seem to be subsumed by any of the other suggestions. I thought that was a pretty standard way to talk about imprecise probabilties. E.g. as is presented in http://plato.stanford.edu/archives/win2014/entries/imprecise-probabilities. --Catrincm (talk) 16:21, 6 February 2015 (UTC)
replies: text: It makes a lot of sense indeed. I've added it. Mtroffaes (talk) 10:55, 15 June 2020 (UTC)
thread_title: Add "Sets of Probability Functions" to Mathematical models

message: An editor might want to look at “Formal Qualitative Probability” by Daniel Kian Mc Kiernan, forthcoming in The Review of Symbolic Logic.  The prior published work that this article most closely resembles on a formal level is that of Koopman.  But it does not impose a logicistic interpretation (nor any other), is not constructed to the purpose of supporting quantification, and is more complete. —184.183.175.18 (talk) 22:20, 20 February 2020 (UTC)
thread_title:  Incomplete Probability Preörderings 

message: At present, the entry says: 
:In the 1920s, in A Treatise on Probability, Keynes[11] formulated and applied an explicit interval estimate approach to probability.
By his own admission, Keynes's discussion of intervals adds nothing analytically to that by George Udny Yule (“On the Theory of Consistence of Logical Class-Frequencies” in Philosophical Transactions of the Royal Society. Series A, Containing Papers of a Mathematical or Physical Character v 197 [1901] and An Introduction to the Theory of Statistics [1911]).  So, at the least, Yule should be mentioned, and prior to Keynes. 
(Yule's interpretation is somewhat different.  He imagines probabilities as the frequencies with which propositions are true, whereas Keynes imagines them as degrees of plausibility.) 
Further, in the case of Boole, of Yule, and of Keynes, all intervals are either the unit interval [0,1] or derived by multiplying the unit interval by a point probability (possibly with some further arithmetic operations).  Yet it is clear that Keynes means elsewhere to discuss non-numeric probabilities of a broader class.  There is a vociferous crackpot who in vanity journals and in self-published books attempts to argue that Keynes meant everywhere to refer to intervals, but it seems that the first researcher to understand how to treat that broader class also in terms of intervals was Bernard Osgood Koopman (“The Axioms and Algebra of Intuitive Probability” in The Annals of Mathematics series 2 v 41 [1940]). —172.58.22.254 (talk) 00:27, 24 March 2020 (UTC)
replies: text: I'm not personally familiar with the work of Yule, but yes, I agree that if it is relevant, a reference and mentioning of the work should be added. Mtroffaes (talk) 11:00, 15 June 2020 (UTC)
thread_title:  Somewhat Misleading Passage on Keynes 

message: The call-for-papers amongst the external links is quite dead.  More generally, this article now seems to be unmaintained. —172.58.19.142 (talk) 01:13, 18 April 2020 (UTC)
replies: text: Thanks for spotting. I've removed the link. Mtroffaes (talk) 10:50, 15 June 2020 (UTC)
thread_title:  Dead Link / Unmaintained Article 

message: Hello, I will probably spend a little of my free time updating this page over the next few weeks. I thought I'd share a plan for how I imagine the page looking once it's finished. 
# Introduction
# History
# Lower and upper probabilities (basic properties)
# Connection to other models (credal sets, DS belief functions, etc)
# Interpretation
I started adding some detail to the history section today, but I hope to do more.
Scmbradley (talk) 16:26, 19 October 2020 (UTC)
replies: text: You are proposing to turn the entry into an article about interval-based approaches, and to treat other approaches as something of an afterthought.  This would be fundamentally wrong.  In the absence of very strong assumptions that do not represent full generality (Walley, “Towards a unified theory of imprecise probability.”, International Journal of Approximate Reasoning 24.2-3), intervals are just proxies — “a matter of affixing quantitative nails so that an arithmetic hammer may be used” (Mc Kiernan, “Formal Qualitative Probability”, The Review of Symbolic Logic). —72.196.168.48 (talk) 23:59, 20 November 2020 (UTC)
thread_title:  Sketch of a structure for new version 

message: This doesn't make sense on its face. Normal logics cannot retain validity in the face of ignorance. If you are talking about a specific logic or group of logics introduced by Boole, you should improve your wording to make this clear. Comiscuous (talk) 07:24, 2 July 2021 (UTC)
replies: text: This is a correct point, and I have edited the article to remove the phrase in parentheses. A revert should add further text explaining how this makes sense, when, on the face of it, logic deals with certain propositions. illywhacker; (talk) 14:31, 10 July 2021 (UTC)
thread_title:  "by George Boole,[3] who aimed to reconcile the theories of logic (which can express complete ignorance)" 

message: While references (Walley, Koopman, Mc Kiernan) have been provided on this talk page, it seems clear that no one is both willing and able to write a proper article about generalized imprecise probability.  Instead, this article remains conceptualized in terms of intervals.  Perhaps someday someone will be willing to construct a more general article, but for now the article misleads its readers. 
My suggestion, then, is that the article be retitled “Interval-valued probability”, and rewritten to be a presentation of just that, with passing mention of incomplete preorderings as the most general notion of imprecise probability. —68.105.244.163 (talk) 01:37, 21 January 2023 (UTC)
thread_title:  Poposed Change of Title and Rewrite