Talk:Probability interpretations

From Wikipedia, the free encyclopedia

A number of important interpretations are missing. The propensity interpretation of Popper as well as the various logical interpretations of probability. Then we have the formalist view. This page should contain 'all' views I think. INic 22:35, 18 April 2006 (UTC)

I think it's safe to say that the propensity interpretation of Popper has not been adopted in practice to any significant extent. I'm not sure what you mean by "the various logical interpretations" or the "formalist view" - you haven't given any links or explanation, but I'm confident that the same wll be true. Feel free to expand these in probability interpretations, but I think it's clear that in practice there are two main views (frequentism and Bayesianism) each of which is dominant in some professional groups and a minority in othersJQ 09:35, 5 May 2006 (UTC).

I agree with INic. The main Probability article says more about probability interpretations than this supposedly more detailed article does! This is currently a fairly poor article. Ben Finn 15:55, 31 December 2006 (UTC)

Ditto. The "frequency interpretation" is really only of historical interest, within philosophy at least, since I know of no present philosopher who advocates it. (The well-known frequentists are Venn, Reichenbach and possibly von Mises.) I wonder then if John Quiggin is referring to what we philosophers call frequency theories of propensity? (E.g. the views of (possibly) von Mises, Popper, Miller, and Gillies). While these face substantial difficulties, there are at least contemporary adherents. I have also heard physicists refer to objective propensities as "frequency probabilities", on the grounds that they're estimated empirically through measuring relative frequencies. But this terminology is rather misleading in my view.

Also, concerning degree-of-belief type probabilities, there are indeed a range of views not covered by the article. The notion of epistemic probability is based on the idea that degrees of belief are subject to rational constraints, so that there are "correct" and "incorrect" degrees of belief in a given state of knowledge. An extreme case of this is the logical interpretation, where degrees of belief are fixed by logic alone. Bayesianism isn't an interpretation of probability, but a theory of confirmation. It's true that Bayesians assume some sort of subjectivist interpretation of probability, but the exact form of this varies quite a bit from one Bayesian to another. Some, so-called "Objective Bayesians", use an epistemic interpretation.--137.82.40.29 21:18, 22 March 2007 (UTC)Richard Johns

Richard I agree completely, just a few remarks. We should mention that there are different kinds of Bayesianism here and explain the differences but not go too deep into it as Bayesianism has it's own page devoted to that. When it comes to "frequentism" I agree that the detailed accounts by Reichenbach and von Mises for example only are of historical interest today. But "frequentism" in a more general sense do have a lot of followers today, as it's the default interpretation taught in all ordinary university courses in probability theory. It's the by far most common opinion among working statisticians, probability theorists and physicists for example. When Bayesians object to "frequentist" reasoning, for example, they object to this dominating view which is in general taught today. iNic 00:45, 23 March 2007 (UTC)

It's not taught in all probability courses, but it is taught in (almost?) all basic statistics courses. Michael Hardy 01:38, 23 March 2007 (UTC)

Michael and INic: Your statement that frequentism is taught in stats courses is puzzling to me. Do you mean that frequentist methods of statistical inference are taught in those classes? Of course that's true, but frequentism as a method of stat. inference (all those p-values, confidence intervals, null hypotheses, etc.) is quite different from frequentism as an interpretation of probability. Actually, after posting my comments yesterday I wondered whether Quiggin was using "frequentism" to refer to frequentist statistical methods. That would explain why he regards frequentism as a direct competitor to Bayesianism. It is all rather confusing, as R.A. Fisher (the founder of frequentist stats) was strongly drawn to the ideal of objectivity in stats, and so (I would guess) used some sort of frequentist interpretation of probability. But in this article we need to distinguish clearly between interpretations of probability and theories of statistical inference/ confirmation. They are quite different projects.--64.180.160.210 17:52, 23 March 2007 (UTC)Richard Johns

I'm not sure that we can say that the projects are that different, really. I would say that they are just the opposite sides of the same coin; one philosophical/ontological and one practical/methodological. And the dependence between the projects is even closer in the "frequentist" case because here the current philosophical definition is via the statistical methods used (and hence, here we get some different philosophical sub-schools due to the existence of some competing statistical methods). In the Bayesian camp they also say that the connection between philosophy and practicality is very close, as they claim that their statistical methods can be derived from their respective ontological core theories. But nevertheless, I agree with you that this article should stress the philosophical side of the matter. iNic 01:43, 25 March 2007 (UTC)

INic: I'm glad we agree that this article ought to focus on the meanings of probability rather than on theories of statistical inference that might be associated with such meanings. That's all that matters here, I think. I think I'll go ahead and make some changes to refocus the article on interpretations of probability.--Richardajohns 05:21, 3 April 2007 (UTC)

Your introduction is good; we need a general introduction like that. However, the traditional classification of interpretations into subjective and objective is a little bit misleading I think. Not all Bayesian interpretations are subjective. In fact, most of them try really hard to get rid of the subjective label by introducing a theory only applicable to rational men for example. Some even claim that Bayesian probability is more objective than reality itself, as it ought to be viewed as a natural extensions to logic. And current frequentist interpretations have been criticized for not being absolutely objective; the statistical methods and models used at a particular instance are ultimately due to the personal judgement of the statistician herself. Bottom line is that I don't know if modern frequentists ever claimed that they are absolutely objective, nor do I think that most Bayesians claim that their theory is absolutely subjective. Therefore, I think we obtain a better characterization of the two groups of interpretations if we instead stress that in one of the groups "probability" is always tied to a conceptual experiment, while in the other group "probability" is always tied to the concept of a statement in a language. iNic 14:24, 4 April 2007 (UTC)

Well, you're right that the terms "objective" and "subjective" aren't without difficulty. As you point out, the subjective interpretations include epistemic and even logical probability, which aren't subjective in the sense that they are subject to rational standards. But they are still subjective in the sense that they depend on the belief or knowledge of a thinking subject, albeit an idealised one. Moreover, tying probability to a statement in a language doesn't make it subjective in this sense. After all, physical outcomes of experiments can also be expressed in statements. "Personal" is another option, but it's probably worse that "subjective" for seeming to be beyond the realm of rationality.

Perhaps it should be changed to something like: "Subjective probability, on the other hand, can be assigned to any statement whatsoever, even when no random process is involved, as a way to represent its subjective plausibility, degree of support by the available evidence, or rational degree of belief". (?)

As for "objective", I don't think we want to replace it with "experimental", as objective probabilities apply to events outside the lab, beyond human control. (E.g. the probability that a 40-year-old Canadian will die in the next year.) I guess you're right in saying that frequencies aren't necessarily all that objective, as there is always the problem of choosing a suitable reference class, but the idea in the introduction is just to give the basic outline, and worry about the details later. The formulation I came up with, that objective probabilities "reveal themselves when a type of event occurs at a persistent rate, or relative frequency, in a long run of trials" is based on a paper by Jerzy Neyman "Frequentist Probability and Frequentist Statistics", Synthese 36 (1977) 97-131. He stresses that the frequentist concept of probability is founded upon the apparent stability of relative frequencies. Frequentists and propensity theorists of all stripes should be happy with that, I think.--Richardajohns 01:35, 5 April 2007 (UTC)