Talk:Frequency probability/Archive 1

From Wikipedia, the free encyclopedia

Archive This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

I, Martin, am the author (U129960) of the corresponding h2g2 text.

Do you mind if I add some more text to this article, as it's rather short? --INic 23:20, 16 Jan 2005 (UTC)

I deleted some stuff that was wildly incorrect. It was about Bayesians having to set priors by means of a reference set, and there being a problem associated with the difficulty of doing this. There is nothing in the works of De Finetti, Lindley or Savage about this. It's just not an issue. Bayesians are not required to set priors this way, nor are they prohibited from doing so.Blaise 10:11, 1 Mar 2005 (UTC)

The article asserts that "Since the 18th century, there has been a debate between frequentists and Bayesians." Is this true? I thought that statistics was essentially Bayesian statistics until the late 19th century, and that frequentism arose about then. Bill Jefferys 20:01, 29 August 2005 (UTC)

I deleted that since it's wrong. Bayesianism is a very recent phenomenon, around 1950. Frequentism is as old as the oldest insurance company (antiquity), but was stated explicitly for the first time as late as 1866 by J Venn. INic 01:23, 15 October 2005 (UTC)
I don't think practice before the 19th century can be claimed as being either frequentist or Bayesian. There wasn't even an explicit notion of probability in antiquity - you can work out an argument for insurance based on symmetry without using probability. And, as the article says, frequentism was worked out because of the weaknesses of the symmetry-based principle of indifference. So, Bayesianism is about 50 years old, and frequentism about 150 years old.
I agree with you here. However, dice is as old as mankind. Some of the most popular ones were small bones from sheep for example. They have an irregular shape. To be able to estimate how to play those games symmetry arguments won't work. I guess it here all boils down to how rational you think that our ancestors were if they considered frequencies or not. If someone did frequentism is very very old. INic 22:37, 8 May 2006 (UTC)

What we are calling Bayesianism has been gradually formalised with the work of Frank Ramsey in 1929 and others since, most especially Savage (1950's), de Finetti (1960s) and Lindley (1960s). Their work draws on ideas expounded by Laplace and Bayes in the 18th century. What we are calling frequentism was formalised in the early 20th century by von Mises, Fisher, Neyman and Pearson, though their work draws on ideas going back to Pascal and others in the 17th century. Blaise 18:23, 5 May 2006 (UTC)

Contents

Bayesians and others in the minority

"Frequentism is, by far, the most commonly held view among working statisticians, probability theorists and physicists." Would anyone care to elaborate on some of the less commonly held, but yet still widespread views of those in the field? I'd be interested to see it here.

There are already pages devoted to other schools of thought, referenced here under the See also heading. Including a page comparing "all" different schools (some schools are missing, though). INic 02:21, 17 February 2006 (UTC)
Bayesianism is the most important alternative (and the dominant viewpoint among decision theorists). The page on Bayesianism includes extensive discussion of frequentism as it should. The "See Also" link is useless to a reader who does not already know this. Deletion of reference to alternative points of view is not consistent with NPOV. JQ 00:23, 1 May 2006 (UTC)
It makes no sense to single out Bayesianism as the only alternative to frequentism. It is, however, important to mention the classical interpretation of probability here as frequentism was developed as a reaction to that interpretation. Likewise, Bayesianism started as a reaction to frequentism why it makes sense to talk about frequentism at the Bayesianism page. However, Bayesianism is not the only reaction to frequentism why the sole mention of Bayesianism as an alternative here would violate NPOV as well as fooling the reader. INic 18:28, 2 May 2006 (UTC)
I'm not aware of any alternatives with currency similar to Bayesianism. It's not true to claim that classical inference is favoured by probability theorists, as opposed to statisticians. Certainly, in econometrics, which is a major field of applied statistics, Bayesianism and frequentism (commonly called classical inference, just to confuse things) are the only viewpoints discussed in standard texts. If you want to write a brief NPOV summary of the main alternatives, go ahead. Otherwise, repeated deletion of alternative viewpoints in the way you have done in this article is POV. In the absence of a summary of alternative viewpoints, I suggest the best thing is to restore the reference to Bayesian theory, and wait for people who want to write about any other alternatives to do so.
What's the point having an extensive list of all different alternatives here? In that case, to be consistent, the same list should be appended to every article about any interpretation of probability. A better idea is if we have that list in an article of its own that every article about any interpretation can refer to, don't you think? Well, that's actually the case already. The article is called probability interpretations and is (or should be) referred to by all articles about any specific interpretation. However, I certainly agree that that article can be improved! Many interesting interpretations are simply lacking there. INic 10:15, 3 May 2006 (UTC)
The probability interpretations article supports my point. There are two main viewpoints, frequentist and Bayesian. It's a straightforward application of NPOV that the article on each one should mention the other. I'm reinstating the deleted text on this. The other material I deleted was left over from some previous discussion and makes no real sense as it stands.
That one article at wikipedia is badly written can never support the claim that other articles at wikipedia should be badly written too. Wikipedia is an encyclopedia and as such all sources should come from outside the encyclopedia itself. That you don't know of any other interpretations than frequentism and Bayesianism is a good argument why you should read an encyclopedia, not write one. INic 13:53, 3 May 2006 (UTC)
You have yet to nominate these other alternatives you keep referring to. How about doing so? JQ 09:48, 4 May 2006 (UTC)
I already did, at the relevant page for that discussion. INic 09:26, 5 May 2006 (UTC)
(The rest of this discussion moved here.)

Regardless of whether you can nominate other alternative views with significant currency (and its pretty clear you can't) deletion of alternative viewpoints is a serious violation of NPOV policy. Feel free to add reference to other alternatives if you want. If you delete reference to Bayesianism again, I'll be calling for administrative intervention. Note that you have violated Wikipedia policy quite a few times, for example with the remark "That you don't know of any other interpretations than frequentism and Bayesianism is a good argument why you should read an encyclopedia, not write one." (You might want to check my Wikipedia entry before offering this kind of gratuitous slur). JQ 09:42, 5 May 2006 (UTC)

Another unjustified deletion from you. JQ 10:35, 5 May 2006 (UTC)

"Frequentism is, by far, the most commonly held view among working statisticians, probability theorists and physicists."

In my experience most working statisticians have little interest in the mathematical and philosophical foundations of statistics and will quite happily use a Neyman-Pearson hypothesis test one day and a Bayesian belief network the next. They are most likely to use whatever is on the GUI of their preferred software package, and (for the moment) this is unlikely to be Bayesian. Many applied workers have simply never been taught Bayesian statistics (though this is changing), perhaps because it requires more mathematical knowledge in order to grasp it. Probabilists that I have met tend to think that you can pick the probability interpretation you like, but what really matters is the Kolmogorov axioms. Any interpretation consistent with the Kolmogorov axioms is fine with them. Physicists have traditionally not been taught Bayesian statistics but this is changing fast and there is now a substantial body of physicists using Bayesian approaches. (Try a Google search on "BIPS" for Bayesian Inference in the Physical Sciences.) The only other approach I have come across as actually being preached (as opposed to ideas such as Fisher's fiducial probability that were preached in the past but no longer have an active body of supporters) is John Nelder's advocacy of the likelihood approach. The likehoodists are a very small bunch indeed. Blaise 19:02, 5 May 2006 (UTC)

I agree that a formalist view is probably the second most common view among pure mathematicians. INic 21:15, 8 May 2006 (UTC)

I've added the link to "BIPS" in Blaise's comment. I'll also remark that I'm aware of some other alternatives to Bayesianism and frequentism; for example, fuzzy logic and Dempster-Shafer theory. Fuzzy logic has quite a following, but to my knowledge, Dempster-Shaefer theory has never gained much of a foothold. Bill Jefferys 22:51, 8 May 2006 (UTC)

Fuzzy logic is certainly in use, but, like Dempster-Shaefer theory, it's an alternative to probability rather than a competing theory of probability. I'll follow up your links.JQ 00:10, 9 May 2006 (UTC)

Fuzzy logic is not supposed to be an alternative to probability. Its creator, Lotfi Zadeh, created it as a way of expressing imprecision. He later went on to create possibility theory as an alternative to probability theory, but which includes fuzzy logic as a special case. In practice, fuzzy logic practitioners often create fuzzy controllers which represent uncertainty (rather than imprecision) by fuzzy sets. Dempster-Shafer theory (sic) is widely taught in the artificial intelligence / machine learning community. It is becoming widely used by engineers working in the area of sensor fusion. Personally, I regard fuzzy logic, possibility theory and Dempster-Shafer theory as unsound approaches. Blaise 19:51, 14 May 2006 (UTC)

I agree with the points you make here, including scepticism wrt fuzzy logic. JQ 23:34, 14 May 2006 (UTC)

Stealth reversion

The last change by INic, described as "(fixed the sample space/events-confusion)" was in fact a large-scale revert. This is bad practice. I've responded in two stages, first reinstating the changes reverted by INic, and then correcting the erroneous description of events provided in the substantive edit. On the general question at issue, INic, an examination of the history shows that a string of contributors to this topic have agreed that it's necessary to mention both main views of the issue, as is done in Bayesian probability and Probability interpretations. You may disagree, but you can't just impose your view on everybody else. JQ 22:41, 8 May 2006 (UTC)

I'm not imposing my view on anybody. But why can't we leave the dicussion about the pros and cons of different views to the page devoted to that? There are quite a few views (not only two) to be considered. That there are only two views is a part of Bayesian propaganda, not a part of reality. The situation is similar to how communists use to argue. A typical communist claims that there are only two different economical systems: capitalism and communism. All flaws communists see in the capitalist system is then, logically, an argument for communism. This kind of rethoric is called "false opposites". The dangers of this kind of rethoric is when certain minds gets so into it that they can't think straight anymore. And it's really bad when encyclopedias are written by men in that confused state of mind. INic 23:27, 8 May 2006 (UTC)
INic, please note that a further reversion from you will violate 3RR. Regarding your response, it really isn't helpful to use analogies with communism - see Godwin's Law. In any case, no one (except you) is trying to censor references to alternative viewpoints. If you want other views to be considered, add reference to them. If you think no views except frequentism should be mentioned, you'll have to persuade other editors of this. Just reverting edits and abusing other editors is not going to get you anywhere. JQ 00:10, 9 May 2006 (UTC)
Please tell me what kind of analogies can be of any help to you, if any. If you read very carefully you will perhaps notice that frequentism is not the only interpretation mentioned in the article. INic 13:31, 10 May 2006 (UTC)

Vandalism ??

INic, if you're calling Michael Hardy a vandal, then you have seriously lost the plot.

Get a grip.

You appear to be in a minority of one here, with both frequentist- and Bayesian-leaning contributors feeling that the idea of "frequency probability" would be made sharper, more explicit and more readable by discussing what it is that the frequentist position rejects (and why), rather than making deletions like this -- which I can't help but find as being at about the level of "la, la, la. I can't hear you" for childishness.

I would ask you to undo your deletion, apologise to Michael Hardy -- and never slight an honest edit like this as "vandalism" again. -- Jheald 14:00, 10 May 2006 (UTC).

Anyone that deletes the very definition of frequency probability from the article about frequency probability does nothing to improve the article, quite the contrary. And even if it were the Pope that did the deletion that would be poor comfort to anyone looking in vain for the definition, believe me. The Pope and others have to excuse me for holding this maybe heretical standpoint. INic 21:17, 10 May 2006 (UTC)
That said I do agree with you that this article can be improved in many ways. I would, for example, like to see:
  • Its relation to the classical interpretation. An explanation of how frequentism solved the various paradoxes of the classical interpretation. How frequentism managed to extend the concept of probability outside of the gambling houses without introducing new paradoxes.
  • Its relation to probability theory. How von Mises very important concept of a sample space was extended by pure mathematicians to measure theory, and how that in turn was essential for Kolmogorov to find a complete set of axioms for the mathematical theory of probability.
  • Its relation to statistical practice. How frequentism bridged the gap between statistics and probability theory and thereby improving both diciplines enormously.
  • Its relation to the physical sciences. How the frequentist notion of randomness have been accepted totally by the physical sciences.
  • Its unsolved problems. The different proposals to define a frequency probability in a philosophically satisfactory way.
The first section here would give a clear answer to your question about what and why the frequency interpretation rejects to assign probability to certain situations. The last section would give an overview of the real serious problems that frequency probability still faces. Contrary to public opinion, the difficulties frequentism have are not at all connected to bayesianism. INic 21:17, 10 May 2006 (UTC)
INic, your edit described as "removing propaganda" managed also to revert discussion of the sample space and events, which are crucial to any understanding of the issue. Was this accidental, or a reaction to the fact that I corrected your erroneous claim that all subsets of the sample space are events? Either way, it was a very bad edit, coming close to vandalism. JQ 20:43, 10 May 2006 (UTC)
My edit "fixed the sample space/events-confusion" incorporated your correct observation about the sample space and event definitions (but with the sigma-agebra part removed). However the edit that I later called "vandalism" removed the definitions of these concepts altogether. INic 21:44, 10 May 2006 (UTC)

INic, are you suggesting that I deleted the definition of frequency probability? Michael Hardy 21:26, 10 May 2006 (UTC)

Yes, and you introduced a definition that is not correct. INic 21:47, 10 May 2006 (UTC)
INic, it was your own edit warring, merging the definition into a para that you were reverting, that caused the problem. You should stop editing this page until you're willing to work co-operatively with everyone else.JQ 22:02, 10 May 2006 (UTC)
My suggestion is that we first discuss the contents of the page here, in a civilized manner, instead of the edit war-strategy you and others have adopted. This is especially true if the war-strategy is too fast for you, so fast that you don't know exactly what you delete. Please don't hold me responsible for neither the choice of the war-strategy itself nor your inability to read the text you delete in the heat of the battle. INic 22:30, 10 May 2006 (UTC)

Just a quick warning from the outside world... edit summaries accusing other people of vandalism are not a good idea when what you really mean is Content Dispute. Baseless accusations of vandalism amount to violation of WP:NPA and just aren't necessary or at all helpful William M. Connolley 22:58, 10 May 2006 (UTC)

INic, would you explain why you regard the definition I wrote as incorrect and what differences between yours and the one I wrote you consider important? Michael Hardy 23:10, 10 May 2006 (UTC)

Your definition lacks a reference to an experiment. Without an experiment (= a set of written instructions how to proceed in the lab for example) you don't know what to repeat. And if you don't know what to repeat you can't measure any frequentistic probability. Then you have to define the different outcomes of the experiment, the sample space. Without that clearly defined the probability is still undefined. Your definition lacks that too. An event is simply a subset of the sample space that you want to measure. There's nothing random about the events. Further down JQ have added his version of a definition where he mentions both random experiment as well as sample space. Both "random" and "experiment" should be stressed with links, I think, as they both are very important concepts in this context. Then JQ mentions the requirement of a sigma-algebra which is a little bit off topic here. That has to do with the measure theoretic concept of probability which is only indirectly connected to frequency probability. This should be explained separately if included here at all. After this JQ defines frequency probability as the "limiting" relative frequency. Actually some frequentists have defined it as the limit, others have not. Thus to be general here and not exclude anyone prudence demands that the word "limit" should be avoided. INic 00:25, 11 May 2006 (UTC)

Can you give examples of frequentists who don't use a limiting frequency definition? Does this mean that the observed frequency in a finite sample is the probability? JQ 04:14, 11 May 2006 (UTC)

Russell and Neyman have finite frequency probability definitions, for example. Please see the references in the article. Please don't contribute to articles if you only have a shallow understanding about the subject matter. INic 13:37, 11 May 2006 (UTC)

INic, as you've been advised on many occasions, please avoid personal abuse of this kind. Read WP:NPA. As regards Russell, his discussion of the issue [[1]] scarcely supports your claim. If Neyman offered a definition other than limiting frequency (and I'd be interested to see a proper, preferably linkable citation supporting this claim), it has very little currency today. The correct approach is to give the limiting frequency definition then note (with citation) that some frequentists offer a finite sample interpretation. On another point, while generally an improvement, your latest edit reinserts the erroneous claim that all subsets of the sample space are events.JQ

With any sample space is associated a family of subsets, called events. Where did the definition of a sample space go? It just "happened" to be deleted once again, or what? I really don't care why you repeatedly destroy this article, if it's on purpose (vandalism) or due to ignorance (shallow understanding), all I care about is that this article should be as accurate as possible. If you found a set of wikipedia rules to the effect that I can't maintain accuracy here, I've found another wikipedia rule I think beats the ones you've found. Read WP:IAR INic 02:52, 22 May 2006 (UTC)

Regarding Russell and Neyman, I'm not referring to any executive summary of thier accounts found on the web. I'm referring to the very books they have written. I'm pretty sure you have a library close to where you live. Please try that instead. INic 02:52, 22 May 2006 (UTC)

In the case where only finitely many outcomes are possible, all subsets of the sample space are normally considered as events. More generally, the family of events is required to be a σ-field, closed under countable union and intersection. The family of subsets called events need to be a Boolean algebra only when defining a measure P over that family of sets. This procedure can, in turn, be generalized to both countable and uncountable infinite families of sets. All this is, however, pure mathematics and is a little bit off topic for this article, as I've told you before. If included here at all it would be apropriate to have it in a separate section explaining the crucial impact the philosophy of frequency probability have had on pure mathematics, via the concept of a sample space. However, as it stands now this is both confusing and in a strict sense wrong. INic 02:52, 22 May 2006 (UTC)

The relative frequency of occurrence of an event, when repeating the experiment, is the probability of that event. Frequentists normally define the probability of an event as the limiting frequency when the number of repetitions is arbitrarily large. Where have you found the first definition? I have never seen that and I doubt that anyone have ever said that. The second sentence is wrong too. This is not how frequentists in general define probability at all. Reichenbach and von Mises had definitions in that direction, but that is not how any current frequentist define probability. INic 02:52, 22 May 2006 (UTC)

For example, a frequentist would refuse to assign a probability to the proposition that there was life on Mars a billion years ago, since it is impossible to say that that happens in some particular proportion of trials. Why repeating the same argument twice? Do you want this article to be invaded by martians? Well, if you do at least be sure to invade the right paragraph. The martians example, as we all know, illustrates the fact that we need to define a random experiment and a sample space in order to talk intelligibly about probabilities. Therefore the martians example should illustrate the preceding paragraph in the article where these concepts are defined (or should have been defined), not the one introducing frequencies where you've put it. That is, if included in the main article at all. As I've told you before I think it's appropriate that all material in the main article is supported by the bibliography. INic 02:52, 22 May 2006 (UTC)

While there are some useful points in the above (and I've responded to a couple), the general tone is not very helpful, and it's often not clear what you are trying to say. I'm still not clear, for example, whether you are denying that the probability is equal to the limiting value of the relative frequency (the only frequentist definition I've ever seen, and one that can be found in dozens of variants by Google, or by looking at standard texts if you prefer) or whether you are making some more subtle distinction. Perhaps you could assist things by quoting a definition (with citation details) that you agree with. But it should be clear to you by now that the combative stance you've adopted is counterproductive. JQ 05:29, 22 May 2006 (UTC)

To say that I'm "often not clear" in what I "try to say" while giving only one example of that isn't very helpful either. Please tell me what else you find unclear in what I've said. INic 02:41, 23 May 2006 (UTC)

You still seem to defend the stance that what you haven't read or seen on the web doesn't exist. If wikipedia easily could be replaced by a Google search there wouldn't be any point having it, would it? I still urge you to read the books mentioned in the bibliography. However, if there are any additional "standard texts" you think should be added to the bibliography, please let me know. INic 02:41, 23 May 2006 (UTC)

Wikipedia is an encycolpedia where the text in the article, as objectively as possible, should reflect what is found in the bibliography of the article. In the current bibliography you will find different proposals how to define frequency probability. It's a still ongoing philosophical debate without any current winner. It's thus definitely not a good idea to claim that one of these proposals is the "correct" one in the article. Nor is it a good idea to mention the one (if any) I happen to "agree with" in the article. My personal views are totally irrelevant in an encyclopedia—of course. The correct approach, I think, is to describe what a frequency probability is in a manner that is so vague that all writers would agree. That is what I've tried to do. INic 02:41, 23 May 2006 (UTC)

"The correct approach, I think, is to describe what a frequency probability is in a manner that is so vague that all writers would agree." I disagree. The correct approach, if there are conflicting definitions, is to state them and show the way in which they disagree. I've made a start by locating (what appears to be) the original use of the term by Kendall, and citing that paper, via OED. Why don't you extract some representative definitions from the bibliography, illustrating differences regarding whether it is necessary to take limits JQ 03:16, 23 May 2006 (UTC)

You don't seem to know the difference between an encyclopedia and a dictionary. However, I've already stated above that I think it would be fun to include a section describing, as briefly as possible, the philosophical debate concerning the different proposals. But to be able to write that you have to both read and understand the books in the bibliography first. INic 10:00, 23 May 2006 (UTC)

INic, this kind of thing is very tiresome. If you read the thread above, you'll see, as a previous commenter has already said, that you're in a minority of one regarding your view that you are an authority on what an encyclopedia should be. Citing the titles of some books doesn't really get you very far in this respect - standard citation practices require page numbers if you're going to use books as authorities for specific assertions. Rather than engaging in one-upmanship, why don't you add some material that is more than POV advocacy for frequentism. For example, you've claimed a number of times that the development of measure theory owes a lot to frequentist theories of probability. If you could back this up with proper citations, that would be very interesting. Alternatively, how about a summary of Reichenbach and von Mises and how current frequentists differ from them? The article would certainly benefit from that JQ 11:33, 23 May 2006 (UTC)

For once I agree with you; this is very tiresome. Why can't you discuss the changes you want here before you make the edits? Your goal seem to be to mess up this page in a random manner without any other purpose than to make some damage. If you can't stand reading about frequency probability why do you do it at all? I would love to have a civilized conversation with you where we could discuss the sources together. But that you would read a book written by a frequentist seem to be totally unthinkable. I'm certainly not an authority and I never want to be one. But I can read and I do know how to use a library. If that is too much to ask for on your part please don't edit this page. When you calm down I will add the sections you want me to add, and some additional ones. With citations, including page numbers, of all the sources. I bet that will be interesting for you to read. But beware, to check those citations might require the ability to use a library. INic 23:37, 23 May 2006 (UTC)

"Your goal seem (sic) to be to mess up this page in a random manner without any other purpose than to make some damage. " Yet another accusation of vandalism, this time for quoting the originator of the term frequentism. You've already violated 3RR here, so please stop reverting immediately. Also note that waiting for the clock to expire and reverting again is a further violation, as are "edits" that amount to reversion. JQ 11:19, 24 May 2006 (UTC)

I note that you refuse to discuss all the recent changes you have done. INic 09:24, 25 May 2006 (UTC)

I'm happy to discuss changes if you agree to behave in a civil fashion. In the para above, you accuse me of vandalism, illiteracy, inability to use a library and so on - this is not the way to promote discussion. So, just indicate that you're going to behave in a civil fashion from now on, and we can work together. Regardless, why don't you just go ahead and add the discussion of von Mises and so on. As long as you avoid POV stuff about the superiority of frequentism, I would welcome this, and will not revert what you've done.

May I suggest that we start the discussion from scratch? INic 13:07, 25 May 2006 (UTC)

Restart

As soon as we agree on the sources appropriate for this article I think the rest will come naturally. Don't you? My suggestion of sources are listed in the bibliography where you have added one source lately. This source is new to me. Can you please tell me why you think this is an important source? Can you please tell me a little about M. G. Kendall and why you think he is important in the history of ideas? You have also talked about "standard texts" before. Can you please tell me what texts you mean by that? Is it something you think should be added to the bibliography? INic 13:17, 25 May 2006 (UTC)

As you might expect, the best place for a quick summary on Kendall is Wikipedia Maurice Kendall. His main relevance here is that he appears to have coined the term frequentist, which presumably makes his views on the subject of interest. As regards a standard text, I meant that we should refer to one or more modern texts on probability, and see how the frequentist concept of probability is presented there. I had in mind, say, Billingsley, Probability and Measure (it might also be useful to provide a more elementary reference, but I don't have a good one to hand). Early on Billingsley presents the Weak Law of Large Numbers and states that it provides the basis for the frequency conception of probability. This seems to me to be the standard current practice, and the one that should be stressed. In particular, I think the appeal of the frequentist approach depends heavily on the Weak Law. However, I agree that attempts to derive the frequency concept without reference to limits or convergence have been made and should be mentioned - Kendall would do as a source for this, since he includes a finite cases definition in his article. Perhaps it would be good to have a separate section on "history of frequentist thought", where von Mises and others could be discussed in more detail. JQ 22:42, 25 May 2006 (UTC)

OK, I read the paper by Kendall you refer to. There he argues for his own special blend of different interpretations. As I understand him he promotes a kind of principle of complementarity á la Bohr but for probability theory. However interesting his blend of existing ideas is, it doesn't make him a major contributor to the development of ideas in this field. In particular, he's not a contributor to frequency probability, at least not in this paper. Nor does the claim that he mentions "frequentist" for the first time in print merits him to be the only one with a citation in the article, even if it's true. This will at most merit him and this paper to be represented by a link under the "external links" section, as a curious etymological fact. Thus, I don't think this paper belong in the bibliography of the article. (And why we should have the Kendall paper as a secondary source for anything when the very primary sources he refer to already are in our bibliography is above my head.) INic 01:47, 31 May 2006 (UTC)

Billingsley's treatment is of a purely mathematical kind and is not concerned with the philosophy of probability. His comment about the weak law doesn't represent the modern view at all. It's there only to give the reader a feeling for the connection to frequencies; and at the same time explain why the theorem merits this peculiar name. In fact his comment is a good representative for the very starting point of the philosophical dicussion, not the end of it. Jacob Bernoulli in his Ars Conjectandi (1713) argued for the very first version of what later became known as the law of large numbers. He stated that we can be morally certain that the frequency of an event can be treated as a good estimate of the probability of that event, as one of his theorems showed that that has a very high probability indeed. A debate concerning the concepts of "moral certainty" and "moral impossibility" took off. We don't talk about these concepts anymore, but essentially the same debate is still alive. Hence, i don't think that Billingsley belong in the bibliography for this article. INic 01:47, 31 May 2006 (UTC)

If we should have a more modern book in the bibliography, which I think is a good idea, I propose we take Feller An Introduction to Probability Theory and Its Applications. Volume one has an introduction where he briefly describes what have become the frequency interpretation of choice for most current statisticians and probability theorists. INic 01:47, 31 May 2006 (UTC)

I agree completely with your last proposal; to have a separate section "history of frequentist thought" where the different ideas can be treated in more detail. This is precisely why I don't want to include the word "limit" in the first general definition of frequency probability. That word belongs only to the history section. INic 01:47, 31 May 2006 (UTC)

As a general comment, I think you have a pretty clear idea of your own view of what is interesting in this field, Wikipedia needs to take account of other perspectives. For example, you say of Billingsley that his "treatment is of a purely mathematical kind and is not concerned with the philosophy of probability" . From my perspective, probability is essentially a mathematical rather than a philosophical concept. The great thing with Wikipedia is that we don't need to resolve this one way or the other. Both perspectives (and others) can and should be presented.
Also, while Feller is an important work, it's not exactly modern. The 1st edition was in 1950 and Feller died in 1970. I think it's pretty clear that in recent decades, the limiting interpretation of frequentism has become dominant (try Google to check this). While it's be interesting and worthwhile to refer to the history, it's important to describe the way in which the idea is used now. To sum up, I'm happy to cite Feller, but we clearly need a more modern source and we can't avoid the mathematical aspects of probability.JQ 09:49, 1 June 2006 (UTC)