Talk:Frequentist probability

Classical statistics redirect

It is my understanding that classical statistics encompasses more than just the frequency probability interpretation, but also focuses on parametric statistics and statistical hypothesis testing. Also, while the Bayesian perspective on probability is an alternative to the frequentist perspective, I think that there are more "alternatives" to classical statistics than just the Bayesian perspective or paradigm alone. For example, nonparametric statistics is decisively non-classical, but it is not necessarily non-frequentist.

On these grounds I think classical statistics deserves its own page. Cazort 19:06, 3 December 2007 (UTC)

Statisticians that are frequentists doesn't have to agree when it comes to statistical practice, and often they don't. So yes, I agree that it's not entirely correct to link classical statistic to this page. I think the main reason why we have this incorrect redirect is simply that no one has started a page under that name yet, so please go ahead! :-) iNic (talk) 19:04, 27 May 2008 (UTC)

Life on Mars

I dispute this "Life on Mars" example... It is not because this thought experiment is traditionally used by the subjectivists to explain the way they think, that they mean this to be a case where you would not be able to solve the problem thinking in other paradigms. A good argument for subjectivism is not necessarily a good counter-argument for frequencialism. This smeels to me as naïve maniqueism.

I believe there is a lot of urban legend and misunderstood statements around the different interpretations of probability. I would like to see a quote from a sound book about probabilities, written by an author of either of the said-to-be-conflicting sides, where he actually says that he believes frequentism cannot conceive to attribute a probability to the existence of life in Mars 1000000 years ago. I am afraid that what is written here is just an echo of uncertain discussions at university cafeterias!...

This statement is controversial only because life on Mars is such a large thing, difficult to grasp. Now, imagine for example the [Alexander_Oparin|Oparin experiment]. If a frequentist can assign a probability to "Life in Oparin's bottle 50 years ago", why wouldn't he assign to "Life on Mars 50 millions of years ago"?

I dislike making such arrogant claims inside Wikipedia, but I believe the use of this Mars thing as being the epitome of the (said) difference between frequencialism and subjectivism is plain wrong. It lacks basis as much as my claims might... Please, let's find something more specific, something de Finetti might have said when contrasting his theories to others, and not when explaining his ideas by their own. Or else we are building and artificial dissent. I believe we are trying hard to find dichotomies to make things look simpler to understand, while the subject is in fact much more difficult. Mixing controversial subjects as life, geology and chaos only make things worse.

In other words: please, let's be careful not to pick up an example of how subjectivism works, and try to transform it in an example of why the paradigms might be different!... I feel someone was feeling bad about the lack of a good example that would contrast the two paradigms, and tried to build one from an example created with other intention. I don't buy it... Please tell me where this use of the “Life on Mars” problem as a way to contrast the two paradigms came from. I bet $0.87 that this did not came from any books by an author with a Wikipedia page, while I would bet $0,95 that such an author might have used the example simply to demonstrate how subjectivism works (and not contrasting). (sorry for the large and confuse posting...) -- NIC1138 (talk) 22:15, 8 March 2008 (UTC)

Yes I think it's silly too and I have tried to delete it several times before. However, there are some quite strong opinions among some authors here that we need to talk about martians on this page, otherwise this page gets too biased toward frequentism, they claim. Well this page IS about frequentism, isn't it? So please go ahead and remove it and we will see what happens. I would also like to know the source for this example about martians. I have never seen it in a book. It is for sure not mentioned anywhere in the books that are listed as references here. iNic (talk) 19:18, 27 May 2008 (UTC)

What kind of experiments?

Spurred by a remark at Talk:Probability#Interpretations that it is doubtful that frequentists only deal with experiments – any repeatable random process will do, even a natural one – I replaced "experiment" by "trial", which I think is standard terminology for an independent observation of an outcome of a repeatable random process. However, this change was reverted (also at Probability interpretations) with edit summary: Experiment in the ordinary sense of the word is exactly what is intended here. I'm not sure what the "ordinary sense" of the word is that is intended here. Is it that of our Wikipedia article Experiment linked to? It defines the notion as follows: "In the scientific method, an experiment ... is a set of observations performed in the context of solving a particular problem or question, to retain or falsify a hypothesis or research concerning phenomena." But someone repeatedly flipping a coin or throwing a die and observing the outcomes does in general not do that to retain or falsify a hypothesis. Determining what fraction of children dies before the age of one year by inspecting statistics will also usually not be considered to be an experiment in the sense of the scientific method. The examples of use of the word given at dictionary.com – a chemical experiment; a teaching experiment; an experiment in living; a product that is the result of long experiment; to experiment with a new procedure[1] – also do not fit well with what I think is intended here.  --Lambiam 13:28, 22 May 2008 (UTC)

The requirement that we need to define an experiment to be able to talk about probabilies at all is very central for the so called frequency interpretation of probability. It is more central for the frequency interpretation than frequencies themselves (which in fact are not required). An experiment in this context doesn't really differ from what we mean with a scientific experiment. An experiment is a set of complete instructions on how to perform some series of actions that will give the same result whoever performs them. In some cases a particular experiment always gives the same result, but in other cases different outcomes are possible. In the latter case, when the different outcomes doesn't depend on different initial conditions, we talk about random experiments. These random experiments can be understood and treated with the use of the probability concept. Not many disagree here. However, the Frequentists also reverse this implication by claiming that the probability concept can only be used in the context of random experiments.

A "trial" is just one actually performed random experiment and should not be confused with the experiment itself. Think of an experiment as the instructions for making a cake, and a trial is the actual cake you do when following the instructions, i.e., when performing the cake experiment. It is easily seen here that if you mix these concepts you might end up trying to eat the instructions, or read the cake.

Other central concepts in the frequency interpretation are design of experiments and hypothesis testing. It would, in fact, make more sense to call the frequency interpretation the experimental interpretation instead.

The Wikipedia article on what an experiment is is almost accurate, but not quite. An experiment is not a set of observations but rather a set of instructions that may or may not end up in some specific observations. If merely a set of claimed observations would count as a scientific experiment, well then observed UFO's with aliens onboard would be science, but it is not. The strict scientific approach is very central here. When determining what fraction of childern dies before the age of one year it is very important to design this experiment in the proper scientific way, for example by picking the children in a truly unbiased (randomized) way so that the result of the experiment will not be misleading. It is also very important to explicitly formulate a hypothesis before performing any experiment. To formulate a valid hypothesis after collecting the data is always possible and is therefore a flagrant example of violating the scientific method. So your comment about this example above is simply not true. Statisticians are commonly recognized as being scientists, in particular classical statisticians endorsing the so called frequency interpretation of probability. iNic (talk) 00:47, 23 May 2008 (UTC)

Let's take a concrete example. I'll be visiting Avignon, France in August, and want to know if I should pack an umbrella. If the chance of rain exceeds 25%, I'll pack one; otherwise, I'll risk it. So could I count what fraction of the same period in the years 1958 through 2007 were recorded for Avignon, France as having days with non-zero precipitation? What, in this case, is the experiment, and what is the hypothesis to be explicitly formulated before performing the experiment?  --Lambiam 15:09, 24 May 2008 (UTC)

Only pack your umbrella if you happen to have a very small one, otherwise I advice you to buy an umbrella in a store in France if you need to. Have a nice trip! Cheers iNic (talk) 21:36, 26 May 2008 (UTC)

Thanks for the advice. What about answering the questions?  --Lambiam 00:13, 27 May 2008 (UTC)

I did answer your questions above. If you use the links you can read more about the subjects you are interested in. However, as is the case with all science, if you really want to learn the craft you have to study the subject for some years at the university. In the process you will discover that science isn't religion, and can never be. If you want to find guidance for every step in life, like if you should bring an umbrella or not for a trip to France, in science you are looking in the wrong direction. Science can never give this kind of guidance to people in everyday situations. iNic (talk) 18:40, 27 May 2008 (UTC)

To me this is a condescending non-answer.  --Lambiam 19:18, 27 May 2008 (UTC)

OK it wasn't my intention to be perceived as condescending. I apologize in that case. I will try to explain what is wrong with your question about the umbrella. You indicate that metrological data for the city during the period 1958-2007 should give a good estimate for rain this year in that city. Sure, if you believe that go ahead and calculate this ratio and act accordingly. But is this frequentism? No. Is this science? No.

The problem is that I can claim that another ratio for rain is the correct one based on some other data (different time period, data from a larger area, or something completely different) and no one of us can really claim that one model is better than any other. And who knows, we might in fact measure exactly the same thing only that random effects make our result different.

In order to handle these issues and to be able to draw correct conclusions, different statistical tests have been developed. However, if all you know is one specific event (rain or not rain in a specific city this year) you will have way too little data (only one datum) to be able to test any hypotheses at all. This is why we need an experimental description so we can (at least in theory) reproduce the desired events as much as we desire. iNic (talk) 00:44, 28 May 2008 (UTC)

If you repeat "well-defined random experiments" you may also get different data. I want to estimate the probability of rain in Avignon during a specific week of August, and the best we can hope for is an approximation. If out of the 50 years 1958 through 2007 there was rain in Avignon in the period from 10 to 16 August in 14 of these years, it is eminently reasonable to use 14/50 = 28% as an estimate of the probability of rain in Avignon in the week from 10 to 16 August 2008. That is in no essential way different from estimating probabilities in "well-defined random experiments" by dividing the number of times an event occurred by the number of trials. Of course somebody can claim that one should instead use the meteorological data for Ouagadougou during March to give the "correct" result of 0%, but so what? Do you really believe that that claim is just as acceptable as the claim that 28% is a reasonable estimate?

If you think this is not "science", you agree with at least part of what I set out to change. But why is this not frequentist (other than your repeated statement that it isn't). Is there some frequentist manifesto that spells out the official frequentist creed?  --Lambiam 07:37, 28 May 2008 (UTC)

This is an old debate and you can read a lot about this controversy elsewhere. Your thoughts and arguments are clearly Bayesian in nature, not frequentist. The essential difference between them is that while Bayesians start with a question about a specific event and then gather information about that event in order to estimate a probability, frequentists go the opposite way by always starting with a class of events and a mathematical (probability) model for the class. This is an essential difference indeed. The frequentist manifesto you ask for is called the Kolmogorov axioms of probability. iNic (talk) 01:06, 1 June 2008 (UTC)

This is getting strange. There is nothing in the formulation of the Kolmogorov axioms that requires a notion of experiment, in the sense of the scientific method or otherwise. The essence of the pure frequentist view is that the probability of an uncertain event is by definition the frequency of that event based on previous observations, as the number of observations increases indefinitely. It appears that your interpretation of the frequentist interpretation as requiring to define an experiment to be able to talk about probabilities at all is more in your head than anywhere in the literature.  --Lambiam 18:07, 1 June 2008 (UTC)

Richard von Mises realized that we can't speak of probabilities unless some class of events is defined. He called this class the sample space, which is nothing more than all possible outcomes of an experiment. Kolmogorov, in turn, used von Mises concept of sample space as a necessary ingredient in his concept of a probability space. Probabilities as defined by Kolmogorov only exists on probability spaces. So in order to speak about probabilities we must have a probability space defined. And in order to have a probability space we must have a sample space, which are simply all possible outcomes of an ordinary experiment. As you can see this dependence on experiments is more fundamental than the Law of Large Numbers which is the canonical theorem within the theory connecting probabilities to frequencies. Very strange that you haven't seen anything of this in the literature you claim you have read. Can you please tell me which books you have read? iNic (talk) 23:42, 1 June 2008 (UTC)

For the Avignon case the sample space is a discrete two-element set, consisting of the well-defined mutually exclusive events "Precipitation was recorded in Avignon in the seven days from 10 to 16 August" and "No precipitation was recorded". The "experiment" of observing whether the precipitation event occurs is repeated each year, if one insists on calling this an experiment, but why should one do so? There is nothing in the concept of a sample space per se that ties the events to a notion of experiment as it is commonly understood. As in any axiomatic approach, the ingredients are essentially uninterpreted; whether the Avignon observations can be modelled by axiomatic probability theory is a matter of belief that can perhaps be bolstered by the success of similar assumptions in similar situations, but does not depend on whether the space is formed by the possible outcomes of an experiment in the sense of the scientific method, performed to test a hypothesis or such, or by the possible outcomes of a trial of any other well-defined and repeatable random process. It is incumbent upon you to come with citations from reliable sources that support the statement whose inclusion in the article you are defending. You could start with the references listed in any of our Frequency probability, Probability space, and Probability axioms articles.  --Lambiam 05:42, 3 June 2008 (UTC)

I'm not sure what you mean by "experiment as it is commonly understood." Anyway, if you want to delete the word "experiment" from the world of classical statistics you have to burn quite a few books. As I told you already some days ago the notions of design of experiments as well as hypothesis testing are very central to this subject, and consequently treated in a lot of books in this subject. But maybe Fisher was wrong when he coined his discipline "design of experiments"? Maybe he should have called it something completely different? But what? Any suggestions? When it comes to your umbrella example I totally agree with you that that isn't an example of proper scientific reasoning at all, and hence doesn't deserve to be called an experiment. At least we agree here. iNic (talk) 23:43, 3 June 2008 (UTC)

I mean experiment as the term is defined by the article it is hyperlinked to: "In the scientific method, an experiment (Latin: ex- periri, "of (or from) trying") is a set of observations performed in the context of solving a particular problem or question, to retain or falsify a hypothesis or research concerning phenomena. The experiment is a cornerstone in the empirical approach to acquiring deeper knowledge about the physical world." Why the rhetoric? There are many contexts in which scientists are trying to retain or falsify a hypothesis, and then it makes sense for them to design an experiment, and Fisher's methodology may well be helpful to them. There are many other contexts in which people try to obtain information that does not fit this description, and then it is not helpful to suggest that they should apply the scientific method, formulate a hypothesis, and design and perform an experiment, to retain or falsify it. The fact that it may often be meaningful to count how often an experimental event occurs, does not mean that everyone who wants to count occurrences of any random event must necessarily turn it into a scientific experiment. Pointing out that this is not a requirement does, conversely, not imply that everything having to do with experiments is pointless and should be scrapped. I'm still waiting for the references, but think I shouldn't hold my breath.  --Lambiam 03:21, 4 June 2008 (UTC)

Your stance is puzzling to me. At first you claimed that all talk about experiments in this context was something I had invented, as you couldn't find it "anywhere in the literature." However, you refused to tell me upon what literature you based this conclusion. Not even a single book. Instead you said that I have to quote someone talking about experiments in this context. This is not hard to do at all. On the contrary, the amount of literature here is vast. When pointing this out to you you changed your position and said that you never claimed that "experiments" wasn't central here, only that it didn't tell the whole story. Your only argument for the latter statement is that it isn't "helpful" to tell people, not interested in science, that they need to think in a scientific manner. Well, science doesn't care if people want to think in an unscientific manner. That's the way science works. If, for example, people in general are more interested in astrology than astronomy, well let them be that. Astronomers won't ever change their methods or results in order to be more "helpful" to people interested in non-science (astrology). Astrologers are of course free to use the precise scientific astronomical data and results in whatever manner they want, but that for sure doesn't turn them into astronomers (scientists). The same applies here. You are free to calculate relative frequencies using precise historical meteorological data, but that doesn't turn you into a frequentist (scientist). It is not the scientific instruments/data themselves that turn their users into scientists, the key factor is how the instruments/data are used. iNic (talk) 01:43, 14 June 2008 (UTC)

You may not have read carefully enough what I wrote. From the start I have made it clear that I questioned the word "experiment" as being used specifically in the sense of experiment in the sense of the scientific method, as suggested by the wikilink in he article, rather than a much looser notion, which however even in its looseness does not cover all things for which the notion of probability applies. Thereupon you confirmed and insisted that this scientific notion of experiment was indeed precisely the intended and required meaning, as amply supported by the literature. My subsequent request for citations was, clearly, for citations that support the claim that the frequentist interpretation requires one to define an experiment to be able to talk about probabilities at all. Of course the word "experiment" is used in the literature, but where does a text espousing frequentism formulate a requirement of the following nature: "to be able to talk about probabilities at all, the scientist must first define a well-defined experiment"? I stated that I had not been able to find this. As to the quality of my arguments: they appeal to what I think is common sense, but if they fail to convince you, what counts in Wikipedia is verifiability, not truth. Does it matter where I could not find support for an uncited and challenged claim? I think it does not. Just tell me where I should look to find it.  --Lambiam 21:18, 15 June 2008 (UTC)

Are we living on the same planet? When I go into a bookstore and pick a book at random from the statistics shelf they always have the scientific method, design of experiments and hypothesis testing as central themes. For example, see Statistics Explained by Steve McKillup from 2007. What kind of books do you find when you visit a bookstore on your planet? Do you find books where they also investigate unscientific experiments? Or maybe unscientific "trials"? Unfortunately, I can't find books of that nature on my planet.

Either you read the same books I read but in a completely different way. Or you read some other exotic books only that you don't dare to tell me which they are. Or you don't read any books at all and base all your strong opinions on your personal version of "common sense." But, as you point out yourself, Wikipedia isn't based on "common sense" but verifiability only. So please do not base any further edit in Wikipedia on your feelings alone. iNic (talk) 02:53, 17 June 2008 (UTC)

I am awed by your capability of not understanding me, in spite of the essential simplicity of the issue. In mathematics, words such as natural and complex may have a specific technical meaning, as in "complex conjugate" or "natural transformation". However, that does not mean that every use of these words in a mathematical context has the same specific technical meaning, or even has a technical meaning at all. This does not mean that other uses of these words are "unmathematical"; it only means that they do not have that specific technical meaning and in many cases it would be misleading and inappropriate to link an occurrence of the word "complex" in one of our mathematics articles to the article on Complex numbers. Likewise, the word experiment can be used with a rather specific meaning related to the so-called scientific method, in which the scientist formulates a hypothesis concerning natural phenomena, and then devises an experiment to test the hypothesis. In many cases, the hypothesis testing involves statistics, and in fact much of statistics revolves around hypothesis testing. However, that does not mean that every use of the word experiment in the context of statistics has that specific meaning of being an experiment devised to test a formulated hypothesis, and should be linked to the article we have on the topic. When a statistics textbook describes the scientific method and hypothesis testing, then of course the text will use the word experiment for the notion of experiment in the sense of the scientific method. I do not deny and have not denied that the word is in active use in that sense. Therefore, pointing out that there are texts that use the word in that specific sense when describing the scientific method is pointless. What I do challenge is that every use has that sense. You are being disingenuous by suggesting that any use of the word in any other sense is tantamount to saying "unscientific experiment". What I challenge, more specifically, is that the frequentist interpretation of probability is described in the literature as requiring a "random experiment" where the word "experiment" is used exclusively in that sense of having been devised to test a hypothesis. Throwing dice and observing how often the "6" event occurs on a long run fits perfectly well with the notion of frequency probability as described in the literature, but a random trial of throwing a die, if you choose to call it an "experiment" at all, is not an experiment performed in order to test some hypothesis that may subsequently be confirmed or rejected depending on the outcome.

All I'm asking for is a quotation from a reliable source, which may be from the planet Earth, that makes it clear that the notion of frequency probability requires an experiment in the sense of the scientific method. Quotations that merely show that such experiments can be subject to statistical hypothesis testing do not cut it.  --Lambiam 09:47, 20 June 2008 (UTC)

I have given you tons of references already, but none of them is good enough for you. If authors like Fisher, von Mises, Kolmogorov, Venn, Feller, Cramér and McKillup aren't defining what is meant by frequency probability (reliable sources) on your intellectual planet, can you please tell me which authors are? If you're not simply pulling my leg you must read some quite exotic literature feeding you with (des)information about frequentism. As long as you don't dare to tell me at least the names of these bizarre authors I can't even begin to understand your twisted view of things, and it's in fact hard to take you seriously. iNic (talk) 23:36, 20 June 2008 (UTC)

Can you give titles and page numbers? For example, on which page of Statistics Explained does McKillup discuss the specific probability interpretation known as frequency probability (or, for that matter, any probability interpretation)? Of course, it is hardly a surprise that a book explicitly addressing scientists as its audience discusses scientific experiments in the specific sense of scientific experiments, and, as I have stated already many times before in this discussion, and presumably will repeat many times in the future, I reiterate that I agree that the term "experiment" is frequently used in the sense of "scientific experiment", also in the context of statistical testing. So this is not in doubt, and you do not need to convince me of that, as I believe, know, am aware of, perceive as true, understand, fathom, grasp, and recognize, that many authors writing on statistical testing have referred to and extolled the virtues of specifically scientific experiments in heaps of reliable and authoritative publications. But what I, somehow, am unable to find in the publications of all these eminent statisticians and probability theorists that you have referred me to now more than googolplex times, is where exactly they require, for a frequentist to even discuss probabilities, that they are dealing with an experiment.  --Lambiam 23:18, 26 June 2008 (UTC)

Aha OK. The content in statistics books like that by McKillup defines what "frequency" probability is. It's nothing more, nothing less. You can start to read chapter 2 in McKillup, called "‘Doing science’ – hypotheses, experiments, and disproof." It starts at page 7 and you can read the rest of the book from there. If you have read the Wikipedia article we are discussing now you should know that the "frequentist" view is the default interpretation of probability. This means that modern statistics books usually don't say anything about any specific interpretation but are nevertheless frequentist. And frequentists rarely call themselves "frequentists" anyway. They refer to themselves as statisticians, probability theorists or simply scientists. "Frequentist" is a label invented and used mainly by Bayesians when talking about those who adhere to the main interpretation of probability (compare "gringo"). For these reasons alone you will not find the kind of statement you stipulate a priori should exist above. Instead, to repeat, the requirements for a frequentistic use of probability is defined by the statistical tradition as described in statistics books like the one by McKillup. iNic (talk) 00:09, 30 June 2008 (UTC)

In Statistics Explained, An Introductory Guide for Life Scientists by Steve McKillup, we find on page 46, Box 5.1 "Basic concepts of probability":

The probability of a particular event is the number of outcomes giving that event, divided by the total number of possible outcomes. For example, when you toss a coin there are only two possible outcomes – a head or a tail. These two events are mutually exclusive – you cannot get both. Consequently, the probability of a head is 1 divided by 2 = ½ (and thus the probability of a tail is also ½).

Are you sure McKillup defines what frequency probability is? This looks awfully much like the classical definition of probability (and under this definition any coin is – by definition – a fair coin). The claim that McKillup's interpretation is frequentist (which I doubt) rests on your assumption of McKillup's tendency, not on something we can verify. Reading from page 7 onwards does nothing to convince me that McKillup requires a notion of scientific experiment as a prerequisite for talking about probabilities, but merely that he thinks the scientific method is the basis for doing science. The chapter and the next two don't even mention "probability". At best I can see that McKillup apparently believes that the notion of probability is useful for statistical hypothesis testing, something with which I agree but which is not the issue. And Box 5.1 convinces me that, in fact, McKillup, whether a frequentist or not, does not at all require a scientific experiment to define the notion of probability.

I have asked for simple citations to back up a disputed claim – standard Wikipedia procedure. You have responded with a string of names of scientists upon whose authority the claim supposedly rests, in a tone as if my request is obviously unnecessary and annoying. Now you tell me that such a statement can't be expected to be found anywhere – it rests on a two-tiered process of interpretation. First, we have to read some author's text to ascertain (by our interpretation) that the author is a frequentist, since they don't identify themselves as such. Then we have to glean, between the lines, from our interpretation of how they handle the concept of probability, that they talk about probabilities only when dealing with scientific experiments, the latter in the sense of the scientific method. That is two levels of interpretation too many. If it is indeed true that frequentists talk about probabilities only when dealing with well-defined random experiments, then surely there is a more direct and verifiable way of supporting that statement. Or is this Wikipedia article really the first source to observe this fact?  --Lambiam 08:18, 4 July 2008 (UTC)

Look Lambiam, I'm not here to teach you anything or tell you how to read books. As you don't have a clue what this article is about just leave it as it is. iNic (talk) 22:39, 9 July 2008 (UTC)

Well, this discussion has been closed for a long time and I don't want to reopen it. Nevertheless, I'd like to point out that referring to the page on "experiment" when talking about a "random experiment" is misleading. The latter has a specific and distinct meaning from the former (it roughly refers to an experiment, trial, observation, ..., that can be repeated under the same conditions (as far as the experimenter can judge), and such that the outcome of one experiment does not influence that of the others). I find it very surprising that there is no page on wikipedia where this concept is introduced, as this is the concept underlying virtually all probability/statistics textbooks. —Preceding unsigned comment added by 84.73.155.58 (talk) 07:44, 13 October 2009 (UTC)

Yes, on the surface it might seem to be two quite distinct uses and interpretations of the word 'experiment.' But the difference is illusory. For Fisher, who introduced 'experiments' into probability theory and statistics, this concept and the ordinary scientific concept is exactly the same. So that he didn't invent a new name for his new concept is no coincidence. According to Fisher, designing a good random experiment guided by his rules should be synonymous with performing a good experiment in any science that can (or should!) collect statistical data. Thinking statistics is thinking science and thinking science is thinking statistics, according to Fisher. I agree that this close connection to modern probability theory and statistics should be highlighted in the article about experiments. iNic (talk) 23:57, 13 October 2009 (UTC)

History

I've dropped-in the beginnings of a history-of-thought section. Unfortunately, while I'm familiar with some of the important frequentists after Venn, I don't really know how they properly fit-together historically, nor do I have familiarity with all of them. (At present, for example, I don't know much about George Chrystal.) —SlamDiego_←T 18:13, 22 December 2008 (UTC)

A history section is a good idea. I'll try to contribute here. But who is George Chrystal? Or rather, what did he do in this field. Never heard that name in this context. iNic (talk) 02:54, 25 December 2008 (UTC)

I'm about as puzzled as you, but I've encountered multiple references to Chrystal as somehow the next important figure after Venn in the history of frequentism. I haven't yet read what, exactly, Chrystal is supposed to have done (and I've been at other things, and not pursued the issue diligently). —SlamDiego_←T 09:24, 25 December 2008 (UTC)

OK, but I have never seen his name in this context. And as long as you don't inform me which references you refer to I can't include anything about this man in the article. iNic (talk) 21:44, 26 December 2008 (UTC)

Chrystal's work in question was “On some Fundamental Principles in the Theory of Probability” (Transactions of the Actuarial Society of Edinburgh new series 2 (1891), 421-439) and Algebra. It is referenced in such works as Fisher's Statistical Methods and Scientific Inference, as Probability Theory editted by Hendricks, Pedersen, & Jørgensen, and as Zabell's Symmetry and Its Discontents. (I've seen many references to Chrystal's work on probability; but, again, I've not pursued the issue.) —SlamDiego_←T 10:16, 27 December 2008 (UTC)

OK thank you for the references. I'll check what this is all about next time I visit a library, which will be quite soon I hope. iNic (talk) 01:11, 30 December 2008 (UTC)

Good luck with that. Again, I know little more than that some authors treat Chrystal as significant, which doesn't even demonstrate that he really is significant, though it does strongly suggest it. —SlamDiego_←T 05:09, 30 December 2008 (UTC)

Actually…

The “Bayesianism” subsection of the “Alternative views” subsection is completely unreferenced. And it makes the claim

frequentists attribute probabilities only to events

Well, actually, Whitehead and Keynes explained how a frequentism could concern itself (non-trivially) with propositions. Keynes relates the idea in Ch VIII §9-10 of his Treatise. —SlamDiego_←T 22:56, 24 December 2008 (UTC)

Personally I think we should delete this paragraph altogether here, and just keep the link to further reading. But if there are strong opinions for keeping this text here I agree we need to add all the proper references. iNic (talk) 03:07, 25 December 2008 (UTC)

I agree that it would be better just removed, and that it needs proper citations if kept. But I would emphasize that it also needs to be corrected if kept. —SlamDiego_←T 08:17, 25 December 2008 (UTC)

This article is clearly the victim of a Bayesian drive-by, as evidenced by a "Alternative Views" section that only includes one alternative view. But the claim isn't completely wrong. The key frequentist for me was Fischer, who explicitly said that talking about the probability of hypotheses was nonsensical. He took a very hard line on the view that probability is a ratio of frequencies of a hypothetically infinite population of relevant measurable objects. For everything else, he talked of likelihoods. As Fischer was developing the null hypothesis significance testing framework, he was actively engaged in a debate with "Bayesians" about the definition of probability. I think this alternative views section should be deleted and replaced with a more complete explanation of the history of the debate and the reasons frequentists reject the Bayesian approach. --Thesoxlost (talk) 20:34, 25 December 2008 (UTC)

Yes, you are completely right about the Bayesian drive-by. If you take a quick glance in the archived talk page you will get more evidence of that. I also agree that we should add a historical section with the reasons why frequentists rejects the Bayesian approach. In any case we should never uncritically include accounts of frequentism by non-frequentists, like Keynes. iNic (talk) 22:07, 26 December 2008 (UTC)

No one here is proposing to uncritically include attacks on frequentism by non-frequentists. What Keynes (and Whitehead) did was to rebut a criticism of frequentism. The fact that the rebuttal is provided by a non-frequentist is secondary in importance and, if anything, strengthens the argument for attending to the rebuttal. —SlamDiego_←T 09:47, 27 December 2008 (UTC)

I removed the section as we all three here agreed that this is the best thing to do. This makes the discussion about Keynes account of frequentism obsolete. But what I tried to say was that it's dangerous to include accounts of frequentism by non-frequentists as they more often than not are bad ones, irrespective of their purpose. If cited at all they should be put into an historical context, but best is to avoid them altogether. iNic (talk)ñ

That may be fair enough. I've certainly not sufficiently surveyed non-frequentists talking about frequentism to deny it. —SlamDiego_←T 23:38, 30 December 2008 (UTC)

Calculus is not Metaphysics

Every time you find a vector you have an error too small to be written as a real number. This level of precision is math, not metaphysics. Even systems that do write it use extreme yet perfectly valid math. However gruesome it is to learn, the objectivity of frequentist probability is not undermined by extrapolating from an infinite series.108.65.0.169 (talk) 02:36, 12 September 2011 (UTC)

Merge from empirical probability

I've proposed a merge from empirical probability as these appear to be covering the same topic. Am I mistaken? linas (talk) 14:57, 5 April 2012 (UTC)

Yes you are mistaken. "Frequency probability" (its contents) is about the interpretaion/meaning of a quantity called probability. "empirical probability" is about a method of estimating a probability, no matter what interpretation is given to it. The existing "Frequency probability" might be better renamed to "Frequentist probability". 81.98.35.149 (talk) 18:05, 5 April 2012 (UTC)

Oh. But how does one tell? I, umm...., am unclear on the difference between "interpreting" and "estimating", in this context; what, exactly, is the difference? When does one do one, as opposed to the other? (The distinction between this and the 'classical interpretation' is clear as a bell, but the diff between frequentist and empirical, not so much.) There is another article, called frequentist statistics which is a bit more clear, although harder to read.

Some context: I've got a PhD in theoretical particle physics, and so know probability theory very well, as its used in physics, both quantum & stat mech. I've also studied measure theory (the mathematical axiomatization of probability) ... as well as dynamical systems e.g. ergodic and mixing systems. Did some combinatorics. Read about about urns and analytic combinatorics. So I feel (felt?) like I "knew everything there is to know" about probability theory... yet I've just now discovered these "interpretation of probability" articles which are rather muddy and unclear; I thought at first they were about history, but there seems to be some kind of controversy that is alive and well, but is hard to make out what, exactly, it is about... what the controversy is. So, coming from the math/physics world, and reading this stuff, its rather, umm... freaky and subtle, in ways that I'm not accustomed to thinking about. So I'm asking for clarification. I'm trying to say I'm not dumb, yet find this whole class of articles are hard to grok. linas (talk) 03:00, 6 April 2012 (UTC)

I understand that these philosophical controversies must be confusing to you. You are even somewhat surprised that they at all exists, right? It's a sad fact that it's possible in todays universities to study mathematics and physics at post graduate level and become a PhD in theoretical physics and yet know nothing at all about the philosophical foundations (and controversies) of these subjects. This is of course not your fault, only a logical consequence of the educational system we currently have in the western culture of today, where philosophy as a subject is for some strange reason looked down at. Anyway, this page is about one of the stances in the philosophical debate regarding what probability should or ought to mean, philosophically. The ontological content of the concept of probability, if you will. The probability interpretations article lists all major ideas. Maybe we should rename this article "Frequentism" to make this more clear? What do you think? iNic (talk) 16:47, 10 April 2012 (UTC)

Well, retitling hardly makes a difference to me, but if this is the common usage, then please do so. I am reading my way through this collection of articles, but honestly, it all kind of goes in one ear and out the other; the distinctions are blurry. I presume that there must be sharp, contrasting differences, somewhere, but these are not clearly illustrated in these articles. Bayesianism, in particular, comes off as new-age voodoo magic; I'm ... rendered speechless. Bayesianism appears to be widely accepted; surely there must be some way of describing it so that it doesn't sound like crackpot science?

Anyway, I've wandered off-topic. I'll remove the merge tag. However, to sharpen/clarify this article, I propose rewording the section ... err.. well, let me make edits directly to this article; please review and revert/correct these as needed? linas (talk) 22:28, 10 April 2012 (UTC)

Done. I think I've cleaned up the article, without altering its content.linas (talk) 23:36, 10 April 2012 (UTC)

Good changes! One exception though. The Scope section is harder to grasp now and also somewhat factually incorrect. It says that "at a superficial level it is not in conflict with the classical interpretation." Where did you get this idea from? It is of course not correct, whatever "superficial level" means. (In philosophy no one is interested in "superficial levels" anyway.) And no interpretation is in conflict with the Kolmogorov axioms, so that vacuous comment can be deleted as well. And frequentism is not an "historical" view. It is still the main view taught as the standard interpretation on all universities on this planet. iNic (talk) 13:28, 11 April 2012 (UTC)

OK, I reworded that section. Perhaps better now? Someone with a mastery of the material and a gift for writing must come by and elaborate; for now, I've just penned some evocative poetry to reserve the space, and get the imagination going of grander things to come.linas (talk) 17:12, 11 April 2012 (UTC)

P.S. Do you want to change the title to frequentism? Because that page already exists, this will require so administrative paperwork, request to move or whatever. The current title is awkward; even frequency interpretation or frequency interpretation of probability would be better. Any of these seem common enough per google. linas (talk) 17:20, 11 April 2012 (UTC)

PPS: here's a charmer: ArXiv: Its time to stop teaching frequentism to non-statisticians linas (talk) 17:25, 11 April 2012 (UTC)

Yes much better now, thank you. I vote for "Frequentism" as the new name for the page. It's currently only used as a redirect to this page so it should be no problem to make the switch. Your other suggestions are better than what we have too. Which name do your prefer? Very funny (and sad) article you found! By the same reasoning we should teach Aristotelian physics in school and only mention modern physics to PhD students... iNic (talk) 15:39, 12 April 2012 (UTC)

Frequentism is not a term that is used in either probability or statistics. It is certainly not appropriate to invent something new on Wikipedia. This article forms one of a set under probability interpretations, with Bayesian probability and classical probability, so a similarity of naming is useful. I have reverted the essentially undiscussed renaming ... if a renaming is still proposed then use the formal voting process. Melcombe (talk) 18:49, 12 April 2012 (UTC)

OK, the new page title is reasonable. "frequentism" is not a neologism, though, google shows plenty of hits. linas (talk) 19:38, 12 April 2012 (UTC)

"Frequentism" is indeed commonly used as the label for this view. "Frequentist probability" isn't that good I think. A Frequentist is a person adhering to Frequentism, so it should be "Frequentist's interpretation of probability" to be correct in that case. But it's clumsy. In the same way as "Liberalist's political view" is more clumsy than the equivalent term "Liberalism." iNic (talk) 22:35, 12 April 2012 (UTC)

The key to understanding the difference between "emprical probability" and "frequency probability" may lie in understanding the alternative approaches to what an "empirical probability" is try do. Such alternatives can involve fitting a probability distribution and then deriving an estimated probability for the target event from the fitted distribution. Melcombe (talk) 22:20, 13 April 2012 (UTC)

No, Frequentism is a philosophical view, not a technical term. Per se, it has nothing to do with fitting probability distributions to data. iNic (talk) 22:44, 13 April 2012 (UTC)

No yourself. I didn't say that frequency probability had anything to do with fitting probability distributions to data. The difference betweeen "emprical probability" and "frequency probability" is the starting topic for this thread/section, and I returned to it. Melcombe (talk) 16:44, 14 April 2012 (UTC)

Deletions

Melcombe, shortly after the article move, you also deleted sections that ascribed the the frequentist approach to certain authors. Why? Is this incorrect? Who, then, are the authors that are proponents of this approach? I mean, clearly, the frequentist approach is a paradigm shift, there was nothing wrong with that sentence. I just finished reading James Franklin's book on probability in the middle ages; although he never uses the words or the concept of "paradigm shift", that seems, to me, to be appropriate. Unless, perhaps, one rejects the very notion and correctness of the idea of a "paradigm shift", in general. Is that the issue? linas (talk) 19:38, 12 April 2012 (UTC)

I restored some of the random deletions. iNic (talk) 22:37, 12 April 2012 (UTC)

They were not random deletions. They related to the introduction of confusion between frequency/frequentist probability and frequentist inference, and to various unsourced statements of opinion. Melcombe (talk) 21:47, 13 April 2012 (UTC)

Change of name of the article

There is a suggestion to change the name of the article to Frequentism, which is commonly used as the label for the topic of this article. Let's vote:

1. I vote yes. iNic (talk) 14:33, 13 April 2012 (UTC)

If you're going to want a vote, then you should do it properly. Procedures are described at Wikipedia:Requested moves. This has various advantages, in particular in terms of notifying appropriate project pages and getting an admin involved in solving any conflicts related to existing articles. Melcombe (talk) 21:47, 13 April 2012 (UTC)

OK but if you think this is the best way to do it why didn't you use this yourself? Instead, you changed the name of the article to "Frequentist probability" without any votings whatsoever. Maybe your rules applies to everyone but yourself? iNic (talk) 22:30, 13 April 2012 (UTC)

No one seem to oppose the change of name of the article to "Frequentism," so this is the decision. iNic (talk) 09:02, 16 April 2012 (UTC) 

Nonsense. Several perople have raised objections already. The standard period for discussing renaming is 1 week under the formal approach. You haven't intestigated the formal vote as requested, so no vote has yet taken place. Melcombe (talk) 10:41, 16 April 2012 (UTC)

No, everyone that can read can see that no one voted against so far, not even you. Your credibility is below zero when you lecture others about formal rules while you don't give a damn about these rules yourself. Please change back to the name this article has had for years. You changed it to the current "Frequentist probability" a week ago without following any rules whatsoever. No voting, no nothing. When you have changed it back you can start to preach again. You know nothing about this subject and yet you think you own this page. Sad. iNic (talk) 02:26, 17 April 2012 (UTC)

One recurring problem with wikipedia is the fair amount of bickering that goes on. Its bad for the ego, and escalations make it hard to reach agreement later. And it leads to editor burnout. Please take care to be gentle. linas (talk) 20:31, 12 July 2012 (UTC)

Incompatibility with measure-theoretic probability theory

Th view that probabilities are limits of relative frequencies is not compatible with the measure-theoretic framework of probability theory in mainstream mathematics. One can show that the limiting relative frequencies are not sigma-additive and hence not a probability measure. One can even show that the collection of sets whose limiting relative frequency exists is not a sigma-algebra. I think this should be mentioned in the article because it is an often repeated misconception. For a summary of the argument that proves the incompatability, see for example Section 3.4 of https://plato.stanford.edu/entries/probability-interpret/. Zakoohl (talk) 21:36, 7 November 2019 (UTC)

I don't understand the author's argument as to how frequentism violates countable additivity.

"the domain of definition of limiting relative frequency is not even a field, let alone a sigma field"

Are they saying that limiting frequencies can't sum to 1 because they are theoretically undefined? They say earlier that by reordering the results of infinitely many coin flips, one can make the fraction of heads converge to any value in [0,1], but I don't think that's relevant, since any experimental observation, by the Law of Large Numbers, will converge to 1/2. Any experiment that can be done an arbitrary number of times does have a set of limiting frequencies, and if I'm not mistaken, they do always add to 1. Justin Kunimune (talk) 13:30, 14 November 2019 (UTC)

In modern probability theory one works in the framework of a probability space, which consists of a sample space (a set), a sigma-algebra/field over the sample space, and a finite measure, which is by definition countably additive and not only finitely additive (and no, this does not mean summing to 1). Definitions of these concepts can be found here: Probability_space#Definition. The problem with the limiting relative frequencies view is that it does not fit that framework. A collection of limiting relative frequencies does not form a sigma field and a function that assigns events its limiting relative frequencies is only finitely additive and hence not a measure. Details can be found for example here: http://www.joelvelasco.net/teaching/3865/vanfraassen_relative%20frequencies.pdf. Hence, the conventional (measure-theoretic) view in mathematics and the limiting relative frequencies view are mutually exclusive. And invoking results as the law of large numbers that are proved in the measure-theoretic framework is then of course problematic. (Although one might be able to prove that specific result also in a only finite additive framework. I don’t know. Nevertheless many results from probability theory are lost if one does not accept the countably additivity axiom). Zakoohl (talk) 13:49, 15 November 2019 (UTC)