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	Bayesians vs. Frequentists (Site not responding. Last check: 2007-10-13)
		The frequentist believes that probabilities are only defined as the quantities obtained in the limit after the number of independent trials tends to infinity.
		Thus, the frequentist risk can be viewed as a constraint on the desirability of strategies, but it usually is not powerful enough to select a single one.
		The frequentist approach attempts to be more conservative and rigorous, with the result being that weaker statements are made regarding decisions.
	msl.cs.uiuc.edu /planning/node479.html (425 words)

	Bayesian probability - Wikipedia, the free encyclopedia
		Whereas a frequentist and a Bayesian might both assign a 1/2 probability to the event of getting a head when a coin is tossed, only a Bayesian might assign 1/1000 probability to a personal belief in the proposition that there was life on Mars a billion years ago.
		The frequentist interpretation of probability was preferred by some of the most influential figures in statistics during the first half of the twentieth century, including R.A. Fisher, Egon Pearson, and Jerzy Neyman.
		One criticism levelled at the Bayesian probability interpretation by frequentists is that a single probability cannot convey how much evidence one has.
	en.wikipedia.org /wiki/Bayesian_probability (1652 words)

	Frequency probability - Wikipédia
		They are usually called frequentists, and their position is called frequentism.
		This school is often associated with the names of Jerzy Neyman and Egon Pearson who described the logic of tes hipotesa statistik.
		The frequentist position is the one you probably heard at school: perform an experiment lots of times, and measure the proportion where you get a positive result - this proportion, if you perform the experiment enough times, is the probability.
	su.wikipedia.org /wiki/Frequentism (252 words)

	The Pseudo-Expert on Statistics
		The frequentists will look at a set of data points that are independent and identically distributed in some distribution and use either a UMVUE or a MLE.
		The interpretation of the 100(alpha)% confidence for the frequentists is that if we have many samples from the same distribution and each sample was put in a range for our estimated parameters, then 100(alpha)% of these intervals shall include the true value for the parameters of interest.
		Interestingly enough, the frequentist philosophy is taught to many students, especially to second year students who have a vague idea on statistics.
	www.mathnews.uwaterloo.ca /Issues/mn7405/OnThought.html (1030 words)

	Frequency probability - Wikipedia, the free encyclopedia
		Frequentists talk about probabilities only when dealing with well defined random experiments.
		The relative frequency of occurrence of an experiment's outcome, when repeating the experiment, is a measure of the probability of that random event.
		This school is often associated with the names of Jerzy Neyman and Egon Pearson who described the logic of statistical hypothesis testing.
	en.wikipedia.org /wiki/Frequency_probability (249 words)

	Cognitive Status of Risk
		Lastly, I consider the degree to which the traditional debate between frequentists and subjectivists is relevant to modern risk analysis, and I argue for a pluralistic view of the role of probability in risk analysis.
		The second reason is that, given the individual successes that the Bayesian and frequentist paradigms have been able to claim, it is patently unreasonable to suppose that one of these paradigms will someday be abandoned at the expense of the other.
		The third reason for de-emphasizing the relevance of the traditional debate between Bayesians and frequentists is that reasonable arguments can be made for adopting an instrumentalist view of both paradigms, thereby conceding that for certain problems, one paradigm may be preferable to another.
	www.fplc.edu /RISK/vol2/fall/valverde.htm (7291 words)

	Subjective Expected Utility - Intro
		In a sense, the relative frequentist view is related to Jacob Bernoulli's (1713) "law of large numbers".
		What the relative frequentists added (or rather subtracted) is that instead of positing the independent existence of an "objective" probability for that event, they defined that probability precisely as the limiting outcome of such an experiment.
		As a consequence, some frequentists have accepted the limitations of probability reasoning merely to controllable "mechanical" situations and allow unique random situations to fall outside their realm of applicability.
	cepa.newschool.edu /het/essays/uncert/subjective.htm (1896 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		This example shows that frequentist methods are dependent on experimental design, whereas Bayesian methods adhere to a general principle, the Likelihood Principle, which says that all interpretations of an experiment must rely on the likelihood of observed data.
		The fundamental dividing line seems to be that frequentists do not accept probability as dependent on information, whereas Bayesians have to attack the problem of translating information to priors, which is difficult and delicate.
		The frequentists observe a non-robustness of Bayesian conclusions caused by reliance on priors which seem to be essentially ad hoc.
	www.nada.kth.se /~stefan/sem1008.html (209 words)

	Re: Bayesian & Frequentist Probability Theory
		The basic difference between Bayesians and frequentists is this: Bayesians condition on the data actually observed, and consider the probability distribution on the hypotheses; they believe it reasonable to put probability distributions on hypotheses and they behave accordingly.
		But the point is that even a frequentist contemplates frequencies of data that have not been actually observed (though they might be), whereas a Bayesian is interested only in the data that have _actually_ been observed.
		For example, frequentist correlation theory is well advanced, but recently someone asked on one of the statistics groups what to do if the data points themselves were measured with error (in both coordinates).
	www.lns.cornell.edu /spr/2002-03/msg0040638.html (1949 words)

	greenpass: Why yes, I am a Bayesian!
		For example, a frequentist would say that there is a fixed level of support for Kerry in the population - call it p% for Kerry - and that 95 times out of 100 a 95% CI will include the number p.
		In practice, Bayesians accept frequentist models for simple examples, often because they are more intuitive and end up with the same result in the long run.
		The orthodox (frequentist) way to express the original poll result would be something like "We are 75% _confident_ that Kerry is ahead of Bush," where "confident" means "long-run frequency." Most people beat their introductory students over the head with this distinction.
	vanderwolk.typepad.com /greenpass/2004/08/why_yes_i_iami_.html (2414 words)

	October 7, 1996, UCLA Statistics Seminar
		Kiefer [J. of the American Statistical Association 72 (1977), 789-827] sought to overcome these problems by developing a "conditional frequentist" theory, in which the error probabilities are allowed to depend on the data.
		The theory never became popular, however, because of the difficulty of choosing an appropriate conditional frequentist procedure from among the many possible.
		A recent look at the problem has revealed a very natural and attractive choice for the conditional frequentist error probabilities, namely the Bayesian posterior probabilities of the hypotheses.
	www.stat.ucla.edu /seminars/seminars/fall96/abstracts/oct7.php (280 words)

	Cryonics Institute -- Feature Article: Cryonics: The Probability Of Rescue
		Von Mises would regard the question of life on Mars as outside the theory; yet it may be as easy to imagine a population of planets Mars--or of Milky Way galaxies for that matter--as to imagine a sequence of tosses of 12-sided dice.
		Since frequentists are generally definite enough about whether a particular event is within the scope of the theory, they are certainly applying some criterion, although they do not seem to know what it is. In the synthesis later on, I claim to make this criterion explicit, and thereby to extend the scope of the theory.
		Frequentists say that the vague common parlance notion of "probability", which applies to single events, hypotheses, etc., is outside the theory.
	www.cryonics.org /probability.html (8476 words)

	Re: Bayesian & Frequentist Probability Theory
		Part of the point of being a frequentist is that you never talk about the probability distribution of the true value of a parameter.
		If you're a frequentist, you think of the data as a bunch of random variables, and you talk about probability distributions on the data or on functions of the data (such as, for instance, confidence intervals).
		So a frequentist would never say that the actual value of the resistance "has a finite probability of being negative," or of being in any other range for that matter.
	www.lns.cornell.edu /spr/2002-04/msg0040694.html (427 words)

	Frequentists and Bayesians
		The frequentists definition sees probability as the long-run expected frequency of occurrence.
		Thus a frequentist believes that a population mean is real, but unknown, and unknowable, and can only be estimated from the data.
		And that's because to a frequentist the true mean, being a single fixed value, doesn't have a distribution.
	www.statisticalengineering.com /frequentists_and_bayesians.htm (350 words)

	Statistics notes: Bayesians and frequentists -- Bland and Altman 317 (7166): 1151 -- BMJ
		There are two competing philosophies of statistical analysis: the Bayesian and the frequentist.
		Frequentist methods regard the population value as a fixed, unvarying (but unknown) quantity, without a probability distribution.
		Most statisticians have become Bayesians or frequentists as a result of their choice of university.
	bmj.bmjjournals.com /cgi/content/full/317/7166/1151 (800 words)

	Signal + Noise: This Is Your Brain on Bayes
		It is not at all unusual, for instance, to see a frequentist use Bayesian methods or to see a Bayesian check a procedure's frequentist performance.
		A frequentist modeler with the same information in the study would behave consistently with what was observed.
		The basic distinction between Bayesians and frequentists lies in how they interpret probability; the implications of that difference are far reaching.
	signalplusnoise.com /archives/000359.html (1333 words)

	[No title]
		Among the frequentists, the probability of an event is said to be the proportion of times that the event has taken place in the past, usually based on a long series of trials.
		The great mathematician Littlewood asserts that the fundamental axiom underlying any philosophical (frequentist) theory of probability that would give the concept of probability meaning in the real world is "inherently incapable of deductive proof...also incapable of inductive proof" (1986, p.
		It seems doubtful that philosophers who are doctrinaire as frequentists or for other positions could throw helpful light on space shuttle flight discussions.
	www.resample.com /content/teaching/philosophy/part1/chapI-4.txt (5557 words)

	The Brights' Movement Forums > Flock Rock (Site not responding. Last check: 2007-10-13)
		As evidenced by the “were strictly adhered to”, this is a cautious start to his task of vilifying the dreaded “frequentists” and their relentless habit of collecting real data by counting events.
		He concentrates on building the case against the frequentists hoping that, by now, his readers are thinking that this “belief” stuff is all over the place.
		Those coin-tossing, die-throwing frequentists would be utterly bewildered by her statement of probability.
	www.the-brights.net /forums/lofiversion/index.php?t1819.html (9475 words)

	Ethics of Chance, E. C. Wit (Site not responding. Last check: 2007-10-13)
		Bayesian inference will return in the fourth chapter, whereas condition of homogeneity for the frequentist theory of probability is an important element in the theory of explanation in the second chapter.
		A frequentist has to specify her null hypothesis or to determine, prior to data collection, what inference she wants to make.
		This criticism reveals the connection between the frequentist theory of probability and the theory of explanation.
	www.stats.gla.ac.uk /~ernst/ethics_of_chance.htm (17076 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		Crudely speaking, frequentists regard probability as the expected frequency with which a given event would occur in an infinite sequence of trials, while Bayesians regard it as a measure of ones degree of belief in a proposition.
		Naturally both these positions need to be made much more precise before a sensible discussion can begin regarding their relative merits.
		The debate between Bayesians and frequentists is relevant to the debate concerning interpretations of quantum mechanics.
	www.math.niu.edu /~rusin/known-math/00_incoming/frequentist (117 words)

	Mailing List complex-science@necsi.org Message 6439
		Because this is the underlying difference between Bayesian approaches and frequentist approaches.
		Or it can be considered a totally inappropriate aspect to statistical inference, as most frequentists believe.
		Frequentists do not use them, but the consequence is equivalent
	necsi.org:8100 /Lists/complex-science/Message/6439.html (1326 words)

	For Debate: The statistical basis of public policy: a paradigm shift is overdue -- Lilford and Braunholtz 313 (7057): ...
		Bayesian statistics The key difference between Bayesian and conven- tribution is formed by weighting the prior probability tional (or frequentist) statistics is the view of what prob- distribution by the likelihood.
		Thus the probability P of a fair that it provides probability distributions for coin landing heads up is 0.5 because in a long series of parameters--which is exactly what is needed to inform tosses it lands heads up half the time.
		In this case the model we have in conflict with this--for instance, when calculating P assumed specifies that the probability distribution for the values, which take into account the probability of obser- "observed" log relative risk will be normal with a mean of vations more extreme than the actual observations.
	bmj.bmjjournals.com /cgi/content/full/313/7057/603 (5150 words)

	Read This: An Introduction to Probability and Inductive Logic
		His discussion of how the frequentists as well as the Bayesians in different ways make an end run round the problem is indeed thought-provoking.
		He explains that the frequentists in effect treat Hume's problem as not material to what they do, by saying that statistical inference is about inductive behavior which is not guaranteed to be correct, but only correct most of the time.
		On the other hand, Bayesians in a different way make Hume's problem irrelevant — by saying that statistical inference is about revision of initial beliefs in the light of evidence, and is not designed to produce certain knowledge.
	www.maa.org /reviews/hacking.html (575 words)

	Probability theory -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-13)
		For an algebraic alternative to Kolmogorov's approach, see (Click link for more info and facts about algebra of random variables) algebra of random variables.
		Others assign probabilities to propositions that are uncertain according either to (Click link for more info and facts about subjective) subjective degrees of belief in their truth, or to logically justifiable degrees of belief in their truth.
		Such persons are (Click link for more info and facts about Bayesians) Bayesians.
	www.absoluteastronomy.com /encyclopedia/p/pr/probability_theory.htm (1029 words)

	Statistical Modeling, Causal Inference, and Social Science: Bayes for medical diagnosis
		In addition to their almost comical cluelessness about the contrast between Bayesians and frequentists, they seem not to have heard about the Nobel-prize winning research on this topic by Kahneman and Tversky, showing that people (including physicians) are not very Bayesian.
		I wouldn't quite say that they are "deeply confused about how a frequentist would approach this question." Rather, there are many different frequentist approaches.
		(In fact, as Rubin always said, one possibly frequentist approach is to use Bayesian inference and evaluate its frequency properties!) The real point, which they make well, I think, is that aggregate frequency properties aren't enough--it can be necessary to use local information as well.
	www.stat.columbia.edu /~cook/movabletype/archives/2005/02/bayes_for_medic.html (562 words)

	ahiajul93.html (Site not responding. Last check: 2007-10-13)
		Unlike frequentists who believe probabilities are derived by witnessing a large series of events, Bayesians look at probability values as a personal belief in the likelihood of an event.
		Rather, an initial estimate is made from studies and the expert then updates that estimate based on information of the specific patient resulting in a belief that this patient has a given disorder.
		Another, simpler, example is the coin toss: Frequentists tell you that a "fair coin" (whatever that is) has a 0.5 chance of coming up heads.
	smi-web.stanford.edu /people/pradhan/articles/ahiajul93.html (995 words)

	Interpretations of Probability
		Starting with a degenerate case: according to the finite frequentist, a coin that is never tossed, and that thus yields no actual outcomes whatsoever, lacks a probability for heads altogether; yet a coin that is never measured does not thereby lack a diameter.
		The problem of the single case is that the finite frequentist fails to see intermediate probabilities in various places where others do.
		A frequentist who thinks that chances just are relative frequencies would presumably think that the Principal Principle just is the Principle of Direct Probability; but Lewis' principle may well appeal to those who have a very different view about chances -- e.g., propensity theorists.
	plato.stanford.edu /entries/probability-interpret (15179 words)

	[Ausrace] 1/1 chances:Peter J.
		I am not interested in bagging mathematicians in general or point-scoring: my interest is in shining a bit of light into some murky and contentious areas.
		In any case there is no SINGLE "mathematicians camp" on many issues of probability and statistics: in fact there has been a "great divide" amongst statisticians with at least two opposing camps, the Bayesians and the Frequentists who have been arguing, at times bitterly, for generations.
		Your comments indicate you are a Bayesian and yes some of the heavy-duty Frequentists would tend to dismiss such positions as being that of the ivory-towered academic mathematicians!!...ouch!!
	home.it.net.au /pipermail/ausrace/2004-August/035768.html (1096 words)

	[No title]
		Another effect of the prior is that unphysical values of a parameter are excluded; this is not necessarily so in frequentist approaches.
		Frequentists construct confidence intervals without invoking P(parameterdata) or P(parameter), and hence do not require a prior.
		Their method is simply to use P(dataparameter) to construct a probability interval for the data (i.e.
	conferences.fnal.gov /acat2000/program/papers/plenary/louis_paper_revised.doc (619 words)

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