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In fact, Bayesian inference can be used to show that when the long-run proportion of different outcomes are unknown but exchangeable ( meaning that the random process from which they are generated may be biased but is equally likely to be biased in any direction ) previous observations demonstrate the likely direction of the bias, such that the outcome which has occurred the most in the observed data is the most likely to occur again.
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fact and Bayesian
In fact, there are non-Bayesian updating rules that also avoid Dutch books ( as discussed in the literature on " probability kinematics " following the publication of Richard C. Jeffrey's rule, which is itself regarded as Bayesian ).
The fact that Bayesian and frequentist arguments differ on the subject of optional stopping has a major impact on the way that clinical trial data can be analysed.
Bayesians would argue that this is right and proper — if the issue is such that reasonable people can put forward different, but plausible, priors and the data are such that the likelihood does not swamp the prior, then the issue is not resolved unambiguously at the present stage of knowledge and Bayesian statistics highlights this fact.
The term " Bayesian ", which displaced " inverse probability ", was in fact introduced by R. A. Fisher as a derogatory term.
Dirichlet distributions are very often used as prior distributions in Bayesian statistics, and in fact the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution.
In fact in the second game there is a perfect Bayesian equilibrium where player 1 plays D and player 2 plays U ' and player 2 holds the belief that player 1 will definitely play D. In this equilibrium, every strategy is rational given the beliefs held and every belief is consistent with the strategies played.
The theory of Bayesian integration is based on the fact that the brain must deal with a number of inputs, which vary in reliability.
In fact, there is a perfect Bayesian equilibrium where player 1 plays D and player 2 plays U ' and player 2 holds the belief that player 1 will definitely play D ( i. e. player 2 places a probability of 1 on the node reached if player 1 plays D ).
In fact, Akaike was so impressed with Schwarz's Bayesian formalism that he developed his own Bayesian formalism, now often referred to as the ABIC for " a Bayesian Information Criterion " or more casually " Akaike's Bayesian Information Criterion ".
fact and inference
The structure of the latter event is such that it … justifies a belief that intelligent design is the cause … Despite the fact that the probability of winning three consecutive 1-in-1, 000 games is exactly the same as the probability of winning one 1-in-1, 000, 000, 000 game, the former event … warrants an inference of intelligent design.
This inference is based on the fact that the term was used in two different ways during the republican era: during Terence's lifetime, it was used to refer to non-Carthaginian Libyco-Berbers, with the term Punicus reserved for the Carthaginians.
Full-blooded Platonism is a modern variation of Platonism, which is in reaction to the fact that different sets of mathematical entities can be proven to exist depending on the axioms and inference rules employed ( for instance, the law of the excluded middle, and the axiom of choice ).
Commenting on the fact that Egyptologists have no problem in reconstructing history using inference of this sort, whereas critics will sometimes not allow the same historical method to be applied to the Bible, Young writes, " Do those who reject the Menahem / Pekah rivalry as improbable also reject as improbable this reconstruction from Egypt's Eighteenth Dynasty that Egyptologists use to explain the regnal dates of Thutmose III?
Besides, if testimony were to be accepted as the only means of the knowledge of the invariable connection between middle term and predicate, then in the case of a man to whom the fact of the connection had not been pointed out by another person, there could be no inference.
The record further details the fact that Gideon lived on the 400-acre ( 1. 6 km² ) tract of land until his death, and the inference that he was buried in the Morris family graveyard ends the record.
Since the vast majority of petitions for certiorari are routinely denied without comment, it is normally unnecessary to indicate that fact in citations to decisions of lower federal courts, unless it happened within the last two years or was otherwise particularly relevant ( e. g., to support an inference that a particular appellant is a vexatious litigant ).
He then made the somewhat reckless, and incorrect, inference that air and, in fact, all gases, were perfect non-conductors of heat.
The spoliation inference is a negative evidentiary inference that a finder of fact can draw from a party's destruction of a document or thing that is relevant to an ongoing or reasonably foreseeable civil or criminal proceeding: the finder of fact can review all evidence uncovered in as strong a light as possible against the spoliator and in favor of the opposing party.
Circumstantial evidence is evidence in which an inference is required to connect it to a conclusion of fact, like a fingerprint at the scene of a crime.
It is not known whether this was just an inference by the writer, based on the fact that also Nicholas was an Englishman.
In fact, the resolution of a goal clause with a definite clause to produce a new goal clause is the basis of the SLD resolution inference rule, used to implement logic programming and the programming language Prolog.
His initial bid was rejected after the State Department concluded that he would return to the United States — a credible inference, as O ' Keefe in fact had returned immediately.
Given a counterfactual conditional, e. g., ' If there had been a circle on the blackboard then there would have been a triangle ', and the subsequent information ' in fact there was no triangle ', participants make the modus tollens inference ' there was no circle ' more often than they do from an indicative conditional ( Byrne and Tasso, 1999 ).
Given the counterfactual conditional and the subsequent information ' in fact there was a circle ', participants make the modus ponens inference as often as they do from an indicative conditional.
No inference is to be read from the fact that during the 20th century Dungarvan had a spectacular number of licenced premises many of which have survived.
The belief that he was of Syrian origin is only an inference from the fact that his mother was a Syrian woman, and from an obscure passage in the Historia Augusta, from which it may be inferred that he could speak the Syriac language.
It showed the middle-American, middle-class town to be a superficially friendly, prosperous, progressive, religious, charitable, arts-and-education oriented bedroom community whose adolescent culture, with the complicity ( and, by inference, example and encouragement ) of the adult population, was in fact clique-ridden, status-oriented, hypercompetitive, hypocritical, prejudiced, and materialistic.
In fact, the spirally coiled nature of chitinozoan chains has been used to suggest that they were laid by a spirally coiled organism, such as the gastropods ; were this inference true, uncoiled chains could be to be attributed to the ( straight ) annelid worms or other organisms.
The only circumstance that suggests anything respecting his age is the fact that among the letters of Aristaenetus there are two between Lucian and Alciphron ; now as Aristaenetus is nowhere guilty of any great historical inaccuracy, we may safely infer that Alciphron was a contemporary of Lucian — an inference which is not incompatible with the opinion, whether true or false, that Alciphron imitated Lucian.
:" The fact remains that western man has never been free to pursue his own choice of sexual gratification without fear of State inference.
fact and can
This understanding provides a very simple example of the fact that one can eliminate fear without instituting any controls.
If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.
Perhaps the mere fact that by plucking on the nerves nature can awaken in the most ordinary of us, temporarily anyway, the sleeping poet, and in poets can discover their immortality, is the most remarkable of all the remarkable phenomena to which we can attest??
In fact, I can only say this seems to me to follow from a wide, continuous, and properly guided exposure to literary art.
Because of the means of publication -- science-fiction magazines and cheap paperbacks -- and because dystopian science fiction is still appearing in quantity the full range and extent of this phenomenon can hardly be known, though one fact is evident: the science-fiction imagination has been immensely fertile in its extrapolations.
No good can come of contemplating the sad, inevitable fact that once youth has passed `` a worse and worse time still succeeds the former ''.
That fact is very clearly illustrated in the case of the many present-day intellectuals who were Communists or near-Communists in their youth and are now so extremely conservative ( or reactionary, as many would say ) that they can define no important political conviction that does not seem so far from even a centrist position as to make the distinction between Mr. Nixon and Mr. Khrushchev for them hardly worth noting.
It recognizes the fact that what helps one county helps its neighbors and that by banding together in an area-wide effort better results can be accomplished than through the go-it-alone approach.
But if anything can bring home to Mr. Khrushchev the idea that he will not really get much enjoyment from watching this Braddock-against-the-Indians contest, it will probably be the fact that SEATO forces are ready to attempt it -- plus the fact that Moscow has something to lose from closing off disarmament and other bigger negotiations with Washington.
What evidence is there of an objective kind that in fact your government proposes to do just that, and that it can be done ''??
Are they indifferent to the fact that the dog can easily pick up germs from the preceding patient??
It is a very interesting fact that these two problems can be handled simultaneously and this is what we shall do in the next chapter.
The fact that there can not be any limit points of the set except in closed intervals follows from the argument used in Lemma 1, namely, that near any tangent point in the C-plane the curves C and Af are analytic, and therefore the difference between them must be a monotone function in some neighborhood on either side of the tangent point.
But few who have experienced marriage can dispute the fact that the focus of interpersonal relationships is different in marriage than in a pre-marital situation.
Since the writer had not noticed this characteristic in married students scattered throughout the various sections previous to this experiment, nor, as a matter of fact, in those who were continuing in `` single sections '', he can only conclude that there must have been something `` contagious '' within the specific group which caused this to occur.
In fact, in the desegregated school system which may have a good many schools with all-Negro population, how can we assure equal opportunity??
He can take security from the fact that the progress he has made by his gentle approach will not be lost.
It can, in fact, wreck a marriage.
" f one regards the Modest Proposal simply as a criticism of condition, about all one can say is that conditions were bad and that Swift's irony brilliantly underscored this fact ".
that any procedure which could " naturally " be called effective, can in fact be realized by a ( simple ) machine.
Ramsey ( 2004: 340 ) stated that " the genetic relationship between Korean and Japanese, if it in fact exists, is probably more complex and distant than we can imagine on the basis of our present state of knowledge ", a concept later restated by Lee ( 2011 ).
Sometimes slightly stronger theories such as Morse-Kelley set theory or set theory with a strongly inaccessible cardinal allowing the use of a Grothendieck universe are used, but in fact most mathematicians can actually prove all they need in systems weaker than ZFC, such as second-order arithmetic.
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