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Topic: Probability interpretations

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  Probability - Wikipedia, the free encyclopedia
In Cox's formulation, probability is taken as a primitive (that is, not further analyzed) and the emphasis is on constructing a consistent assignment of probability values to propositions.
Probabilities are equivalently expressed as odds, which is the ratio of the probability of one event to the probability of all other events.
Governments typically apply probability methods in environment regulation where it is called "pathway analysis", and are often measuring well-being using methods that are stochastic in nature, and choosing projects to undertake based on their perceived probable effect on the population as a whole, statistically.
en.wikipedia.org /wiki/Probability   (2712 words)

 Probability interpretations - Wikip├ędia
There are two broad categories of probability interpretations: Frequentists assign probabilities only to random events according to their relative frequencies of occurrence or to subsets of populations as proportions of the whole.
Bayesians assign probabilities to any statement, even when no random process is involved, as a way to represent its plausibility.
The mathematics of probability can be developed on an entirely axiomatic basis that is independent of any interpretation: see the articles on probability theory and probability axioms for a detailed treatment.
su.wikipedia.org /wiki/Probability_interpretations   (318 words)

 Encyclopedia: Probability
In probability theory and statistics the odds in favor of an event or a proposition are the quantity p / (1 − p), where p is the probability of the event or proposition.
In probability theory, the cumulative distribution function (abbreviated cdf) completely describes the probability distribution of a real-valued random variable, X. For every real number x, the cdf is given by where the right-hand side represents the probability that the variable X takes on a value less than or...
In probability and statistics, the t-distribution or Students distribution is a probability distribution that arises in the problem of estimating the mean of a normally distributed population when the sample size is small.
www.nationmaster.com /encyclopedia/Probability   (5636 words)

 Probability - Open Encyclopedia   (Site not responding. Last check: 2007-10-21)
(There are other rules for quantifying uncertainty, such as the Dempster-Shafer theory and fuzzy logic, but those are essentially different and not compatible with the laws of probability as they are usually understood.) However, there is ongoing debate over what, exactly, the rules apply to; this is the topic of probability interpretations.
The probability of an event is generally represented as a real number between 0 and 1.
For example, if two events are assumed equally probable, such as a flipped coin landing heads-up or tails-up, we can express the probability of each event as "1 in 2", or, equivalently, "50%" or "1/2".
open-encyclopedia.com /Probability   (2628 words)

 Probability interpretations - Wikipedia, the free encyclopedia
There are two broad categories of probability interpretations: 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.
Bayesians, on the other hand, assign probabilities to any statement whatsoever, even when no random process is involved, as a way to represent its subjective plausibility.
en.wikipedia.org /wiki/Probability_interpretations   (354 words)

 Frequency probability - Wikip├ędia
Statistical regularity has motivated the development of the relative frequency concept of probability.
Most of the procedures commonly used to make statistical estimates or tests were developed by statisticians who used this concept exclusively.
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)

Different interpretations of verbal probability expressions would be unacceptable to the IASC as not only does it have the potential to undermine the credibility of financial reporting, it strikes at the very core of the development of the global accounting language.
The IASC needs to ensure that the verbal probability expression is interpreted in a consistent manner as different interpretations of the same verbal probability expression have the potential to undermine the credibility of financial reporting.
While guidance in the interpretation of verbal probability expressions may be useful, the IASC must ensure that it selects terminology that is numerically interpreted as a synonym.
www.sec.gov /rules/concept/s70400/shying1.htm   (4030 words)

 Probability and Induction
These theories have various forms: probabilities may be interpreted as actual relative frequencies of occurrent events, or as limiting relative frequencies of infinite sequences of occurrent and imagined events, or as modal relative frequencies of possible events.
This is probability thought of as a measure of degree of justification or warrant.
Like subjective probability it is a concept of probability tied to belief systems of a rational agent, but it is not typically developed in terms of variably strong dispositions to act or choose.
www.ditext.com /clay/armendt2.html   (5096 words)

 Interpretations of Probability
The ratio of this number to that of all the cases possible is the measure of this probability, which is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible.
Probability is thought of as a physical propensity, or disposition, or tendency of a given type of physical situation to yield an outcome of a certain kind, or to yield a long run relative frequency of such an outcome.
The laws of probability then are claimed to be constraints on these estimates: putative necessary conditions for minimizing her ‘losses’ in a broad sense, be they monetary, or measured by distances from the assignments of these experts.
plato.stanford.edu /entries/probability-interpret   (15179 words)

 ProbabilityTheory - PineWiki
The usual argument against frequentist probability is that it only works for repeatable experiments, and doesn't allow for statements like "the probability that it will rain tomorrow is 50%" or the even more problematic "based on what I know, there is a 50% probability that it rained yesterday".
The probability that we roll a 7 is the sum of the cases (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1), or 6/36 = 1/6.
So one of the ways to compute the probability of two events occurring is to compute the probability of one of them, and the multiply by the probability that the second occurs conditioned on the first.
pine.cs.yale.edu /pinewiki/ProbabilityTheory   (1980 words)

 Learn more about Probability in the online encyclopedia.   (Site not responding. Last check: 2007-10-21)
One of the simplest of discrete sample spaces is a finite set to each of whose members the same probability 1/n is assigned.
An example of a sample space that is not discrete is the closed interval [0, 1] to which the length of any subinterval (a, b) is assigned as the probability of that subinterval.
The probability assigned to any one-member subset is 0.
www.onlineencyclopedia.org /p/pr/probability.html   (1648 words)

 Probability - FreeEncyclopedia   (Site not responding. Last check: 2007-10-21)
While the existence of gambling games of chance shows that there has been a lively interest in quantifying the ideas of probability for millenia, exact mathematical descriptions of use in these types of problems only arose much later.
=P(A_1)+P(A_2)+P(A_3)+\cdots. In the special case of a "discrete probability distribution" the sample space is a set \left\{\,x_1,x_2,x_3,...\,\right\} of outcomes to each of which a positive number has been assigned as its probability.
A law of small numbers[?] tends to apply to all such choices and perception of the impact of such choices, which makes probability measures a political matter.
openproxy.ath.cx /pr/Probability.html   (1522 words)

 [No title]   (Site not responding. Last check: 2007-10-21)
What does it mean to say that a probability of a fair coin is one half, or that the chances I pass this class are 80 percent, or that the probability that the Steelers win the Super Bowl this season is.1?
A probability is a numerical measure of the likelihood of the event.
A probability is a number from 0 to 1.
www-math.bgsu.edu /~albert/m115/probability/interp.html   (267 words)

 M241 Probability Class Notes Chapter 1
For a partition of a set B the probability of B is the sum of the probabilities of the sets in the partition.
We show that the probability of drawing the ticket number i on the first draw and j on the second draw, P(i,j), is the product of the probabilities, P(i)P(j).
Two calculate the probability of a particular event, select the paths that are part of that event and add their probabilities.
www.saintjoe.edu /~karend/m241/m241-1.html   (1487 words)

 On the Propensity Interpretations of Probability in the Analy...   (Site not responding. Last check: 2007-10-21)
On the Propensity Interpretations of Probability in the Analysis of Causation
It seems that the notion of the propensity interpretations of probability can answer that question: The propensity interpretations of probability consider the conception of "propensity" as "dispositions as causal tendencies," (p.123.) which are represented as probabilities.
Then, it seems trivial that the propensity interpretations dependent on disposition as causal tendencies explicate causal relevance in terms of probabilistic relations.
philosophy.wisc.edu /960/_disc1/0000001e.htm   (150 words)

 SSRN-Interpretations of Probability Expressions: A Comparison Between Standard-Setters and Accountants by Fawzi Laswad, ...   (Site not responding. Last check: 2007-10-21)
This study extends the study by Laswad and Mak (1997) on the interpretation of probability expressions used in accounting standards by New Zealand standard setters, by comparing the interpretations of standard-setters with practicing accountants.
The reduction of probability expressions may facilitate greater consistency in the application of accounting standards and consequently greater comparability in financial reporting.
The results also indicate that, similar to standard-setters, there is considerable disagreement among accountants in the interpretation of probability expressions, which suggest that to enhance comparability in financial reporting, guidance in the interpretation of such phrases is needed.
papers.ssrn.com /sol3/papers.cfm?abstract_id=213245   (257 words)

Probability is a very familiar concept to most people but it is also a strange concept because its interpretation or meaning varies depending on the context
The interpretation that is used depends on which is applicable to the situation
The probability that the student is from out of state GIVEN that the student is female is written as
www.engr.uconn.edu /~garrick/ce251/lec5-7.htm   (972 words)

 Interpretations of Probability and Their p-Adic Extensions
This paper is devoted to foundations of probability theory.
We discuss interpretations of probability, corresponding mathematical formalisms, and applications to quantum physics.
One of the aims of this paper is to show that the probability model based on Kolmogorov's axiomatics cannot describe all stochastic phenomena, i.e., that quantum physics induces natural restrictions of the use of Kolmogorov's theory and that we need to develop non-Kolmogorov models for describing some quantum phenomena.
epubs.siam.org /sam-bin/dbq/article/97892   (206 words)

 Interpretations of Probability
Like geometry, probability can not be reduced to just one model to describe all physical and biological phenomena.
Such paradoxes can be resolved by using non-Kolmogorov probability models, developed on the basis of purely classical interpretations of probability: frequency and ensemble.
This book will be of value and interest to specialists in probability theory, statistics, functional analysis, quantum physics and (partly) specialists in cognitive sciences and psychology.
www.vsppub.com /books/mathe/bk-IntPro.html   (236 words)

 [No title]
Frequentists assign probabilities only to random events according to their relative frequencies of occurrence or to subsets of populations as proportions of the whole.
In order to resolve a particular problem using probability theory, Bayesians will accept to apply a particular probability model, such as the urn model, to a
The mathematics of probability can be developed on an entirely axiomatic basis that is independent of any interpretation: see the articles on probability theory and
en-cyclopedia.com /wiki/Probability_interpretations   (288 words)

 Interpretations of Probability   (Site not responding. Last check: 2007-10-21)
MB24.1 From Classic to Subjective Interpretations of Probability Ralph F. Miles, Jr.
Van Fraassen, Joyce and others argue that it is that the degree of belief be well calibrated; roughly, that it agrees with the appropriate relative frequency.
The state 'q' of a quantum mechanical system is given by a wave function Psi(q), where the probability that the system is in state 'q' is P(q) = Psi(q) * Psi (q).
www.informs.org /Conf/SD97/TALKS/MB24.html   (271 words)

 [No title]
Find the probability of no more than one imperfection in a minute.
What is the probability that the 6th device will show excessive drift?
Find the probability of the 1st drift on the 6th trail.
www.uh.edu /~tech132/prob.ppt   (297 words)

 Interpretations of Probability: Contents
The origin of negative probabilities in the ensemble and frequency theories
Subjective probability as probability with respect to the statistical ensemble of human ideas
p-Adic probability measures on the space of binary sequences
www.vsppub.com /books/mathe/cbk-IntPro.html   (91 words)

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