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CLs Method (particle Physics)
In particle physics, CLs represents a statistical method for setting ''upper limits'' (also called ''exclusion limits'') on model parameters, a particular form of interval estimation used for parameters that can take only non-negative values. Although CLs are said to refer to Confidence Levels, "The method's name is ... misleading, as the CLs exclusion region is not a confidence interval." It was first introduced by physicists working at the LEP experiment at CERN and has since been used by many high energy physics experiments. It is a frequentist method in the sense that the properties of the limit are defined by means of error probabilities, however it differs from standard confidence intervals in that the stated confidence level of the interval is not equal to its coverage probability. The reason for this deviation is that standard upper limits based on a most powerful test necessarily produce empty intervals with some fixed probability when the parameter value is zero, and thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle Physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and bosons (force-carrying particles). There are three generations of fermions, but ordinary matter is made only from the first fermion generation. The first generation consists of up and down quarks which form protons and neutrons, and electrons and electron neutrinos. The three fundamental interactions known to be mediated by bosons are electromagnetism, the weak interaction, and the strong interaction. Quarks cannot exist on their own but form hadrons. Hadrons that contain an odd number of quarks are called baryons and those that contain an even number are called mesons. Two baryons, the proton and the neutron, make up most of the mass of ordinary matter. Mesons are unstable and the longest-lived last for only a few hundredths of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Probability Distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a random phe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Likelihood Function
The likelihood function (often simply called the likelihood) represents the probability of random variable realizations conditional on particular values of the statistical parameters. Thus, when evaluated on a given sample, the likelihood function indicates which parameter values are more ''likely'' than others, in the sense that they would have made the observed data more probable. Consequently, the likelihood is often written as \mathcal(\theta\mid X) instead of P(X \mid \theta), to emphasize that it is to be understood as a function of the parameters \theta instead of the random variable X. In maximum likelihood estimation, the arg max of the likelihood function serves as a point estimate for \theta, while local curvature (approximated by the likelihood's Hessian matrix) indicates the estimate's precision. Meanwhile in Bayesian statistics, parameter estimates are derived from the converse of the likelihood, the so-called posterior probability, which is calculated via Bayes' r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Likelihood Function
The likelihood function (often simply called the likelihood) represents the probability of random variable realizations conditional on particular values of the statistical parameters. Thus, when evaluated on a given sample, the likelihood function indicates which parameter values are more ''likely'' than others, in the sense that they would have made the observed data more probable. Consequently, the likelihood is often written as \mathcal(\theta\mid X) instead of P(X \mid \theta), to emphasize that it is to be understood as a function of the parameters \theta instead of the random variable X. In maximum likelihood estimation, the arg max of the likelihood function serves as a point estimate for \theta, while local curvature (approximated by the likelihood's Hessian matrix) indicates the estimate's precision. Meanwhile in Bayesian statistics, parameter estimates are derived from the converse of the likelihood, the so-called posterior probability, which is calculated via Bayes' r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The American Statistical Association
The ''Journal of the American Statistical Association (JASA)'' is the primary journal published by the American Statistical Association, the main professional body for statisticians in the United States. It is published four times a year in March, June, September and December by Taylor & Francis, Ltd on behalf of the American Statistical Association. As a statistics journal it publishes articles primarily focused on the application of statistics, statistical theory and methods in economic, social, physical, engineering, and health sciences. The journal also includes reviews of academic books which are important to the advancement of the field. It had an impact factor of 2.063 in 2010, tenth highest in the "Statistics and Probability" category of ''Journal Citation Reports''. In a 2003 survey of statisticians, the ''Journal of the American Statistical Association'' was ranked first, among all journals, for "Applications of Statistics" and second (after ''Annals of Statistics'') f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Likelihood Principle
In statistics, the likelihood principle is the proposition that, given a statistical model, all the evidence in a sample relevant to model parameters is contained in the likelihood function. A likelihood function arises from a probability density function considered as a function of its distributional parameterization argument. For example, consider a model which gives the probability density function \; f_X(x \,\vert\, \theta)\; of observable random variable \, X \, as a function of a parameter \,\theta~. Then for a specific value \,x\, of \,X~, the function \,\mathcal(\theta \,\vert\, x) = f_X(x \,\vert\, \theta)\; is a likelihood function of \,\theta\;:~ it gives a measure of how "likely" any particular value of \,\theta\, is, if we know that \,X\, has the value \,x~. The density function may be a density with respect to counting measure, i.e. a probability mass function. Two likelihood functions are ''equivalent'' if one is a scalar multiple of the other. The like ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancillary Statistic
An ancillary statistic is a measure of a sample whose distribution (or whose pmf or pdf) does not depend on the parameters of the model. An ancillary statistic is a pivotal quantity that is also a statistic. Ancillary statistics can be used to construct prediction intervals. This concept was introduced by Ronald Fisher in the 1920s. Examples Suppose ''X''1, ..., ''X''''n'' are independent and identically distributed, and are normally distributed with unknown expected value ''μ'' and known variance 1. Let :\overline_n = \frac be the sample mean. The following statistical measures of dispersion of the sample *Range: max(''X''1, ..., ''X''''n'') − min(''X''1, ..., ''Xn'') *Interquartile range: ''Q''3 − ''Q''1 *Sample variance: :: \hat^2:=\,\frac are all ''ancillary statistics'', because their sampling distributions do not change as ''μ'' changes. Computationally, this is because in the formulas, the ''μ'' terms cancel – adding a constant number to a distrib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditionality Principle
The conditionality principle is a Fisherian principle of statistical inference that Allan Birnbaum formally defined and studied in his 1962 JASA article. Informally, the conditionality principle can be taken as the claim that experiments which were not actually performed are statistically irrelevant. Together with the sufficiency principle, Birnbaum's version of the principle implies the famous likelihood principle. Although the relevance of the proof to data analysis remains controversial among statisticians, many Bayesians and likelihoodists consider the likelihood principle foundational for statistical inference. Formulation The conditionality principle makes an assertion about an experiment ''E'' that can be described as a mixture of several component experiments ''E''h where ''h'' is an ancillary statistic An ancillary statistic is a measure of a sample whose distribution (or whose pmf or pdf) does not depend on the parameters of the model. An ancillary statistic is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Probability
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is and the event is known or assumed to have occurred, "the conditional probability of given ", or "the probability of under the condition ", is usually written as or occasionally . This can also be understood as the fraction of probability B that intersects with A: P(A \mid B) = \frac. For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person is sick, then they are much more likely to be coughing. For example, the conditional probability that someone unwell (sick) is coughing might be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Distribution
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and Statistical independence, independently of the time since the last event. It is named after France, French mathematician Siméon Denis Poisson (; ). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume. For instance, a call center receives an average of 180 calls per hour, 24 hours a day. The calls are independent; receiving one does not change the probability of when the next one will arrive. The number of calls received during any minute has a Poisson probability distribution with mean 3: the most likely numbers are 2 and 3 but 1 and 4 are also likely and there is a small probability of it being as low as zero and a very smal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tevatron
The Tevatron was a circular particle accelerator (active until 2011) in the United States, at the Fermilab, Fermi National Accelerator Laboratory (also known as ''Fermilab''), east of Batavia, Illinois, and is the second highest energy particle collider ever built, after the Large Hadron Collider (LHC) of the CERN, European Organization for Nuclear Research (CERN) near Geneva, Switzerland. The Tevatron was a synchrotron that accelerated protons and antiprotons in a ring to energies of up to 1 TeV, hence its name. The Tevatron was completed in 1983 at a cost of $120 million and significant upgrade investments were made during its active years of 1983–2011. The main achievement of the Tevatron was the discovery in 1995 of the top quark—the last Elementary particle#Fundamental fermions, fundamental fermion predicted by the Standard Model of particle physics. On July 2, 2012, scientists of the Collider Detector at Fermilab, CDF and D0 experiment, DØ collider experiment teams ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Test Statistic
A test statistic is a statistic (a quantity derived from the sample) used in statistical hypothesis testing.Berger, R. L.; Casella, G. (2001). ''Statistical Inference'', Duxbury Press, Second Edition (p.374) A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test. In general, a test statistic is selected or defined in such a way as to quantify, within observed data, behaviours that would distinguish the null from the alternative hypothesis, where such an alternative is prescribed, or that would characterize the null hypothesis if there is no explicitly stated alternative hypothesis. An important property of a test statistic is that its sampling distribution under the null hypothesis must be calculable, either exactly or approximately, which allows ''p''-values to be calculated. A ''test statistic'' shares some of the same qualities o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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