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Conditional Inference
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 (i.e. a statistic whose probability distribution does not depend on unknown parameter values). This means that observing a specific outcome ''x'' of experiment ''E'' is e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Inference
Statistical inference is the process of using data analysis to infer properties of an underlying probability distribution, distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers properties of a Statistical population, population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is Sampling (statistics), sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population. In machine learning, the term ''inference'' is sometimes used instead to mean "make a prediction, by evaluating an already trained model"; in this context inferring properties of the model is referred to as ''training'' or ''learning'' (rather than ''inference''), and using a model for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Allan Birnbaum
Allan Birnbaum (May 27, 1923 – July 1, 1976) was an American statistician who contributed to statistical inference, foundations of statistics, statistical genetics, statistical psychology, and history of statistics. Life and career Birnbaum was born in San Francisco. His parents were Russian-born Orthodox Jews. He studied mathematics at the University of California, Berkeley, doing a premedical programme at the same time. After taking a bachelor's degree in mathematics in 1945, he spent two years doing graduate courses in science, mathematics and philosophy, planning perhaps a career in the philosophy of science. One of his philosophy teachers, Hans Reichenbach, suggested he combine philosophy with science. He went to Columbia University to do a PhD with Abraham Wald but, when Wald died in a plane crash, Birnbaum asked Erich Leo Lehmann, who was visiting Columbia to take him on. Birnbaum's thesis and his early work was very much in the spirit of Lehmann's classic text ''Testi ... [...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] |
Sufficiency Principle
In statistics, a statistic is ''sufficient'' with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample (statistics), sample provides any additional information as to the value of the parameter". In particular, a statistic is sufficient for a Parametric family, family of probability distributions if the sample from which it is calculated gives no additional information than the statistic, as to which of those probability distributions is the sampling distribution. A related concept is that of linear sufficiency, which is weaker than ''sufficiency'' but can be applied in some cases where there is no sufficient statistic, although it is restricted to linear estimators. The Kolmogorov structure function deals with individual finite data; the related notion there is the algorithmic sufficient statistic. The concept is due to Ronald Fisher, Sir Ronald Fisher in 1920. Stephen Stigler noted in 1973 that the c ... [...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] |
Bayesian Inference
Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability". Introduction to Bayes' rule Formal explanation Bayesian inference derives the posterior probability as a consequence of two antecedents: a prior probability and a "likelihood function" derived from a statistical model for the observed data. Bayesian inference computes the posterior probability according to Bayes' theorem: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Likelihoodist
Likelihoodist statistics or likelihoodism is an approach to statistics that exclusively or primarily uses the likelihood function. Likelihoodist statistics is a more minor school than the main approaches of Bayesian statistics and frequentist statistics, but has some adherents and applications. The central idea of likelihoodism is the likelihood principle: data are interpreted as evidence, and the strength of the evidence is measured by the likelihood function. Beyond this, there are significant differences within likelihood approaches: "orthodox" likelihoodists consider data ''only'' as evidence, and do not use it as the basis of statistical inference, while others make inferences based on likelihood, but without using Bayesian inference or frequentist inference. Likelihoodism is thus criticized for either not providing a basis for belief or action (if it fails to make inferences), or not satisfying the requirements of these other schools. The likelihood function is also used in Ba ... [...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] |
Dice
Dice (singular die or dice) are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random values, commonly as part of tabletop games, including dice games, board games, role-playing games, and games of chance. A traditional die is a cube with each of its six faces marked with a different number of dots ( pips) from one to six. When thrown or rolled, the die comes to rest showing a random integer from one to six on its upper surface, with each value being equally likely. Dice may also have polyhedral or irregular shapes, may have faces marked with numerals or symbols instead of pips and may have their numbers carved out from the material of the dice instead of marked on it. Loaded dice are designed to favor some results over others for cheating or entertainment. History Dice have been used since before recorded history, and it is uncertain where they originated. It is theorized that dice developed from the practice ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bioinformatics
Bioinformatics () is an interdisciplinary field that develops methods and software tools for understanding biological data, in particular when the data sets are large and complex. As an interdisciplinary field of science, bioinformatics combines biology, chemistry, physics, computer science, information engineering, mathematics and statistics to analyze and interpret the biological data. Bioinformatics has been used for '' in silico'' analyses of biological queries using computational and statistical techniques. Bioinformatics includes biological studies that use computer programming as part of their methodology, as well as specific analysis "pipelines" that are repeatedly used, particularly in the field of genomics. Common uses of bioinformatics include the identification of candidates genes and single nucleotide polymorphisms (SNPs). Often, such identification is made with the aim to better understand the genetic basis of disease, unique adaptations, desirable properties (e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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