|
Bhattacharyya Coefficient
In statistics, the Bhattacharyya distance measures the similarity of two probability distributions. It is closely related to the Bhattacharyya coefficient which is a measure of the amount of overlap between two statistical samples or populations. It is not a metric, despite named a "distance", since it does not obey the triangle inequality. Definition For probability distributions P and Q on the same domain \mathcal, the Bhattacharyya distance is defined as :D_B(P,Q) = -\ln \left( BC(P,Q) \right) where :BC(P,Q) = \sum_ \sqrt is the Bhattacharyya coefficient for discrete probability distributions. For continuous probability distributions, with P(dx) = p(x)dx and Q(dx) = q(x) dx where p(x) and q(x) are the probability density functions, the Bhattacharyya coefficient is defined as :BC(P,Q) = \int_ \sqrt\, dx. More generally, given two probability measures P, Q on a measurable space (\mathcal X, \mathcal B), let \lambda be a ( sigma finite) measure such that P and Q are absolute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistician
A statistician is a person who works with theoretical or applied statistics. The profession exists in both the private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, and statisticians may work as employees or as statistical consultants. Nature of the work According to the United States Bureau of Labor Statistics, as of 2014, 26,970 jobs were classified as ''statistician'' in the United States. Of these people, approximately 30 percent worked for governments (federal, state, or local). As of October 2021, the median pay for statisticians in the United States was $92,270. Additionally, there is a substantial number of people who use statistics and data analysis in their work but have job titles other than ''statistician'', such as actuaries, applied mathematicians, economist An economist is a professional and practitioner in the social science discipline of economics. The individual may also study, develop, and apply ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Distance
In statistics, probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be two random variables, or two probability distributions or samples, or the distance can be between an individual sample point and a population or a wider sample of points. A distance between populations can be interpreted as measuring the distance between two probability distributions and hence they are essentially measures of distances between probability measures. Where statistical distance measures relate to the differences between random variables, these may have statistical dependence,Dodge, Y. (2003)—entry for distance and hence these distances are not directly related to measures of distances between probability measures. Again, a measure of distance between random variables may relate to the extent of dependence between them, rather than to their individual values. Statistical distance measures are not typically m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Biosciences
The ''Journal of Biosciences'' is a peer-reviewed scientific journal published by the Indian Academy of Sciences, Bengaluru, India. The current editor-in-chief is Prof. B J Rao (IISER Tirupati, Tirupati). According to the ''Journal Citation Reports'', the journal has a 2019 impact factor of 1.65. History The ''Journal of Biosciences'' was established in 1934 as the ''Proceedings of the Indian Academy of Sciences (Section B)''. In 1978, the ''Proceedings'' were split into three sections: ''Proceedings-Animal Sciences, Proceedings-Plant Sciences,'' and ''Proceedings-Experimental Biology''. The latter section was renamed ''Journal of Biosciences'' in 1979, and in 1991 it was merged again with the other two sections. Aim and Scope The journal covers all areas of biology and is considered the premier journal in the country within its scope. It publishes research and reviews, series articles, perspectives, clipboards, commentaries, and short communications. Special theme issues a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE Transactions On Pattern Analysis And Machine Intelligence
''IEEE Transactions on Pattern Analysis and Machine Intelligence'' (sometimes abbreviated as ''IEEE PAMI'' or simply ''PAMI'') is a monthly peer-reviewed scientific journal published by the IEEE Computer Society. Background The journal covers research in computer vision and image understanding, pattern analysis and recognition, machine intelligence, machine learning, search techniques, document and handwriting analysis, medical image analysis, video and image sequence analysis, content-based retrieval of image and video, and face and gesture recognition. The editor-in-chief is Kyoung Mu Lee (Seoul National University). According to the ''Journal Citation Reports'', the journal has a 2021 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... of 24.314. References Ext ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fidelity Of Quantum States
In quantum mechanics, notably in quantum information theory, fidelity is a measure of the "closeness" of two quantum states. It expresses the probability that one state will pass a test to identify as the other. The fidelity is not a metric on the space of density matrices, but it can be used to define the Bures metric on this space. Given two density operators \rho and \sigma, the fidelity is generally defined as the quantity F(\rho, \sigma) = \left(\operatorname \sqrt\right)^2. In the special case where \rho and \sigma represent pure quantum states, namely, \rho=, \psi_\rho\rangle\!\langle\psi_\rho, and \sigma=, \psi_\sigma\rangle\!\langle\psi_\sigma, , the definition reduces to the squared overlap between the states: F(\rho, \sigma)=, \langle\psi_\rho, \psi_\sigma\rangle, ^2. While not obvious from the general definition, the fidelity is symmetric: F(\rho,\sigma)=F(\sigma,\rho). Motivation Given two random variables X,Y with values (1, ..., n) ( categorical random variab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
F-divergence
In probability theory, an f-divergence is a function D_f(P\, Q) that measures the difference between two probability distributions P and Q. Many common divergences, such as KL-divergence, Hellinger distance, and total variation distance, are special cases of f-divergence. History These divergences were introduced by Alfréd Rényi in the same paper where he introduced the well-known Rényi entropy. He proved that these divergences decrease in Markov processes. ''f''-divergences were studied further independently by , and and are sometimes known as Csiszár f-divergences, Csiszár-Morimoto divergences, or Ali-Silvey distances. Definition Non-singular case Let P and Q be two probability distributions over a space \Omega, such that P\ll Q, that is, P is absolutely continuous with respect to Q. Then, for a convex function f: , \infty)\to(-\infty, \infty/math> such that f(x) is finite for all x > 0, f(1)=0, and f(0)=\lim_ f(t) (which could be infinite), the f-divergence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rényi Entropy
In information theory, the Rényi entropy is a quantity that generalizes various notions of entropy, including Hartley entropy, Shannon entropy, collision entropy, and min-entropy. The Rényi entropy is named after Alfréd Rényi, who looked for the most general way to quantify information while preserving additivity for independent events. In the context of fractal dimension estimation, the Rényi entropy forms the basis of the concept of generalized dimensions. The Rényi entropy is important in ecology and statistics as index of diversity. The Rényi entropy is also important in quantum information, where it can be used as a measure of entanglement. In the Heisenberg XY spin chain model, the Rényi entropy as a function of can be calculated explicitly because it is an automorphic function with respect to a particular subgroup of the modular group. In theoretical computer science, the min-entropy is used in the context of randomness extractors. Definition The Rényi entro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chernoff Bound
In probability theory, the Chernoff bound gives exponentially decreasing bounds on tail distributions of sums of independent random variables. Despite being named after Herman Chernoff, the author of the paper it first appeared in, the result is due to Herman Rubin. It is a sharper bound than the first- or second-moment-based tail bounds such as Markov's inequality or Chebyshev's inequality, which only yield power-law bounds on tail decay. However, the Chernoff bound requires the variates to be independent, a condition that is not required by either Markov's inequality or Chebyshev's inequality (although Chebyshev's inequality does require the variates to be pairwise independent). The Chernoff bound is related to the Bernstein inequalities, which were developed earlier, and to Hoeffding's inequality. The generic bound The generic Chernoff bound for a random variable is attained by applying Markov's inequality to . This gives a bound in terms of the moment-generating function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kullback–Leibler Divergence
In mathematical statistics, the Kullback–Leibler divergence (also called relative entropy and I-divergence), denoted D_\text(P \parallel Q), is a type of statistical distance: a measure of how one probability distribution ''P'' is different from a second, reference probability distribution ''Q''. A simple interpretation of the KL divergence of ''P'' from ''Q'' is the expected excess surprise from using ''Q'' as a model when the actual distribution is ''P''. While it is a distance, it is not a metric, the most familiar type of distance: it is not symmetric in the two distributions (in contrast to variation of information), and does not satisfy the triangle inequality. Instead, in terms of information geometry, it is a type of divergence, a generalization of squared distance, and for certain classes of distributions (notably an exponential family), it satisfies a generalized Pythagorean theorem (which applies to squared distances). In the simple case, a relative entropy of 0 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bhattacharyya Angle
In statistics, Bhattacharyya angle, also called statistical angle, is a measure of distance between two probability measures defined on a finite probability space. It is defined as : \Delta(p,q) = \arccos \operatorname(p,q) where ''p''''i'', ''q''''i'' are the probabilities assigned to the point ''i'', for ''i'' = 1, ..., ''n'', and : \operatorname(p,q) = \sum_^n \sqrt is the Bhattacharya coefficient. The Bhattacharya distance is the geodesic distance in the orthant of the sphere S^ obtained by projecting the probability simplex on the sphere by the transformation p_i \mapsto \sqrt,\ i=1,\ldots, n. This distance is compatible with Fisher metric. It is also related to Bures distance and fidelity between quantum states as for two diagonal states one has : \Delta(\rho,\sigma) = \arccos \sqrt. See also * Bhattacharyya distance * Hellinger distance In probability and statistics, the Hellinger distance (closely related to, although different from, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sankhya (journal)
''Sankhyā: The Indian Journal of Statistics'' is a quarterly peer-reviewed scientific journal on statistics published by the Indian Statistical Institute (ISI). It was established in 1933 by Prasanta Chandra Mahalanobis, founding director of ISI, along the lines of Karl Pearson's ''Biometrika''. Mahalanobis was the founding editor-in-chief. Each volume of ''Sankhya'' consists of four issues, two of them are in Series A, containing articles on theoretical statistics, probability theory, and stochastic processes, whereas the other two issues form Series B, containing articles on applied statistics, i.e. applied probability, applied stochastic processes, econometrics, and statistical computing. ''Sankhya'' is considered as "core journal" of statistics by the Current Index to Statistics. Publication history ''Sankhya'' was first published in June 1933. In 1961, the journal split into two series: Series A which focused on mathematical statistics and Series B which focused on stat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
