In algorithmic information theory , algorithmic Solomonoff probability is a method of assigning a probability to each hypothesis algorithm program that explains a given observation, with the simplest hypothesis the shortest program having the highest probability and the increasingly complex hypotheses longer programs receiving increasingly small probabilities. These probabilities form a priori a probability distribution for the observation, which Ray Solomonoff proved to be machine invariant called the invariance theorem and can be used with Bayes theorem to predict the most likely continuation of that observation. A theoretic computer, the universal Turing machine , is used for the computer operations. Solomonoff invented the concept of algorithmicprobability with its associated invariance theorem around 1960. ref http world.std.com rjs barc97.pdf The Discovery of AlgorithmicProbability , Journal of Computer and System Sciences, Vol. 55, No. 1, pp. 73 88, August 1997. ref He first published his results at a conference at Caltech in 1960, ref Paper from conference on Cerebral Systems and Computers , California Institute of Technology, Feb 8 11, 1960, cited in A Formal Theory of Inductive ... high probability. Algorithmicprobability is the main ingredient of Solomonoff s theory of inductive .... Algorithmicprobability is closely related to the concept of Kolmogorov complexity . Kolmogorov complexity, however, focuses on the information content of a string while algorithmicprobability ... scholarpedia.org article Algorithmicprobability detailed description of AlgorithmicProbability in Scholarpedia http world.std.com rjs pubs.html Solomonoff s publications DEFAULTSORT AlgorithmicProbability Category Algorithmic information theory Category Probability interpretations Category Artificial ... Inference, Part II Information and Control , Vol 7, No. 2 pp 224 254, June 1964. ref The algorithmicprobability of any given finite output prefix q is the sum of the probability probabilities of the programs ... more details
For the Law & Order Criminal Intent episode Probability Law & Order Criminal Intent Certainty Probability ... Event probability theory event occur? The attitude of mind is of the form How certain are we that the event ..., between 0 and 1, we call probability. ref An Introduction to Probability Theory and Its Applications, William Feller. 3rd Ed 1968 ref The higher the probability of an event, the more certain we are that the event will occur. Thus, probability in an applied sense is a measure of the likeliness ... derivation in probability theory , which is used widely in such areas of study as mathematics , statistics ..., draw inferences about the likeliness of events. Probability is used to describe the underlying mechanics and regularities of complex systems . Interpretations Main Probability interpretations The word probability does not have a singular direct definition for practical application. In fact, there are several broad categories of probability interpretations , whose adherents possess different and sometimes conflicting views about the fundamental nature of probability. For example Frequentists ... . The probability of a random event denotes the relative frequency of occurrence of an experiment s outcome, when repeating the experiment. Frequentists consider probability to be the relative frequency ... last Hacking year 1965 isbn ref Subjective probability Objective and subjective Bayesian probabilities Subjectivists assign numbers per subjective probability, i.e., as a degree of belief. ref cite journal title Logical foundations and measurement of subjective probability first Bruno de last Finetti ... ref Bayesian probability Bayesians include expert knowledge as well as experimental data to produce probabilities. The expert knowledge is represented by a prior probability distribution. The data is incorporated ... in a posterior probability distribution that incorporates all the information known to date. ref ... isbn 0130085073 ref Etymology The word Probability Derivation linguistics derives from the Latin ... more details
Algorithmic finance ref cite web url http algorithmicfinance.org title Algorithmic finance month December year 2010 ref is a new discipline that applies insights from theoretical computer science to questions involving finance, markets, or risk. References Reflist Finance Category Mathematical finance Econ stub ... more details
merge High frequency trading discuss Talk Algorithmic trading Merger proposal date February 2011 Financial market participants In electronic trading electronic financial markets , algorithmic trading or automated ... without human intervention. Algorithmic trading is widely used by pension fund s, mutual fund ... 20050328.php Algorithmic Trading Hype or Reality? ref Sell side traders, such as market maker s and some ... class of algorithmic trading is high frequency trading HFT , in which computers make elaborate ..., Liquidity Crashes and the Probability of Informed Trading work The Journal of Portfolio Management, Vol. 37, No. 2, pp. 118 128, Winter year 2011 ssrn 1695041 ref Algorithmic trading may be used in any ... at any stage with algorithmic support or may operate completely automatically. A third of all ... easily integrated into algorithmic trading, ref http www.economist.com finance displaystory.cfm?story ... last first author link year title Algorithmic trading, Ahead of the tape periodical The Economist ... id 9370718 date June 21, 2007 ref Bond finance Bond markets are moving toward more access to algorithmic ... Exclusive High frequency trading under the microscope date 4 August 2009 author Opalesque ref Algorithmic ... size from 1 16 of a dollar US 0.0625 to US 0.01 per share, may have encouraged algorithmic trading as it changed ... weighted average price . A further encouragement for the adoption of algorithmic trading in the financial ... of the electronic auctions used in the financial markets, two algorithmic strategies IBM s own MGD ... paper generated international media coverage. As more electronic markets opened, other algorithmic ... Most strategies referred to as algorithmic trading as well as algorithmic liquidity seeking fall ... Citation last Aldridge first Irene authorlink work High Frequency Trading A Practical Guide to Algorithmic ... by Charles Duhigg, November 23, 2006 ref blockquote One of the unintended adverse effects of algorithmic ... Algorithmic Trading Improve Liquidity? work Journal of Finance forthcoming year 2010 url http papers.ssrn.com ... more details
Algorithmic inference gathers new developments in the statistical inference methods made feasible by the powerful computing devices widely available to any data analyst. Cornerstones in this field are computational learning theory , granular computing , bioinformatics , and, long ago, structural probability harv Fraser 1966 . The main focus is on the algorithms which compute statistics rooting the study .... This shifts the interest of mathematicians from the study of the probability distribution distribution ... a companion dispute as to the nature of probability is it a physical feature of phenomena to be described ... deduces from a sample of its specifications. With this law he computes, for instance the probability ..., or the probability that it lies between any assigned values, or, in short, its probability distribution ..., such as Bayes posterior distribution , Fraser s constructive probability and Neyman s confidence ... the phenomenological nature of probability. With this perspective, when you deal with a Gaussian ... with a given probability that you denote confidence . Example Let X be a Gaussian variable ... data by first and probability distribution of their properties as a consequence, or fixed properties by first and probability distribution of the observed data as a corollary. The classic solution has ... very low probability of failing. The analytical solution is allowed for a very limited number ... 0.99 when the error is identified with the probability that a 20 year old man living in New ... a set of uniform seeds. Transferring to the parameters the probability density affecting the seeds ... compatible distribution is a distribution having the same Algorithmic inference Sampling mechanism ... to be learnt falls with a confidence of 90 . The former concerns the probability with which an extended ... Structural probability and generalization journal Biometrika volume 53 issue 1 2 pages 1 9 ref harv ... B. last2 Malchiodi first2 D. last3 Gaito first3 S. title Algorithmic Inference in Machine Learning ... more details
For the technique of performing basic arithmetic Algorism No footnotes date August 2009 Algorithmic art , also known as algorithm art , is art, mostly visual art , of which the design is generated by an algorithm . Algorithmic artists are sometimes called algorists . Overview Image Octopod by syntopia.jpg thumb Octopod by Mikael Hvidtfeldt Christensen. An example of algorithmic art produced with the software Structure Synth . Algorithmic art is a subset of generative art , and is practically always executed by a computer . If executed by a computer , it is also classified as computer generated ..., in algorithmic art the creative design is the result of an algorithmic process, usually using a random or pseudo random process to produce variability. Algorithmic art is also related to systems ... is an example of algorithmic art. History Some of the earliest known examples of computer generated algorithmic art were created by Georg Nees and Frieder Nake in the early 1960s. These artworks were ... the earliest algorithmic art was drawn by a plotter , fractal art simply creates an image in computer ... on a computer this is also true of very nearly all equation art and of most recent algorithmic art in general. However, in a stricter sense fractal art is not considered algorithmic art, because ... algorithmic art, its creation must include a process based on an algorithm devised by the artist ..., algorithmic art is not to be confused with graphical methods such as generating a fractal ... is a term used for digital artist s who create algorithmic art. One group of algorists is known as Les ... not an algorist Algorithmic artists unreferenced section date March 2011 Arambilet Spain Dominican ... algorist in art http www.verostko.com algorithm.html Algorithmic Art Composing the Score for Visual Art Roman Verostko http www.geneticart.org geneticart.org Algorithmic art based on the 1994 work ... Compart Database of Digital and Algorithmic Art DEFAULTSORT Algorithmic Art Category Art genres ... more details
Unreferenced date January 2012 Algorithmic composition is the technique of using algorithm s to create ... be reduced to algorithmic determinacy. The term is usually reserved, however, for the use of formal ...? says who? date January 2012 Models for algorithmic composition There is no universal method to sort ... of nature. For example, since the 1970s fractals have been studied also as models for algorithmic composition ... of music similar to the example material. This method of algorithmic composition is strongly linked to algorithmic modeling of style, machine improvisation, and such studies as cognitive science and the study of neural networks . Hybrid systems Programs based on a single algorithmic model rarely ... hybrid systems for music composition has opened up the field of algorithmic composition and created .... Works and applications Algorithmic techniques have also been employed in a number of systems intended for direct musical performance, with many using algorithmic techniques to generate infinitely ... s musical director Peter Langston later in the life of that company, now rechristened LucasArts , an algorithmic .... Notable composers known for their use of algorithmic procedures Aphex Twin Autechre Clarence Barlow ... AI Methods for Algorithmic Composition A survey, a Critical View and Future Prospects. AISB Symposium ... Karlheinz Essl Algorithmic Composition. in Cambridge Companion to Electronic Music, ed. by N. Collins ... algo comp.html Abstract Gerhard Nierhaus Algorithmic Composition Paradigms of Automated Music ..., Joachim, & Berry, Rodney 2005 A framework for comparison of process in algorithmic music ... 6544 External links Samples of algorithmic music http vimeo.com impromptu videos sort plays Andrew Sorensen s real time algorithmic improvisations A jazz saxophone solo automatically generated by Band ... wa viewPodcast?id 218454321 free subscription , algorithmic, computer generated Podcast series ... made with Tune Smithy http www.uvnitr.cz mg abacus abacus.html Abacus Milan Gu tar s algorithmic ... more details
Web Page . ref See also Algorithmicprobability . Effect of programming paradigms POV check section date June 2009 The effect that different programming paradigm s have on algorithmic efficiency is fiercely ... of an algorithm s execution, can often increase algorithmic efficiency substantially ... including human readable. From the perspective of algorithmic efficiency, minimizing subsequent decoding ... or brute force search depends critically on the nature of the input data, and their probability ... but he also cautioned use them sparingly ref name steele1997 See section Algorithmic efficiency Avoiding ... frequently built from the output of earlier computer processing, the actual probability of a field containing ... more details
In computing , algorithmic skeletons a.k.a. Parallelism Patterns are a high level parallel programming model for parallel and distributed computing. Algorithmic skeletons take advantage of common programming ... The most outstanding feature of algorithmic skeletons, which differentiates them from other high .... Springer Verlag, London, UK, 1999. ref Second, that algorithmic skeleton programming reduces ..., MPI . History Algorithmic skeletons were first introduced by Cole ref name cole thesis Murray Cole. Algorithmic Skeletons structured management of parallel computation MIT Press, Cambdridge, MA, USA ... of algorithmic skeleton frameworks can be found in. ref name survey 2010 Horacio Gonz lez V lez and Mario Leyton A survey of algorithmic skeleton frameworks high level structured parallel programming ... patterns This section describes some well known Algorithmic Skeleton patterns. Additionally, the patterns ... for parallel programming. The objective is to implement an Algorithmic Skeleton based parallel ... by Lithium and Muskel. As such, it provides algorithmic skeleton programming as a Java library ... features for algorithmic skeleton programming. First, a performance tuning model which helps ... algorithmic skeletons. In 13th International Euro Par Conference Parallel Processing, volume 4641 ... using Java Generics. ref D. Caromel, L. Henrio, and M. Leyton. Type safe algorithmic skeletons. In Proceedings ..., pages 45 53, Toulouse, France, Feb. 2008. IEEE CS Press. ref Third, a transparent algorithmic skeleton .... Leyton. A transparent non invasive file data model for algorithmic skeletons. In 22nd International ... programming. ref Mario Leyton, Jose M. Piquer. Skandium Multi core Programming with algorithmic ... scheme that describes a parallel implementation of an algorithmic skeleton. eSkel The Edinburgh ... in Algorithmic skeleton Skil Skil , e.g. higher order functions, currying, and polymorphic ... and data parallel skeletons. Skeleton nesting composition is similar to the two tier approach of Algorithmic ... more details
In probability and statistics , a posteriori probability may mean posterior probability in Bayes theorem empirical probability Disambig Category Applied probability Category Statistical terminology ... more details
Algorithmicprobability Chaitin s constant Chaitin Kolmogorov randomness Computationally indistinguishable ... 224 254 Solomonoff, R.J. 2009 AlgorithmicProbability Theory and Applications, Information Theory and Statistical ...Expert subject Computer science date November 2008 Algorithmic information theory is a subfield of information ... research groups CDMTCS docs ait.php Algorithmic Information Theory Bot generated title ref Overview Algorithmic information theory principally studies asymptotic complexity complexity measures on string .... Informally, from the point of view of algorithmic information theory, the information content ..., but the encyclopedia has more useful information. Unlike classical information theory, algorithmic ... of the choice of universal machine. Some of the results of algorithmic information theory, such as Kolmogorov ... of Chaitin s constant , a real number which expresses the probability that a self delimiting ... coin sometimes thought of as the probability that a random computer program will eventually halt . Although ... Algorithmic information theory was founded by Ray Solomonoff ref Vitanyi, P. http homepages.cwi.nl paulv obituary.html Obituary Ray Solomonoff, Founding Father of Algorithmic Information Theory ref , who published the basic ideas on which the field is based as part of his invention of algorithmicprobability a way to overcome serious problems associated with the application of Bayes rules in statistics ...., Cambridge, Ma., November Revision of Feb 4, 1960 report. ref Algorithmic information theory was later ... variants of Kolmogorov complexity or algorithmic information the most widely used one is based ... significantly to the information theory of infinite sequences. An axiomatic approach to algorithmic ... approaches in the algorithmic information theory. It is possible to treat different measures of algorithmic information as particular cases of axiomatically defined measures of algorithmic information ... approach to algorithmic information theory was further developed in the book Burgin 2005 and applied ... more details
Probability density may refer to Probability density function in probability theory The product of the probability amplitude with its complex conjugate in quantum mechanics disambig cs Hustota pravd podobnosti ... more details
Unreferenced date December 2009 Probability and statistics are two related but separate academic discipline s. Statistical analysis often uses probability distribution s, and the two topics are often studied together. However, probability theory contains much that is of mostly of mathematics mathematical interest and not directly relevant to statistics. Moreover, many topics in statistics are independent of probability theory. See also List of probability topics List of statistical topics Notation in probability and statistics External links http wiki.stat.ucla.edu socr index.php EBook Probability and Statistics EBook http www.cs.sunysb.edu skiena jaialai excerpts node12.html Probability versus Statistics DEFAULTSORT Probability And Statistics Category Probability and statistics Notstub ar eo Probablo kaj statistiko ... more details
of algorithmicprobability are used in inductive inference as a basis for induction in very general ... date October 2010 Other priors The concept of algorithmicprobability provides a route to specifying ...Bayesian statistics In Bayesian probability Bayesian statistical inference , a prior probability distribution ... of voters who will vote for the politician named Smith in a future election is the probability ... probability distribution , which is the conditional distribution of the uncertain quantity given the data ... prior. Some attempts have been made at finding a priori probability a priori probabilities , i.e. probability distributions in some sense logically required by the nature of one s state of uncertainty ... representing complete uncertainty about a probability should be the Haldane prior p sup &minus 1 sup ... was proposed by J.B.S. Haldane in A note on inverse probability , Mathematical Proceedings of the Cambridge ... dissolve every time or never dissolve, with equal probability. However, if one has observed samples ... an improper posterior distribution that puts 100 of the probability content at either p ... the prior probability as a constant improper prior . Similarly, some measurements are naturally ... the principle of maximum entropy MAXENT . The motivation is that the Shannon entropy of a probability ... a suitable set of probability distributions on X , one finds the distribution that is least informative ... that define the set. For example, the maximum entropy prior on a discrete space, given only that the probability is normalized to 1, is the prior that assigns equal probability to each state. And in the continuous ... sets, it should have good frequentist properties. Normally a Bayesian probability Bayesian would ... warn against the danger of over interpreting those priors since they are not probability densities ... author Rosenkrantz, Roger D. title E. T. Jaynes papers on probability, statistics, and statistical ... pages 116&ndash 130 cite book last Jaynes first Edwin T. authorlink Edwin T. Jaynes title Probability ... more details
In theoretical computer science , the algorithmic Lov sz local lemma gives an algorithmic way of constructing ... events math A 1, ldots, A n math in a probability space with limited dependence amongst the math A i ... that with non zero probability all of these events can be avoided. However, the lemma is non constructive ... the Lov sz Local Lemma to bound the probability that any of the features is missing. The absence ... simultaneously with non zero probability, the existence follows. The lemma itself reads as follows Let math mathcal A A 1, ldots, A n math be a finite set of events in the probability space math Omega ... such that math forall A in mathcal A Pr A leq x A prod B in Gamma A 1 x B math then the probability ... A 1 wedge ldots wedge overline A n , right geq prod A in mathcal A 1 x A . math Algorithmic version ... be found or constructed efficiently in practice. Note that random sampling from the probability space math Omega math is likely to be inefficient, since the probability of the event of interest math ... and Tardos, earlier work had also made progress in developing algorithmic versions of the Lov sz Local Lemma. J zsef Beck in 1991 first gave proof that an algorithmic version was possible. ref name ... An algorithmic approach to the Lov sz Local Lemma. I journal Random Structures and Algorithms volume .... Since the initial algorithm, work has been done to push algorithmic versions of the Local Lemma ... be a finite set of mutually independent random variables in the probability space math Omega math ... p math , i.e. the probability of each event math A math is at most math p math , math e p D 1 leq 1 ... the Symmetric Lov sz Local Lemma . We can also state the Symmetric Algorithmic Lov sz Local Lemma Let ... is at most math frac n D math . Example The following example illustrates how the algorithmic ... math is satisfiable. This statement can be proven easily using the symmetric version of the Algorithmic ... k math variables and since all variables are sampled uniformly at random, we can bound the probability ... more details
about the treatment of probability in expected utility theory the gambling uses of the term Lottery In Expected utility hypothesis expected utility theory , a lottery is a Probability distribution Discrete probability distribution discrete distribution of probability on a set of states of nature . The elements of a lottery correspond to the probability that a certain outcome arises from a given state of nature. ref Andreu Mas Colell Mas Colell, Andreu , Michael Whinston and Jerry R. Green economist Jerry Green 1995 . Microeconomic theory . Oxford Oxford University Press . ISBN 0 19 507340 1 ref In economics , individuals are assumed to rank lotteries according to a rational choice theory rational system of preferences , unless one follows a behavioral economics approach. Citation needed date December 2011 References Reflist DEFAULTSORT Lottery probability Category Probability theory Category Utility Probability stub ... more details
DISPLAYTITLE A priori probability The term a priori probability is used in distinguishing the ways in which values for probabilities can be obtained. In particular, an a priori probability is derived purely by deductive reasoning . ref Mood A.M., Graybill F.A., Boes D.C. 1974 Introduction to the Theory of Statistics 3rd Edition . McGraw Hill. Section 2.2 http www.colorado.edu Economics morey 7818 7818readings.html available online ref One way of deriving a priori probabilities is the principle of indifference , which has the character of saying that, if there are N mutually exclusive and exhaustive events and if they are equally likely, then the probability of a given event occurring is 1 N . Similarly the probability of one of a given collection of K events is K N . One disadvantage of defining probabilities in the above way is that it applies only to finite collections of events. In Bayesian inference , a priori probabilities are known as prior probability Uninformative priors uninformative priors or objective priors note that prior probability is a broader concept. See also A priori statistics A priori statistics References references Category Probability Category Statistical theory probability stub sr sh A priori vjerojatnost ... more details
ProbabilityTopicsTOC Probability is the likelihood or chance that something is the case or will happen. Probability theory is used extensively in statistics , mathematics , science and philosophy to draw ... the subject of probability. Introduction Probability and randomness . Basic probability Related topics set theory , simple theorems in the algebra of sets Events Event probability theory Events in probability ... Elementary probability The axioms of probability Boole s inequality Meaning of probabilityProbability interpretations Bayesian probability Frequency probability Calculating with probabilities Conditional probability The law of total probability Bayes theorem Independence Independence probability theory Probability theory Related topics measure theory Measure theoretic probability Sample space s, sigma algebra algebras and probability measure s Probability space Sample space Standard probability space Random element Random compact set Dynkin system Probability axioms Event probability theory Complementary event Elementary event Almost surely Independence Independence probability theory The Borel Cantelli lemma s and Kolmogorov s zero one law Conditional probability Conditional probability Conditioning probability Conditional expectation Conditional probability distribution Regular conditional probability Disintegration theorem Bayes theorem Rule of succession Conditional independence ... and continuous random variables Discrete random variable s Probability mass function s Continuous random variable s Probability density function s Normalizing constant s Cumulative distribution function ... Related topics integral transform s Common generating functions Probability generating function ... index convergence Modes of convergence Convergence in distribution and convergence in probability ... and autocorrelation Martingale probability theory Martingales Martingale central limit theorem Azuma s inequality See also Catalog of articles in probability theory Glossary of probability and statistics ... more details
In probability theory , inverse probability is an obsolete term for the probability distribution of an unobserved variable. Today, the problem of determining an unobserved variable by whatever method is called inferential statistics , the method of inverse probability assigning a probability distribution to an unobserved variable is called Bayesian probability , the distribution of an unobserved variable given data is rather the likelihood function which is not a probability distribution , and the distribution of an unobserved variable, given both data and a prior distribution , is the posterior distribution . The development of the field and terminology from inverse probability to Bayesian probability is described by Fienberg 2006 . ref name fienberg cite journal last Fienberg first Stephen ... 06 BA101 ref The term Bayesian , which displaced inverse probability , was in fact introduced by R. A. Fisher as a derogatory term. Citation needed date April 2009 The term inverse probability appears in an 1837 paper of Augustus De Morgan De Morgan , in reference to Laplace Laplace s method of probability ..., and 1812 book , though the term inverse probability does not occur in these. ref name fienberg Inverse probability, variously interpreted, was the dominant approach to statistics until the development ... terms, given a probability distribution p x for an observable quantity x conditional on an unobserved variable , the inverse probability is the posterior distribution p x , which depends both on the likelihood function the inversion of the probability distribution and a prior distribution. The distribution p x itself is called the direct probability . The inverse probability problem in the 18th ... now be considered one of inferential statistics . The terms direct probability and inverse probability ... distribution became prevalent. See also Bayesian probability Bayes theorem References reflist DEFAULTSORT Inverse Probability Category Statistical inference Category Probability interpretations ... more details
Empirical probability , also known as Frequency statistics relative frequency , or experimental probability , is the ratio of the number of favorable outcomes to the total number of trials, ref http www.answers.com topic empirical probability statistics Empirical probability at answers.com ref ref name Mood Mood A.M., Graybill F.A., Boes D.C. 1974 Introduction to the Theory of Statistics 3rd Edition . McGraw Hill. Section 2.3 ref not in a sample space but in an actual sequence of experiments. In a more general sense, empirical probability estimates probabilities from experience and observation ... probability is an estimate of a probability. If modelling using a binomial distribution is appropriate ... assumptions are made for the prior distribution of the probability. Advantages and disadvantages ... is relatively free of assumptions. For example, consider estimating the probability among ... could be found by counting the number of men who satisfy both conditions to give the empirical probability ... involved actually do hold. For example, consider estimating the probability that the lowest ... degrees Celsius. A record of such temperatures in past years could be used to estimate this probability. A model based alternative would be to select of family of probability distributions and fit it to the dataset ... of the desired probability. This alternative method can provide an estimate of the probability ... probability is also used as an alternative to empirical probability or relative frequency. ref name ... , but is not directly related to Bayesian inference , where a posteriori probability is occasionally used to refer to posterior probability , which is different even though it has a confusingly similar name. See also Empirical distribution function Empirical measure Frequency probability Realization probability Realization Sample statistics Sample A priori probability in relation to a posteriori probabiliy References references probability stub Category Applied probability Category Statistical ... more details
citations date February 2012 Infobox Journal abbreviation Ann. Prob. discipline Probability theory website http www.imstat.org aop link1 http projecteuclid.org aop link1 name Project Euclid publisher Institute of Mathematical Statistics country USA history 1973 present impact impact year ISSN 0091 1798 eISSN JSTOR 00911798 The Annals of Probability is a peer reviewed statistics Academic journal journal published by the Institute of Mathematical Statistics . It was started in 1973 as a continuation in part of the Annals of Mathematical Statistics , which was split into the Annals of Statistics and the Annals of Probability . Articles older than 3 years are available on JSTOR , and all articles since 2004 are freely available on the arXiv . External links http www.imstat.org aop Annals of Probability homepage http projecteuclid.org aop Annals of Probability at Project Euclid Category Probability journals ... more details
In probability theory probability and statistics , decoupling is a reduction of a sample statistic to an average of the statistic evaluated on several statistical independence independent sequences of the random variable . This sum, conditional probability conditioned on all but one of the independent sequences becomes a sum of independent random variables. Decoupling is used in the study of U statistic s, where decoupling should not be confused with Hoeffding s decomposition, however. ref cite book author Victor H. de la Pe a and Evariste Gin title Decoupling From Dependence to Independence publisher Springer Verlag year 1999 isbn 978 0387986166 ref Such decoupling is unrelated to the use of Coupling probability coupling s in the study of stochastic processes . References refs Category Probabilityprobability stub statistics stub ... more details
nofootnotes date March 2008 onesource date March 2008 Terminology Algorithmic learning theory is a mathematical framework for analyzing machine learning problems and algorithms. Synonyms include formal learning theory and algorithmic inductive inference . Algorithmic learning theory is different from statistical learning theory in that it does not make use of statistical assumptions and analysis. Both algorithmic and statistical learning theory are concerned with machine learning and can thus be viewed as branches of computational learning theory . Distinguishing Characteristics Unlike statistical learning theory and most statistical theory in general, algorithmic learning theory does not assume that data are random samples, that is, that data points are independent of each other. This makes the theory suitable for domains where observations are relatively noise free but not random, such as language learning ref Jain, S. et al 1999 Systems That Learn , 2nd ed. Cambridge, MA MIT Press. ref and automated scientific discovery ref Langley, P. Simon, H. Bradshaw, G. & Zytkow, J. 1987 , Scientific Discovery Computational Explorations of the Creative Processes , MIT Press, Cambridge ref ref Schulte, O. 2009 , Simultaneous Discovery of Conservation Laws and Hidden Particles With Smith Matrix Decomposition , in Proceedings of the Twenty First International Joint Conference on Artificial Intelligence IJCAI 09 , pp. 1481 1487 ref . The fundamental concept of algorithmic learning theory is learning in the limit as the number of data points increases, a learning algorithm should converge ... convergence to a correct model in the limit, but allows a learner to fail on data sequences with probability measure 0. Algorithmic learning theory investigates the learning power of Turing machine s. Other ... provides a highly accessible introduction to key concepts in algorithmic learning theory, especially as they apply to the philosophical problems of inductive inference. Ref end DEFAULTSORT Algorithmic ... more details
Exotic probability is a branch of probability theory that deals with probabilities which are outside the normal range of 0, 1 . The most common author of papers on exotic probability theory is Saul Youssef . According to Youssef, the valid possible alternatives for probability values are the real number s, the complex number s and the quaternion s. Youssef also cites the work of Richard Feynman , P. A. M. Dirac , Stanley Gudder and S. K. Srinivasan as relevant to exotic probability theories. Of the application of such theories to quantum mechanics , Bill Jefferys has said Such approaches are also not necessary and in my opinion they confuse more than they illuminate. ref Jefferys 2002 http www.lns.cornell.edu spr 2002 03 msg0040195.html Newsgroup discussion on sci.physics.research accessed 1 Sept 2010 ref Notes reflist External links http physics.bu.edu youssef quantum quantum refs.html http xxx.lanl.gov abs hep th 0110253 Physics with exotic probability theory paper by Youssef on arXiv . http fnalpubs.fnal.gov library colloq colloqyoussef.html http flux.aps.org meetings YR97 BAPSAPR97 vpr layn18 4.html Measuring Negative Probabilities, Demystifying Schroedinger s Cat and Exploring Other Quantum Peculiarities With Trapped Atoms http www.mathpages.com home kmath309.htm MathPages The Complex Domain of Probability Category Probability theory Category Exotic probabilities probability stub ... more details
In statistics , in the theory relating to sampling statistics sampling from finite Statistical population population s, the inclusion probability of an Element statistics element or member of the population is its probability of becoming part of the sample during the drawing of a single sample. ref Dodge, Y. 2003 The Oxford Dictionary of Statistical Terms , OUP ISBN 0 19 850994 4 ref Each element of the population may have a different probability of being included in the sample. The inclusion probability is also termed the first order inclusion probability to distinguish it from the second order inclusion probability , i.e. the probability of including a pair of elements. Generally, the first order inclusion probability of the i th element of the population is denoted by the symbol sub i sub and the second order inclusion probability that a pair consisting of the i th and j th element of the population that is sampled is included in a sample during the drawing of a single sample is denoted by sub ij sub . cn date May 2011 See also Sampling design References Reflist Further reading Refbegin Sarndal, Swenson, and Wretman 1992 , Model Assisted Survey Sampling , Springer Verlag, ISBN 0 387 40620 4 Refend Category Sampling statistics Category Statistical terminology de Auswahlsatz ... more details
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