Refimprove date December 2009 Statistical physics is the branch of physics that uses methods of probability theory and statistics , and particularly the Mathematics mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic nature. Its applications include many problems in the fields of physics, biology , chemistry , neurology , and even some social sciences, such as sociology . Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion. ref cite book title Introduction to Statistical Physics last Huang first Kerson year publisher CRC Press isbn 978 1 4200 7902 9 page 15 edition 2nd ref In particular, statistical mechanics ... microscopic systems. Historically, one of the first topics in physics where statistical ... or objects when subjected to a force. Statistical mechanics Statistical mechanics provides a framework ... level. Because of this history, the statistical physics is often considered synonymous with statistical mechanics or statistical thermodynamics . ref group note This article presents a broader sense of the definition of statistical physics ref One of the most important equations in Statistical mechanics ... of occurring, a result that is consistent with intuition. A statistical approach can work well .... Statistical mechanics can also describe work in non linear dynamics , chaos theory , thermal physics ... in statistical physics can be solved analytically using approximations and expansions, most current .... A common approach to statistical problems is to use a Monte Carlo simulation to yield insight into the dynamics of a complex system. See also Statistical ensemble mathematical physics Statistical ensemble Statistical field theory Mean sojourn time Dynamics of Markovian particles Complex network ... Statistical Physics Categories Category Statistical mechanics Category Formal sciences Physics ... more details
otheruses4 the journal the mathematical science of statistics Statistics Infobox Journal title Statistical Science cover discipline Statistics language English website http www.imstat.org sts publisher Institute of Mathematical Statistics country United States USA history 1986 to present frequency ISSN 0883 4237 OCLC 12143452 LCCN sn98 23316 impact 3.523 impact year 2009 link1 http projecteuclid.org handle euclid.ss link1 name Access via Project Euclid JSTOR 08834237 Statistical Science is a review journal published by the Institute of Mathematical Statistics . The founding editor was Morris H. DeGroot . Further reading cite journal url http www.imstat.org sts degroot.pdf title Editorial The purpose of Statistical Science first Morris H last DeGroot authorlink Morris H. DeGroot journal Statistical Science volume 1 pages 1 2 External links http www.imstat.org sts Statistical Science home page Statistics journals Category Institute of Mathematical Statistics Category Statistics journals socialscience journal stub ... more details
Statistical literacy is a term used to describe an individual s or group s ability to understand statistics . Statistical literacy is necessary for citizens to understand material presented in publications ... to critically evaluate statistical material and to appreciate the relevance of statistically based approaches to all aspects of life in general. ref Dodge, Y. 2003 The Oxford Dictionary of Statistical Terms , OUP. ISBN 0 19 920613 9 ref ref Wallman, K. 1993 Enhancing statistical literacy Enriching our society. J. American Statistical Association , 88, 1&ndash 8 ref ref http www.stat.auckland.ac.nz iase publications isr 02.Gal.pdf Gal, I. 2002 . Adults statistical literacy Meaning, components, responsibilities with Discussion . International Statistical Review , 70 1 , 1 51. ref H.G. Wells is often cited as saying that statistical understanding will one day be as important as being able to read or write ref Wallman, K. 1993 Enhancing statistical literacy Enriching our society. J. American Statistical Association , 88, 1&ndash 8 ref but he may have been referring more to the older idea of political arithmetic than modern statistics. Aspects of statistical literacy Many official statistical ... iase islp The International Statistical Literacy Project ref of the International Statistical Institute ... the statistical literacy of all members of society. Numerous resources and activities, as well .... The UNECE has taken the notion of statistical literacy as the subject for its fourth guide to making ... of statistics, in 2010 the Royal Statistical Society launched a ten year statistical literacy .... People involved in these fields generally have studied the meaning of statistical quantities ... course in statistics as part of a professional program. Each day people are inundated with statistical ... re talking about . Experts and advocates often use numerical claims to bolster their arguments, and statistical ... that may seem valid. The aim of statistical literacy proponents is to improve the public understanding ... more details
Orphan date April 2012 Statistical epidemiology is an emerging branch of the disciplines of epidemiology and biostatistics that aims to Bring more statistical rigour to bear in the field of epidemiology Recognise the importance of applied statistics , especially with respect to the context in which statistical methods are appropriate and inappropriate Aid and improve our interpretation of observations Introduction The science of epidemiology has had enormous growth, particularly with charity and government funding. Many researchers have been trained to conduct studies, requiring multiple skills ranging from liaising with clinical staff to the statistical analysis of complex data , such as using Bayesian method s. The role of a Statistical Epidemiologist is to bring the most appropriate methods available to bear on observational study from medical research, requiring a broad appreciation of the underpinning methods and their context of applicability and interpretation. The earliest mention of this phrase was in an article by EB Wilson, ref name W taking a critical look at the way in which statistical methods were developing and being applied in the science of epidemiology. Academic recognition There are two Professors of Statistical Epidemiology in the United Kingdom http www.leeds.ac.uk light staff Mark S Gilthorpe University of Leeds and http www1.ic.ac.uk medicine research researchthemes publicandint ide research groups stats Imperial College , London and a Statistical Epidemiology group Oxford University . Related fields Statistical epidemiology draws upon quantitative methods ... Interior.aspx International Biometric Society American Statistical Association Royal Statistical ... Biostatistics References reflist refs ref name W Wilson, E.B. 1963 A critical look at statistical ... abstract ref External links http statisticalepidemiology.org Statistical Epidemiology webpage Category Epidemiology Category Demography Category Fields of application of statistics Category Statistical ... more details
Image statsol.jpg 150px right link http www.statistical solutions software.com StatSol br Statistical Solutions is a developer and distributor of statistical software mainly in the niche clinical trials market. The origins of this company can be traced to 1984 with the establishment of a company called BMDP statistical software, a Los Angeles based company with a European subsidiary based in Cork city Cork, Ireland . BMDP launched the very first statistical software package, named after the company designed for use by general as opposed to niche markets. In exchange for government funding BMDP made the algorithms behind its software package available to the public domain. Mary Byrne who would later become the CEO and managing director of Statistical Solutions, lead a buyout of the European subsidiary in 1995. Thus the former subsidiary became an independent Irish firm by the name of Statistical Solutions. Initially Statistical Solutions had intended to operate in the general application software market however a number of events triggered the redirection of the company s focus. They set about developing a new and innovative software programme to address a statistical phenomenon called missing data which threatened to compromise the validity of clinical trials. With the aid of Harvard scholar Dr. Donald Rubin ref Donald Rubin s Harvard Webpage http www.stat.harvard.edu faculty page.php?page rubin.html ref the company developed Solas software Solas , one of the world s first software .... Around the same time Statistical Solutions also successfully negotiated the global exclusive ... data analysis. ref Ken Deal 2004 http statistical solutions software.com wp content uploads 2009 11 Ken Deal Missing Something.pdf ref As a Cork based company, Statistical Solutions are members of IT Cork. ref http www.itcork.ie index.cfm page viewCompanyProfile memberCompanyId 387 ref Statistical ... Statistical Solutions webpage Category Software companies of Ireland Category Statistical software ... more details
Statistical fluctuations are fluctuations in quantities derived from many identical random processes. They are fundamental and unavoidable. It can be proved that the relative fluctuations reduce as the square root of the number of identical processes. Statistical fluctuations are responsible for many results of statistical mechanics and thermodynamics , and phenomena such as shot noise in electronics. Description When a number of random processes occur, it can be shown that the outcomes fluctuate vary in time and that the fluctuations are proportional to the square root of the number of processes. Examples As an example that will be familiar to all, if a fair Coin flipping coin is tossed many times and the number of heads and tails counted, the ratio of heads to tails will be very close to 1 about as many heads as tails but after only a few throws, outcomes with a significant excess of heads over tails or vice versa are common if an experiment with a few throws is repeated over and over, the outcomes will fluctuate a lot. An electric current so small that not many electrons are involved flowing through a p n junction is susceptible to statistical fluctuations as the actual number of electrons per unit time the current will fluctuate this produces detectable and unavoidable electrical noise known as shot noise . See also Thermal fluctuations not a very good stub yet, but such an important phenomenon in all physics that it really needs an article Unreferenced date February 2011 No footnotes date February 2011 Category Statistical randomness Category Stochastic processes Category Statistical mechanics Probability stub Statistics stub ... more details
Statistical noise is the colloquialism for recognized amounts of unexplained variation in a sample statistics sample . See errors and residuals in statistics . Examples Gaussian noise External links cite web url http www.faqs.org faqs ai faq neural nets part3 section 2.html title How does noise affect generalization? date 2001 05 21 publisher faqs.org accessdate 2008 07 13 Category Noise Category Statistical deviation and dispersion statistics stub ... more details
is impossible . Legislation concerning gambling imposes certain standards of statistical randomness ... Babington Smith in the Journal of the Royal Statistical Society in 1938. They were built on statistical ... s original four tests were statistical hypothesis testing hypothesis tests , which took as their null ... it would not be random it would not pass their tests , and would be useless for a number of statistical ... s Universal Statistical Test. See also Checking if a coin is fair Normal number Randomness Statistical ..., Journal of the Royal Statistical Society 101 1 1938 , 147 166. External links http www.phy.duke.edu ... Normal Distributed Random Numbers DEFAULTSORT Statistical Randomness Category Statistical randomness ... more details
In statistics , probability theory , and information theory , a statistical distance quantifies the distance between two statistical objects, which can be two Sample statistics samples , two random variable s, or two probability distribution s, for example. Metrics A metric on a set X is a function mathematics function called the distance function or simply distance d X X R where R is the set of real number s . For all x , y , z in X , this function is required to satisfy the following conditions d x , y 0 Non negative non negativity d x , y 0 if and only if x y identity of indiscernibles . Note that condition 1 and 2 together produce Positive definite function positive definiteness d x , y d y , x Symmetric relation symmetry d x , z d x , y d y , z subadditivity triangle inequality . Distances Generalized metrics Many statistical distances are not metric mathematics metric s, because they lack one or more properties of proper metrics. For example, pseudometric space pseudometric s can violate the Positive definite function In dynamical systems positive definiteness alternatively, metric mathematics Pseudometrics identity of indescernibles property quasimetric s can violate the metric mathematics Quasimetrics symmetry property and semimetric s can violate the metric mathematics Semimetrics triangle inequality . Some statistical distances are referred to as divergence statistics divergence s . Examples Some important statistical distances include the following f divergence includes Kullback Leibler divergence Hellinger distance Total variation distance R nyi entropy R nyi s divergence Jensen Shannon divergence L vy Prokhorov metric Bhattacharyya distance Wasserstein metric also known as the Kantorovich ... date February 2012 Notes Reflist References Dodge, Y. 2003 Oxford Dictionary of Statistical Terms , OUP. ISBN 0 19 920613 9 Category Statistical distance measures statistics stub Probability stub ... more details
Statistical parsing is a group of parsing methods within natural language processing . The methods have in common that they associate grammar rules with a probability. Grammar rules are traditionally viewed in computational linguistics as defining the valid sentences in a language. Within this mindset, the idea of associating each rule with a probability then provides the relative frequency of any given grammar rule and, by deduction, the probability of a complete parse for a sentence. The probability associated with a grammar rule may be induced, but the application of that grammar rule within a parse tree and the computation of the probability of the parse tree based on its component rules is a form of deduction. Using this concept, statistical parsers make use of a procedure to search over a space of all candidate parses, and the computation of each candidate s probability, to derive the most probable parse of a sentence. The expectation maximization algorithm is one popular method of searching for the most probable parse. Search in this context is an application of the very useful search algorithm in artificial intelligence . By way of example, think about the sentence The can can hold water . A reader would instantly see that there is an object called the can and that this object ... the first interpretation rather than the second and statistical parsers achieve this by ranking the interpretations ... of methods that statistical parsing algorithms frequently use. While few algorithms will use all of these they give a good overview of the general field. Most statistical parsing algorithms ... separately Viterbi algorithm . Notable people in statistical parsing Eugene Charniak Author of http www.cs.brown.edu people ec home.html Statistical techniques for natural language parsing ... Collins computational linguist http people.csail.mit.edu mcollins First very high performance statistical ... parsing Category Statistical natural language processing ... more details
to have occurred by Randomness chance . The phrase Statistical hypothesis testing test of significance ... is or is not significantly different from the first. R. A. Fisher 1925 . Statistical Methods for Research ... Ronald Fisher Fisherian statistical hypothesis testing , the p value is the probability of observing ... date December 2011 An alternative but nevertheless related statistical hypothesis testing framework ... , 0.5 0.005 , and 0.1 0.001 . If a Statistical hypothesis testing test of significance gives a p ... chance in a thousand this could have happened by coincidence, a 0.001 level of statistical significance ... ref cite book author Fisher RA year 1925 title Statistical Methods for Research Workers edition first ... the statistical significance as 1 &minus . In general, when interpreting a stated significance ... error , or false negative determination , and so have less statistical power . The selection of the level ... the Type I error and the Type II error . More statistical power powerful experiments usually experiments ... of sigma In some fields, for example nuclear and particle physics, it is common to express statistical significance in units of the standard deviation of a normal distribution . A statistical significance ... be regarded as useful in exploratory data analyses. However, modern statistical advice is that, where ... literature contains extensive discussion of the use of the concept of statistical significance and in particular of its Statistical hypothesis testing Potential misuse potential misuse and Statistical ... of significance Statistical significance can be considered to be the confidence one has in a given result ... statistical independence independent statistical hypothesis testing test s of significance Legal burden ... of Statistical Significance How the Standard Error Costs Us Jobs, Justice, and Lives . Ann Arbor, University .... Journal of Socio Economics , 33, pp. 607 613. Chow, Siu L., 1996 . Statistical Significance Rationale, Validity and Utility, Volume 1 of series Introducing Statistical Methods, Sage Publications ... more details
A statistical syllogism or proportional syllogism or direct inference is a non deductive syllogism . It argues from a generalization true for the most part to a particular case in contrast to inductive inference induction , which argues from particular cases to generalizations . Introduction Statistics Statistical syllogisms may use qualifier qualifying words like most , frequently , almost never , rarely , etc., or may have a statistical generalization as one or both of their premises. For example Almost all people are taller than 26 inches Bob is a person Therefore, Bob is taller than 26 ... class and people is the reference class. Unlike many other forms of syllogism, a statistical ... simpliciter fallacies can occur in statistical syllogisms. They are accident fallacy accident and converse .... A problem with applying the statistical syllogism in real cases is the reference class ... of attribute G may differ widely, how should one decide which class to use in applying the statistical syllogism? The importance of the statistical syllogism was urged by Henry E. Kyburg, Jr ... intervals in statistics is often justified using a statistical syllogism, in such words as Were this procedure ... happen in multiple samples to the confidence we should have in the particular sample involves a statistical ... insured against, which involves an implicit use of a statistical syllogism. John Venn pointed .... The problem of induction The statistical syllogism was used by Donald Cary Williams and David ... the argument, which has the form of a statistical syllogism The great majority of large samples of a population ... they are all white, then it is likely, using this statistical syllogism, that the population is all or nearly all white. That is an example of inductive reasoning. Legal examples Statistical syllogisms ... for non payment of the entrance fee. The statistical syllogism 501 of the 1000 attendees have ... DEFAULTSORT Statistical Syllogism Category Logic and statistics Category Arguments Category Term logic ... more details
linguistics Statistical semantics is the study of how the statistical patterns of human word usage can be used to figure out what people mean, at least to a level sufficient for information access George Furnas Furnas , 2006 . How can we figure out what words mean, simply by looking at patterns of words in huge collections of text? What are the limits to this approach to understanding words? History The term Statistical Semantics was first used by Warren Weaver Weaver 1955 in his well known paper on machine translation . He argued that word sense disambiguation for machine translation should be based on the co occurrence frequency of the context words near a given target word. The underlying assumption that a word is characterized by the company it keeps was advocated by J. R. Firth J.R. Firth ... . Delavenay 1960 defined Statistical Semantics as Statistical study of meanings of words and their frequency ... contribution to Statistical Semantics. An early success in the field was Latent semantic analysis Latent Semantic Analysis . Applications of statistical semantics Research in Statistical ... many aspects of semantics , by applying statistical techniques to Text corpus large corpora ... and Littman, 2003 Related fields Statistical Semantics focuses on the meanings of common words ..., document collections, or named entities names of people, places, and organizations . Statistical Semantics ... and natural language processing . Many of the applications of Statistical Semantics listed ... of Statistical Semantics. One advantage of corpus based algorithms is that they are typically ..., and Dumais, S.T. 1983 . Statistical semantics Analysis of the potential performance of keyword information ... for statistical word similarity measures. In Proceedings of the Human Language Technology and North ... Translation of Languages , Cambridge, MA MIT Press. ISBN 0 8371 8434 7 DEFAULTSORT Statistical Semantics ... retrieval Category Semantics Category Statistical natural language processing Category Fields ... more details
notability date February 2012 Statistical regularity is a notion in statistics and probability theory that random events exhibit regularity when repeated enough times or that enough sufficiently similar random events exhibit regularity. It is an umbrella term that covers the law of large numbers , all central limit theorem s and ergodic theorem s. If one throws a die once, it is difficult to predict the outcome, but if we repeat this experiment many times, we will see that the number of times each result occurs divided by the number of throws will eventually stabilize towards a specific value. Repeating a series of trials will produce similar, but not identical, results for each series the average, the standard deviation and other distributional characteristics will be around the same for each series of trials. The notion is used in games of chance , demographic statistics , quality control of a manufacturing process, and in many other parts of our lives. Observations of this phenomenon provided the initial motivation for the concept of what is now known as frequency probability . This phenomenon should not be confused with the Gambler s fallacy , it only concerns regularity in the possibly very long run. Gambler s fallacy does not apply to statistical regularity because the latter considers the whole rather than individual cases. See also Impossibility of a gambling system inline date February 2012 References Leon Garcia, Albert 1994 Probability and Random Processes for Electrical Engineering 2nd edition , Prentice Hall Whitt, Ward 2002 Stochastic Process Limits, An Introduction to Stochastic Process Limits and their Application to Queues , Chapter 1 Experiencing Statistical Regularity, http www.columbia.edu ww2040 book.html link to selected chapters Category Statistical terminology ... more details
When two probability distribution s overlap, statistical interference exists. Knowledge of the distributions can be used to determine the likelihood that one parameter exceeds another, and by how much. This technique can be used for dimensioning of mechanical parts, determining when an applied load exceeds the strength of a structure, and in many other situations. This type of analysis can also be used to estimate the probability of failure or the frequency of failure . Dimensional interference Image Interference.jpg right thumb 300px Interference of measurement distributions to determine fit of parts Mechanical parts are usually designed to fit precisely together. For example, if a shaft is designed to have a sliding fit in a hole, the shaft must be a little smaller than the hole. Traditional tolerance engineering tolerances may suggest that all dimensions fall within those intended tolerances. A process capability study of actual production, however, may reveal normal distribution s with long tails. Both the shaft and hole sizes will usually form normal distributions with some average arithmetic mean and standard deviation . With two such normal distributions, a distribution of interference can be calculated. The derived distribution will also be normal, and its average will be equal to the difference between the means of the two base distributions. The variance of the derived distribution will be the sum of the variances of the two base distributions. This derived distribution can be used to determine how often the difference in dimensions will be less than zero i.e., the shaft ..., the statistical interference may be calculated as above. This problem is also workable for transformed ... of statistical interference. See also Tolerance engineering Specification Process capability ... date September 2010 References Paul H. Garthwaite, Byron Jones, Ian T. Jolliffe 2002 Statistical ... DEFAULTSORT Statistical Interference Category Engineering Category Statistical models Category Quality ... more details
refimprove date December 2010 In statistics , statistical dispersion also called statistical variability or variation is variability or spread in a Variable mathematics variable or a probability distribution . Common examples of measures of statistical dispersion are the variance , standard deviation and interquartile range . Dispersion is contrasted with location or central tendency , and together they are the most used properties of distributions. Measures of statistical dispersion A measure of statistical dispersion is a real number that is zero if all the data are identical, and increases as the data become more diverse. It cannot be less than zero. Most measures of dispersion have the same scale as the quantity being measured. In other words, if the measurements have units of measurement unit s, such as metres or seconds, the measure of dispersion has the same units. Such measures of dispersion include Standard deviation Interquartile range or Interdecile range Range statistics Range Mean difference Median absolute deviation Average absolute deviation or simply called average deviation Distance standard deviation These are frequently used together with scale factor s as estimator s of scale parameter s, in which capacity they are called estimates of scale. Robust measures of scale are those unaffected by a small fraction of outliers. All the above measures of statistical dispersion have the useful property that they are location invariant , as well as linear in scale. So if a random variable X has a dispersion of S sub X sub then a linear transformation Y aX b for real number real a and b should have dispersion S sub Y sub a S sub X ... information entropy entropy . Sources of statistical dispersion In the physical sciences , such variability ... ref cite book last McQuarrie first Donald A. title Statistical Mechanics year 1976 publisher Harper ... Statistical Dispersion Category Statistical deviation and dispersion Category Summary statistics ... more details
The T Model is a formula that states the returns earned by holders of a company s stock in terms of accounting ... the period book value The T Model connects fundamentals with investment return, allowing an analyst ... in, the T Model gives a close approximation of actually realized stock returns ref Estep, Tony, Security ..., it has the advantage of being correct in a mathematical sense see T Model Derivation derivation ... and Richard Lynn, Is The Estep T Model Consistently Useful? Financial Analysts Journal, November ... techniques such as price earnings or the simplified dividend discount model it is mathematically ... Estep published a T Model The Cash Flow T Model version of the T Model driven by cash items cash ... models such as the Capital Asset Pricing Model and its various descendants financial models attempt ... PB PB mathit 1 g math Substituting 3 and 4 into 2 gives 1 , the T Model. The Cash Flow T Model In 2003 Estep published a version of the T Model that does not rely on estimates of Return on Equity, but rather ... from the balance sheet. The Cash flow T Model is math mathit T frac mathit CF mathit P boldsymbol ..., and Investment Returns , The Journal Of Portfolio Management, Spring 2003 ref that this model is mathematically identical to the original T Model, and gives identical results under certain simplifying ... it may be preferable to the standard T Model, because the specific accounting items used as input values ... valuation formulas and techniques can be understood as simplified cases of the T Model. For example ... period. The third term of the T Model becomes zero, and the remaining terms simplify to math ... Gordon yield plus growth model. It will be a correct estimate of T if PB does not change ... and the required return, T . The T Model is also closely related to the P B ROE model of Wilcox ref Wilcox, Jarrod W., The P B ROE Valuation Model, Financial Analysts Journal, Jan Feb 1984, pp 58 66 ... dei rendimenti azionari il T model, Economia & Management 1988, v. 2, p. 93 104 http www.northinfo.com ... more details
The Heisenberg model can refer to two models in statistical mechanics Heisenberg model classical , a classical nearest neighbour spin model Heisenberg model quantum , a model where the spins are treated Quantum mechanics quantum mechanically using Pauli matrices . disambig ... more details
A terminology model ref cite conference url http www.odaba.com content downloads documentation P2 TerminologyModel v1.pdf title A terminology model approach for defining and managing statistical metadata first R. last Karge month April year 2005 conference Eighth Open Forum on Metadata Registries conferenceurl www.berlinopenforum.de location Berlin format Power Point ref is a refinement of a concept system. ref http www.iso.org iso catalogue detail.htm?csnumber 31696 ISO 704 2000 Terminology work Principles and methods ref Within a terminology model the concept s object type s of a specific problem or subject area are defined by subject matter experts in terms of concept object type definitions and definitions of subordinated concepts or characteristics properties . Besides object types, the terminology model allows defining hierarchical classifications, definitions for object type and property behavior and definition of casual relations. The terminology model is a mean for subject matter experts to express their knowledge about the subject in subject specific terms. Since the terminology model is structured rather similar to an object oriented database schema, is can be transformed without loss of information into an object oriented database schema . Thus, the terminology model is a method ... model for classifications ref http www1.unece.org stat platform download attachments 14319930 Part I Neuchatel version 2 1.pdf?version 1 Neuch tel Terminology Model PART I Classification database object types and their attributes ref Terminology model for statistcal variables ref http www1.unece.org stat platform download attachments 14319930 Neuchatel Model V1.pdf?version 1 Neuch tel Terminology Model PART II Variables and related concepts ref Reference model for statistical metadata ref http www.epros.ed.ac.uk metanet working groups Reference model ReferenceModel.doc METANET Reference Model ref References See Wikipedia Footnotes on how to create references using ref ref tags which will then appear ... more details
Statistical shape analysis is a geometry geometrical analysis from a set of shape s in which statistics are measured to describe geometrical properties from similar shapes or different groups, for instance, the difference between male and female Gorilla skull shapes, normal and pathology pathological bone shapes, etc. Some of the important aspects of shape analysis are to obtain a measure of distance between shapes, to estimate average shapes from a possibly random sample and to estimate shape variability in a sample ref name drydenBook cite book author I.L. Dryden and K.V. Mardia title Statistical Shape Analysis publisher John Wiley & Sons date 1998 isbn 0471958166 ref . One of the main methods used is principal component analysis . Modeling see also Point distribution model The first step after collecting a set of shapes is creating a proper shape model for further statistical analysis. A shape is determined by a finite set finite number of coordinate points, known as landmark point s the Cartesian coordinate system Cartesian coordinates is the most commonly used one. Shape deformation In physics , Deformation engineering deformation is a change of a shape due to an applied force physics force . Investigating shape deformation can reveal the transformation mathematics transformation between two similar shapes and give information about local and global shape differences. Mathematically, a deformation is defined as a mapping mathematics mapping from a shape t to y by a transformation function &Phi , i.e. math y Phi t math . See Definition 10.2 of cite book author I.L. Dryden and K.V. Mardia title Statistical Shape Analysis publisher John Wiley & Sons date 1998 isbn 0471958166 See also Geometric data analysis Shape analysis Procrustes analysis References reflist Category Statistical data types Category Spatial data analysis Category Computer vision statistics stub ... more details
out at the physical layer in the OSI model and TCP IP model , while statistical multiplexing is carried out at the data link layer and above. Channel identification In statistical multiplexing, each packet ...Unreferenced date December 2009 Multiplex techniques Statistical multiplexing is a type of communication link sharing, very similar to dynamic bandwidth allocation DBA . In statistical multiplexing , a communication channel is divided into an arbitrary number of variable bit rate digital channels or data ... correctly, statistical multiplexing can provide a link utilization improvement, called the statistical multiplexing gain . Statistical multiplexing is facilitated through packet mode or packet ... for fair queuing or differentiated and or guaranteed quality of service . Statistical multiplexing ... to different users. Statistical multiplexing normally implies on demand service rather than one that preallocates resources for each data stream. Statistical multiplexing schemes do not control user data transmissions. Comparison with static TDM Time domain statistical multiplexing packet mode communication ... order, and experience varying delay while the delay is fixed in TDM . Statistical multiplexing ... of channels and the channel data rate are fixed in TDM . Statistical multiplexing ensures that slots ... complete destination address information. Usage Examples of statistical multiplexing are The MPEG transport stream for digital TV transmission. Statistical multiplexing is used to allow several ... channel see Statistical multiplexer . The packets have constant lengths. The channel number is denoted ... circuits.3F Virtual Path Identifier VPI . Statistical multiplexer In digital audio and video broadcasting, for example, a statistical multiplexer is a content aggregating device that allows broadcasters ... http igorfuna.com dvb t slovenia multiplex a usage chart Example of Statistical Multiplexing Chart from a real DVB T multiplex Cdma DEFAULTSORT Statistical Multiplexing Category Multiplexing Category ... more details
model Parametric model Nonparametric statistics Model selection A statisticalmodel is a probability ... of mental events as well as models of physical events. For example, a statisticalmodel of customer behavior is a model that is conceptual, because behavior is physical but a statisticalmodel ...Other uses Model disambiguation Refimprove date February 2011 Original research date February 2011 In the most general sense, a wikt modelmodel is anything used in any way to represent anything else. Some physical model models are physical object s, for instance, a toy model which may be assembled, and may ... and understanding understand the subject matter they represent. The term conceptual model may be used ... The term conceptual model is ambiguous. It could mean a model of concept or it could mean a model that is conceptual ... of iconic models, such as a scale model of Winchester Cathedral , most models are concepts. But they are, mostly, intended to be models of real world states of affairs. The value of a model ... or potential state of affairs. A model of a concept is quite different because in order to be a good model it need not have this real world correspondence. ref Gregory, Frank Hutson 1992 http en.wikisource.org ... model s which do not appear to the mind as an image. Conceptual models also range in terms of the scope of the subject matter that they are taken to represent. A model may, for instance, represent a single ... Mental model See Mental model Representation psychology Cognitive model In cognitive psychology and philosophy of mind, a mental model is a representation of something in the mind, ref Mental Representation ... entries mental representation ref but a mental model may also refer to a nonphysical external model ... ref Metaphysical models A metaphysical model is a type of conceptual model which is distinguished from other conceptual models by its proposed scope. A metaphysical model intends to represent ... substances or whether or not humans have free will . Conceptual model vs. semantics model Semantics ... more details
Statistical relational learning SRL is a subdiscipline of artificial intelligence and machine learning that is concerned with models of Domain model domains that exhibit both uncertainty which can be dealt with using statistical methods and complex, relation mathematics relational structure. Typically, the knowledge representation formalisms developed in SRL use a subset of first order logic to describe relational properties of a domain in a general manner universal quantification and draw upon probabilistic graphical model probabilistic graphical models such as Bayesian network Bayesian networks or Markov network Markov networks to model the uncertainty some also build upon the methods of inductive logic programming . Significant contributions to the field have been made since the late 1990s. As is evident from the characterization above, the field is not strictly limited to learning aspects it is equally concerned with reasoning specifically statistical inference probabilistic inference and knowledge representation . Therefore, alternative terms that reflect the main foci of the field include statistical relational learning and reasoning emphasizing the importance of reasoning and first order probabilistic languages emphasizing the key properties of the languages with which models are represented . Canonical tasks A number of canonical tasks are associated with statistical relational learning, the most common ones being ref Matthew Richardson and Pedro Domingos, http www.cs.washington.edu ... in recent years. ref Lise Getoor and Ben Taskar Introduction to statistical relational learning, MIT ... logic networks Multi entity Bayesian networks Probabilistic relational model Probabilistic relational ... to statistical relational learning , MIT Press, 2007 Brian Milch, and Stuart J. Russell First Order ... in Computational Intelligence, Springer, 2008 Hassan Khosravi and Bahareh Bina A Survey on Statistical ... Statistical models Category Machine learning ... more details
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