Statistical assumptions are general assumptions about statistical populations. Statistics , like all mathematical disciplines, does not generate valid conclusions from nothing. In order to generate interesting conclusions about real statistical population s, it is usually required to make some background assumptions. These must be made with care, because inappropriate assumptions can generate wildly inaccurate conclusions. The most commonly applied statistical assumptions are Citation needed date March 2010 independence of observations from each other This assumption is a common error. ref cite journal title Miracles and Statistics The Casual Assumption of Independence ASA Presidential address authorlink William Kruskal first William last Kruskal journal Journal of the American Statistical Association volume 83 issue 404 month December year 1988 pages 929 940 jstor 2290117 ref see statistical ... responses to quantitative stimuli see linear regression Types of assumptions Statistical assumptions can be categorised into a number of types Non modelling assumptions. Statistical analyses of data involve making certain types of assumption, whether or not a formal statistical model is used. Such assumptions underlie even descriptive statistics . Population assumptions. A statistical analysis ... types Distributional assumptions. Where a statistical model involves terms relating to random .... Structural assumptions. Statistical relationships between variables are often modelled by equating ... assumptions Given that the validity of conclusions drawn from a statistical analysis depend on the validity ... data are available, various types of procedure for statistical model validation are available, in particular ... Journal of the American Statistical Association volume 83 issue 404 month December year 1988 pages ... Basis, Application and Interpretation , Springer Verlag. ISBN 0 387 97137 8 DEFAULTSORT Statistical Assumption Category Statistical theory Category Data analysis ar ... 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
A statistical parameter is a parameter that indexes a family of probability distribution s. It can be regarded as a numerical characteristic of a Statistical population population or a Statistical model model . ref Everitt, B.S. 2002 The Cambridge Dictionary of Statistics. CUP. ISBN 0 521 81099 X ref Among parametric family parameterized families of distributions are the normal distribution s, the Poisson distribution s, the binomial distribution s, and the exponential distribution s. The family of normal distribution s has two parameters, the mean and the variance if these are specified, the distribution is known exactly. The family of chi squared distribution s, on the other hand, has only one parameter, the number of degrees of freedom. In statistical inference , parameters are sometimes taken to be unobservable, and in this case the statistician s task is to infer what he can about the parameter based on observations of random variables distributed according to the probability distribution in question, or, more concretely stated, based on a random sample taken from the population of interest. In other situations, parameters may be fixed by the nature of the sampling procedure used or the kind of statistical procedure being carried out for example, the number of degrees of freedom ... of the population from which a sample is drawn. Statistical procedures can still attempt ... to their roles, including location parameter Statistical dispersion dispersion parameter ... that index how variable the outcomes would be. Quantities such as regression coefficient s, are statistical ... to the independent variables. Analogy A parameter is to a statistical population population as a statistic is to a statistical sample sample . See also Precision statistics , another parameter not specific ... off of many or few parameters in data fitting References Reflist Category Statistical theory Category Statistical terminology Category Theory of probability distributions Link FA es statistics ... more details
in statistics ref The theory covers approaches to statistical decision theory statistical decision problems and to statistical inference , and the actions and deductions that satisfy the basic principles stated for these different approaches. Within a given approach, statistical theory gives ways of comparing statistical procedures it can find a best possible procedure within a given context for given statistical problems, or can provide guidance on the choice between alternative procedures. ref name RaoOpt ref cite book author Erich Leo Lehmann Lehmann, Erich title Testing Statistical Hypotheses year 1959 ref Apart from philosophical considerations about how to make statistical inferences and decisions, much of statistical theory consists of mathematical statistics , and is closely ... . Scope Statistical theory provides an underlying rationale and provides a consistent basis for the choice of methodology used in applied statistics . Modelling Statistical model s describe the sources ... Measuring observational error and refining procedures Studying statistical multivariate statistics relations Statistical models, once specified, can be tested to see whether they provide useful ... Statistical Models Theory and Practice publisher Cambridge University Press isbn 9780521671057 ... Statistical theory provides a guide to comparing methods of data collection , where the problem ... of Statistical Concepts in Psychology and Educational Research journal American Journal of Education ... the cost of data while satisfying statistical goals, ref name OptDoE cite book author1 Atkinson, A. C ... inferences. Statistical theory provides a basis for good data collection and the structuring of investigations ... . ref Survey sampling to describe statistical population populations ref Kish 1965 ref ref cite ... 387 40620 4 ref Summarising data The task of summarising statistical data in conventional forms also ... aspects of statistical samples need to be described and how well they can be described from a typically ... more details
Statistical graphics , also known as graphical techniques , are information graphics in the field of statistics used to visualize quantitative data . Overview Whereas statistics and data analysis procedures generally yield their output in numeric or tabular form, graphical techniques allow such results to be displayed in some sort of pictorial form. They include Plot graphics plots such as scatter plot s, histogram s, probability plot s, spaghetti plot s, residual plots, box plot s, block plots and biplot ... in NIST SEMATECH e Handbook of Statistical Methods , 2003 2010. Accessed May 5, 2011. ref ..., the choice of appropriate statistical graphics can provide a convincing means of communicating the underlying message that is present in the data to others. ref name NIST03 Graphical statistical methods have four objectives ref William G. Jacoby 1997 . Statistical Graphics for Univariate and Bivariate Data Statistical Graphics pp.2&ndash 4 ref The exploration of the content of a data set The use to find structure in data Checking assumptions in statistical models Communicate the results of an analysis. If one is not using statistical graphics, then one is forfeiting insight into one or more aspects of the underlying structure of the data. History Statistical graphics have been central ... forms, including Bivariate map bivariate plots , Thematic map statistical maps , bar chart s, and coordinate paper were used in the 18th century. Statistical graphics developed through attention to four .... Since the 1970s statistical graphics have been re emerging as an important analytic tool with the revitalisation ... , who used statistical graphics to persuade the British Government to improve army hygiene, John ... Napoleon s campaign in Russia is the best known. A special type of statistical graphic are the so ... DataScope a website devoted to data visualization and statistical graphics Statistics descriptive state collapsed Visualization Category Statistical charts and diagrams Category Infographics fr Repr sentations ... 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
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
A unit in a statistical analysis refers to one member of a set of entities being studied. It is the material source for the mathematical abstraction of a random variable . Common examples of a unit would be a single person, animal, plant, or manufactured item that belongs to a larger collection of such entities being studied. Units are often referred to as being either experimental units , sampling units or, more generally, Unit of observation units of observation An experimental unit is typically thought of as one member of a set of objects that are initially equivalent, with each object then subjected to one of several experimental treatments. A sampling unit is typically thought of as an object that has been sampled from a statistical population . This term is commonly used in opinion polling and survey sampling . In most statistical studies, the goal is to generalize from the observed units to a larger set consisting of all comparable units that exist but are not directly observed. For example, if we randomly sample 100 people and ask them which candidate they intend to vote for in an election, our main interest is in the voting behavior of all eligible voters, not exclusively on the 100 observed units. In some cases, the observed units may not form a sample from any meaningful population, but rather constitute a accidental sampling convenience sample , or may represent the entire population of interest. In this situation, we may study the units descriptive statistics descriptively ... in a study, there would be seven data values for each statistical unit. While a unit is often the lowest level at which observations are made, in some cases, a unit can be further decomposed as a statistical assembly . Many statistical analyses use quantitative data that have units of measurement . This is a distinct and non overlapping use of the term unit. See also Research subject Specimen Statistical ... Category Statistical terminology Category Articles lacking sources Erik9bot Category Sampling statistics ... 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
context date January 2012 Statistical finance , ref J P Bouchaud, An introduction to Statistical Finance, Physica A 313 2002 238&ndash 251 ref is the application of econophysics ref V. Perou, E. Gopikrishnan, L A Amaral, M. Meyer, H. E. Stanley, Phys. Rev. E 60 6519 1999 ref to financial markets. Instead of the Normative economics normative roots of much of the field of finance , it uses a positivist framework including exemplars from statistical physics with an emphasis on emergent or collective properties of financial markets. The starting point for this approach to understanding financial markets are the empirically observed stylized fact s. Stylized facts Stock markets are characterised by bursts of price volatility. Price changes are less volatile in bull markets and more volatile in bear markets. Price change correlations are stronger with higher volatility, and their auto correlations ... are negatively correlated with future volatilities. Research objectives Statistical finance is focused on three areas Empirical studies focused on the discovery of interesting statistical features ... stylized facts with an emphasis on agent based model s. Behavioral finance and statistical finance .... Statistical finance is concerned with emergent properties arising from systems with many interacting ... of models of statistical physics has been argued as flawed because it has transpired these do ... organize into a stable statistical equilibrium, rather, markets are unstable. Although markets could ... to more rigorous and robust statistical methodology. The belief that universal empirical regularities ... 10.1073 pnas.0708664104 ref Some of the ideas arising from nonlinear sciences and statistical physics ... finance Econophysics Complexity Statistical physics Modeling and analysis of financial markets ... coauthors Kertesz, Janos year 2010 month title Focus on Statistical Physics Modelling in Economics ... quote External links http arxiv.org list q fin.ST recent Statistical Finance at arXiv.org Finance ... more details
A statistical model is a formalization of relationships between variables in the form of mathematical equations. A statistical model describes how one or more random variables are related to one or more random variables. The model is statistical as the variables are not Deterministic system deterministically but stochastic ally related. In mathematical terms, a statistical model is frequently thought of as a pair math Y, P math where math Y math is the set of possible observations and math P math the set of possible probability distributions on math Y math . It is assumed that there is a distinct element of math P math which generates the observed data. Statistical inference enables us to make statements about which element s of this set are likely to be the true one. Most statistical tests can be described in the form of a statistical model. For example, the Student s t test for comparing the means of two groups can be formulated as seeing if an estimated parameter in the model is different from 0. Another similarity between tests and models is that there are assumptions involved. Error is assumed to be normally distributed in most models. ref Field, A. 2005 . Discovering statistics using SPSS. Sage, London. ref Formal definition A Statistical model, math mathcal P math , is a collection of Cumulative distribution function probability distribution functions or probability density function s collectively referred to as distributions for brevity . A parametric model is a collection of distributions, each of which is indexed by a unique finite dimensional parameter math mathcal P mathbb P theta theta in Theta math , where math theta math is a parameter and math Theta subseteq ... space . A statistical model may be used to describe the set of distributions from which one assumes .... Some other statistical models are the general linear model restricted to continuous dependent variables ... Statistical Model Category Statistical models Category Statistical theory Category Scientific modeling ... more details
A statistical population is a set of entities concerning which statistical inference s are to be drawn, often based on a random sample taken from the population. For example, if we were interested in generalizations about crows , then we would describe the set of crows that is of interest. Notice that if we choose a population like all crows , we will be limited to observing crows that exist now or will exist in the future. Probably, geography will also constitute a limitation in that our resources for studying crows are also limited. Population is also used to refer to a set of potential measurement s or values, including not only cases actually observed but those that are potentially observable . Suppose, for example, we are interested in the set of all adult crows now alive in the county of Cambridgeshire , and we want to know the mean weight of these birds. For each bird in the population of crows there is a weight, and the set of these weights is called the population of weights . Subpopulation Expand section date March 2009 A subset of a population is called a subpopulation. If different subpopulations have different properties, the properties and response of the overall population can often be better understood if it is first separated into distinct subpopulations. For instance, a particular medicine may have different effects on different subpopulations, and these effects may be obscured or dismissed if such special subpopulations are not identified and examined in isolation. Similarly, one can often estimate parameters more accurately if one separates out subpopulations distribution of heights among people is better modeled by considering men and women as separate subpopulations, for instance. Populations consisting of subpopulations can be modeled by mixture model ... http www.socialresearchmethods.net kb sampstat.htm Statistical Terms Made Simple statistics Category Statistical theory Category Statistical terminology stat stub ar da Population statistik ... more details
Statistical mechanics or statistical thermodynamics ref group note The terms statistical mechanics and statistical thermodynamics are used interchangeably. Statistical physics is a broader term which includes statistical mechanics, but is sometimes also used as a synonym for statistical mechanics ref ... of a large number of particles . Statistical mechanics provides a framework for relating the microscopic ... and quantum mechanical description of statistics and mechanics at the microscopic level. Statistical ... advantage of statistical mechanics over classical thermodynamics . Both theories are governed by the second ... only be known empirically, whereas in statistical mechanics, it is a function of the distribution of the system on its micro states. Statistical mechanics was initiated in 1870 with the work of Austrian ... on Gas Theory . ref cite book title Statistical Thermodynamics and Stochastic Theory of Nonequilibrium ... section 1.2 ref Boltzmann s original papers on the statistical interpretation of thermodynamics .... The term statistical thermodynamics was proposed for use by the American thermodynamicist and physical chemist Josiah Willard Gibbs J. Willard Gibbs in 1902. According to Gibbs, the term statistical , in the context of mechanics, i.e. statistical mechanics, was first used by the Scottish physicist James Clerk Maxwell in 1871. Probabilistic mechanics might today seem a more appropriate term, but statistical ... books?id zmwEfXUdBJ8C&pg PA174 ref Statistical mechanics Overview The essential problem in statistical thermodynamics is to calculate the distribution of a given amount of energy E over N identical systems. ref cite book author Schrodinger, Erwin title Statistical Thermodynamics publisher Dover Publications, Inc. year 1946 isbn 0 486 66101 6 oclc 20056858 ref The goal of statistical ... in statistical thermodynamics are the Boltzmann factor and the Partition function statistical mechanics partition function . Fundamentals Central topics covered in statistical thermodynamics include Microstate ... more details
City of republic significance or importance is a type of an administrative division in some countries of the former Soviet Union. in Russia see city of federal subject significance in Ukraine see administrative divisions of Ukraine Geodis ... more details
City of oblast significance or importance is a type of an administrative division in some countries of the former Soviet Union. in Russia see city of federal subject significance in Ukraine see administrative divisions of Ukraine Geodis ... more details
over whether classification methods that do not involve a statistical model can be considered statistical ... . Algorithms of this nature use statistical inference to find the best class for a given ... . Frequentist procedures Early work on statistical classification was undertaken by Fisher, ref ... , 7, 179&ndash 188 ref ref Fisher R.A. 1938 The statistical utilization of multiple measurements ... G1977 Gnanadesikan, R. 1977 Methods for Statistical Data Analysis of Multivariate Observations , Wiley ... be linear . ref name G1977 ref C. R. Rao Rao, C.R. 1952 Advanced Statistical Methods in Multivariate ... to be nonlinear ref T. W. Anderson Anderson,T.W. 1958 An Introduction to Multivariate Statistical ... kernel density estimation Use for statistical classification Kernel estimation k nearest neighbor ... Efficient statistical classification of satellite measurements journal International Journal of Remote ... detailed statistical modeling is undertaken. Computer vision Medical imaging and medical image analysis ... recognition Biometric identification Biological classification Statistical natural language processing ... cmp software stprtool Statistical Pattern Recognition Toolbox for Matlab . http sites.google.com ... DEFAULTSORT Statistical Classification Category Machine learning Category Classification algorithms Category Statistical classification ar de Klassifikationsverfahren fa ... more details
Expert subject Geography date August 2009 Statistical geography is the study and practice of collecting, analysing and presenting data that has a geographic or areal dimension, such as census or demographics data. It uses techniques from spatial analysis , but also encompasses geographical activities such as the defining and naming of geographical regions for statistical purposes. For example, for the purposes of statistical geography, the Australian Bureau of Statistics uses the Australian Standard Geographical Classification, a hierarchical regionalisation that divides Australia up into states and territories of Australia states and territories , then statistical divisions, statistical subdivisions, statistical local areas, and finally census collection districts. Background Image Devils Punchbowl Waterfall, New Zealand.jpg thumb 200px right Devil s Punchbowl Waterfall, New Zealand may be studied using geostatistics Geography Geographers study how and why elements differ from place to place, as well as how spatial patterns change through time. Geographers begin with the question Where? , exploring how features are distributed on a physical or cultural landscape, observing spatial patterns and the variation of phenomena. Contemporary geographical analysis has shifted to Why? , determining why a specific spatial pattern exists, what spatial or ecological processes may have affected a pattern, and why such processes operate. Only by approaching the why? questions can social scientists begin to appreciate the mechanisms of change, which are infinite in their complexity. Role of statistics in geography Statistical techniques and procedures are applied in all fields of academic research wherever data are collected and summarized or wherever any numerical information is analyzed ..., Otis Dudley, Raymond Paul Cuzzort and Beverly Duncan title Statistical Geography Problems in Analyzing ... title Statistical mapping and the presentation of statistics publisher Edward Arnold isbn 0713156414 ... more details
In protein structure prediction , a statistical potential or knowledge based potential is an energy function derived from an analysis of known protein structures in the Protein Data Bank . Many methods exist to obtain such potentials two notable method are the quasi chemical approximation due to Miyazawa and Jernigan ref Miyazawa S, Jernigan R 1985 Estimation of effective interresidue contact energies from protein crystal structures quasi chemical approximation. Macromolecules 18 534 552. ref and the potential of mean force due to Sippl ref name Sippl a Sippl MJ 1990 Calculation of conformational ensembles from potentials of mean force. An approach to the knowledge based prediction of local structures in globular proteins. J Mol Biol 213 859 883. ref . Although the obtained energies are often considered as approximations of the Thermodynamic free energy free energy , this physical interpretation is incorrect. ref name Thomas Thomas PD, Dill KA 1996 Statistical potentials extracted from ... Statistical potentials extracted from protein structures Are these meaningful potentials? J Chem ... amino acid contacts or distances. For pairwise amino acid contacts, a statistical potential ... Z math is the partition function statistical mechanics partition function , with math Z int e frac ..., qualitative justification of PMFs is due to Sippl, and based on an analogy with the statistical ... Chandler Chandler D 1987 Introduction to Modern Statistical Mechanics. New York Oxford University ... on the subject ref name BenNaim blockquote ... the quantities, referred to as statistical potentials ... Q X math . Applications Statistical potentials are used as energy function s in the assessment of an ensemble ... statistical potentials have been shown to successfully identify the native state structure from ... 41 40 46. ref ref name Sali Shen MY & Sali A. 2006 . Statistical potential for assessment and prediction ... motif. Proteins 16 1 92 112. ref Statistical potentials are not only used for protein structure prediction ... more details
Unreferenced stub auto yes date December 2009 Policy Debate Significance is a stock issues stock issue in policy debate which establishes the importance of the harms policy debate harms in the status quo . As a stock issue has fallen out of favor with the debate community almost all debaters and judge policy debate judges now believe that any plan policy debate plan which is preferable to the status quo is significant. Significance derives from the word wiktionary substantial substantially which appears in most resolution policy debate resolutions , and one can argue that Significance has been subsumed by the option for the negative to use a On topic Topicality violation on that word. Stock Issues DEFAULTSORT Significance Policy Debate Category Policy debate Speech and debate stub ... more details
instructions DEFAULTSORT Significance Analysis Of Microarrays Category Statistical genetics Category ...Howto date May 2009 Expert subject date May 2009 Image Expressionpic2.jpg thumb right Significance analysis of microarrays SAM is a statistics statistical technique , established in 2001 by Virginia Tusher, Robert Tibshirani and Gilbert Chu , for determining whether changes in gene expression are statistically significant. With the advent of DNA microarray s it is now possible to measure the expression of thousands of genes in a single hybridization experiment. The data generated is considerable and a method for sorting out what is significant and what isn t is essential. SAM is distributed by Stanford University in an R programming language R package . SAM identifies statistically significant genes by carrying out gene specific Student s t test t tests and computes a statistic d sub j sub for each gene j , which measures the strength of the relationship between gene expression and a response variable. ref name R1 ref name R7 ref name R8 This analysis uses non parametric statistics , since the data may not follow a normal distribution . The response variable describes and groups the data based on experimental conditions. In this method, repeated permutations of the data are used to determine if the expression of any gene is significant related to the response. The use of permutation based analysis accounts for correlations in genes and avoids parametric assumptions about the distribution of individual genes. This is an advantage over other techniques for example ANOVA and Bonferroni ... ref name R1 Chu, G., Narasimhan, B, Tibshirani, R, Tusher, V. SAM Significance Analysis of Microarrays ... R5 Larsson, O. W., C Timmons, JA. 2005 . Considerations when using the significance analysis of microarrays .... 2001 . Significance analysis of microarrays applied to the ionizing radiation response. Proceedings ... ref ref name R7 Zang, S., R. Guo, et al. 2007 . Integration of statistical inference methods ... more details
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