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*Statistics*.Department of Labor Bureau of Labor *Statistics*.

Some kinds of *statistical* tests employ calculations based on ranks. Examples include: The distribution of values in decreasing order of rank is often of interest when values vary widely in scale; this is the rank-size distribution (or rank-frequency distribution), for example for city sizes or word frequencies. These often follow a power law. Some ranks can have non-integer values for tied data values. For example, when there is an even number of copies of the same data value, the above described fractional *statistical* rank of the tied data ends in ½.

It is *theoretically* possible to break such a system, but it is infeasible to do so by any known practical means. These schemes are therefore termed computationally secure; *theoretical* advances, e.g., improvements in integer factorization algorithms, and faster computing technology require these solutions to be continually adapted. There exist information-*theoretically* secure schemes that cannot be broken even with unlimited computing power—an example is the one-time pad—but these schemes are more difficult to use in practice than the best *theoretically* breakable but computationally secure mechanisms.

Online matrix calculators., a freeware package for matrix algebra and *statistics*. Operation with matrices in R (determinant, track, inverse, adjoint, transpose). Matrix operations widget in Wolfram|Alpha., a freeware package for matrix algebra and *statistics*. Operation with matrices in R (determinant, track, inverse, adjoint, transpose). Matrix operations widget in Wolfram|Alpha., a freeware package for matrix algebra and *statistics*. Operation with matrices in R (determinant, track, inverse, adjoint, transpose). Matrix operations widget in Wolfram|Alpha. Operation with matrices in R (determinant, track, inverse, adjoint, transpose). Matrix operations widget in Wolfram|Alpha.

In *statistics*, an outlier is a data point that differs significantly from other observations. An outlier may be due to variability in the measurement or it may indicate experimental error; the latter are sometimes excluded from the data set. An outlier can cause serious problems in *statistical* analyses. Outliers can occur by chance in any distribution, but they often indicate either measurement error or that the population has a heavy-tailed distribution.

From a *statistical* point of view, the moving average, when used to estimate the underlying trend in a time series, is susceptible to rare events such as rapid shocks or other anomalies. A more robust estimate of the trend is the simple moving median over n time points: where the median is found by, for example, sorting the values inside the brackets and finding the value in the middle. For larger values of n, the median can be efficiently computed by updating an indexable skiplist. *Statistically*, the moving average is optimal for recovering the underlying trend of the time series when the fluctuations about the trend are normally distributed.

Growth curve (*statistics*). Recurrent neural network. Regression analysis includes a large group of methods for predicting future values of a variable using information about other variables. These methods include both parametric (linear or non-linear) and non-parametric techniques. Autoregressive moving average with exogenous inputs (ARMAX). Composite forecasts. Cooke's method. Delphi method. Forecast by analogy. Scenario building. *Statistical* surveys. Technology forecasting. Artificial neural networks. Group method of data handling. Support vector machines. Data mining. *Machine* *learning*. Pattern recognition. Simulation. Prediction market.

Similarly, psychologists have found that due to cognitive *bias* people are more likely to remember notable or unusual examples rather than typical examples. Thus, even when accurate, anecdotal evidence is not necessarily representative of a typical experience. Accurate determination of whether an anecdote is typical requires *statistical* evidence. Misuse of anecdotal evidence is an informal fallacy and is sometimes referred to as the "person who" fallacy ("I know a person who..."; "I know of a case where..." etc.) which places undue weight on experiences of close peers which may not be typical.

The term is also used, especially in the description of algorithms, to mean associative array or "abstract array", a *theoretical* *computer* *science* model (an abstract data type or ADT) intended to capture the essential properties of arrays. The first digital computers used machine-language programming to set up and access array structures for data tables, vector and matrix computations, and for many other purposes. John von Neumann wrote the first array-sorting program (merge sort) in 1945, during the building of the first stored-program computer. p. 159 Array indexing was originally done by self-modifying code, and later using index registers and indirect addressing.

Good blinding may reduce or eliminate some sources of experimental *bias*. The randomness in the assignment of subjects to groups reduces selection *bias* and allocation *bias*, balancing both known and unknown prognostic factors, in the assignment of treatments. Blinding reduces other forms of experimenter and subject *biases*. A well-blinded RCT is often considered the gold standard for clinical trials. Blinded RCTs are commonly used to test the efficacy of medical interventions and may additionally provide information about adverse effects, such as drug reactions.

Other models are based on matching pursuit, a sparse approximation algorithm which finds the "best matching" projections of multidimensional data, and dictionary *learning*, a representation *learning* method which aims to find a sparse matrix representation of the input data in the form of a linear combination of basic elements as well as those basic elements themselves. Sparse coding may be a general strategy of neural systems to augment memory capacity. To adapt to their environments, animals must *learn* which stimuli are associated with rewards or punishments and distinguish these reinforced stimuli from similar but irrelevant ones.

Link archive of *learning* resources for students: biophysika.de (60% English, 40% German). Journal of Medicine, Physiology and Biophysics,(IISTE), USA. Chief Editor of the journal is Ignat Ignatov. Chief editor of all IISTE journals is Alexander Decker.

The social network is a *theoretical* construct useful in the social sciences to study relationships between individuals, groups, organizations, or even entire societies (social units, see differentiation). The term is used to describe a social structure determined by such interactions. The ties through which any given social unit connects represent the convergence of the various social contacts of that unit. This *theoretical* approach is, necessarily, relational.

In *statistics*, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modelled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E(y |x). Although polynomial regression fits a nonlinear model to the data, as a *statistical* estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the data. For this reason, polynomial regression is considered to be a special case of multiple linear regression.

Management, e.g., defining strategies, setting objectives and goals; planning and directing the work; allocating funds, people and other resources; prioritization relative to other activities; team building, leadership, control, motivation and coordination with other business functions and activities (e.g., IT, facilities, human resources, risk management, information risk and security, operations); monitoring the situation, checking and updating the arrangements when things change; maturing the approach through continuous improvement, *learning* and appropriate investment.

Recently they have also sponsored a *machine*-*learned* ranking competition "Internet Mathematics 2009" based on their own search engine's production data. Yahoo has announced a similar competition in 2010. As of 2008, Google's Peter Norvig denied that their search engine exclusively relies on *machine*-*learned* ranking. Cuil's CEO, Tom Costello, suggests that they prefer hand-built models because they can outperform *machine*-*learned* models when measured against metrics like click-through rate or time on landing page, which is because *machine*-*learned* models "*learn* what people say they like, not what people actually like".

The *statistic* generated to measure association is the odds ratio (OR), which is the ratio of the odds of exposure in the cases (A/C) to the odds of exposure in the controls (B/D), i.e. OR = (AD/BC). If the OR is significantly greater than 1, then the conclusion is "those with the disease are more likely to have been exposed," whereas if it is close to 1 then the exposure and disease are not likely associated. If the OR is far less than one, then this suggests that the exposure is a protective factor in the causation of the disease. Case-control studies are usually faster and more cost effective than cohort studies, but are sensitive to *bias* (such as recall *bias* and selection *bias*).

(Note that the sample standard deviation (S) is not an *unbiased* estimate of the population standard deviation : see *Unbiased* estimation of standard deviation.) It is possible to make *statistical* inferences without assuming a particular parametric family of probability distributions. In that case, one speaks of non-parametric *statistics* as opposed to the parametric *statistics* just described.

For example: as cultures change and the political environment shifts, societies may criminalise or decriminalise certain behaviours, which directly affects the *statistical* crime rates, influence the allocation of resources for the enforcement of laws, and (re-)influence the general public opinion. Similarly, changes in the collection and/or calculation of data on crime may affect the public perceptions of the extent of any given "crime problem". All such adjustments to crime *statistics*, allied with the experience of people in their everyday lives, shape attitudes on the extent to which the state should use law or social engineering to enforce or encourage any particular social norm.

In data mining tools (for multivariate *statistics* and *machine* *learning*), the dependent variable is assigned a role as (or in some tools as label attribute), while an independent variable may be assigned a role as regular variable. Known values for the target variable are provided for the training data set and test data set, but should be predicted for other data. The target variable is used in supervised *learning* algorithms but not in unsupervised *learning*. In mathematical modeling, the dependent variable is studied to see if and how much it varies as the independent variables vary.

If the Fisher information matrix is positive definite for all θ, then the corresponding *statistical* model is said to be regular; otherwise, the *statistical* model is said to be singular. Examples of singular *statistical* models include the following: normal mixtures, binomial mixtures, multinomial mixtures, Bayesian networks, neural networks, radial basis functions, hidden Markov models, stochastic context-free grammars, reduced rank regressions, Boltzmann machines. In *machine* *learning*, if a *statistical* model is devised so that it extracts hidden structure from a random phenomenon, then it naturally becomes singular.

In *statistics*, self-selection *bias* arises in any situation in which individuals select themselves into a group, causing a *biased* sample with nonprobability sampling. It is commonly used to describe situations where the characteristics of the people which cause them to select themselves in the group create abnormal or undesirable conditions in the group. It is closely related to the non-response *bias*, describing when the group of people responding has different responses than the group of people not responding. Self-selection *bias* is a major problem in research in sociology, psychology, economics and many other social sciences.

Rules post-processed by *statistics*: Translations are performed using a rules based engine. *Statistics* are then used in an attempt to adjust/correct the output from the rules engine. *Statistics* guided by rules: Rules are used to pre-process data in an attempt to better guide the *statistical* engine. Rules are also used to post-process the *statistical* output to perform functions such as normalization. This approach has a lot more power, flexibility and control when translating.