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Sensitivity Index
The sensitivity index or discriminability index or detectability index is a dimensionless statistic used in signal detection theory. A higher index indicates that the signal can be more readily detected. Definition The discriminability index is the separation between the means of two distributions (typically the signal and the noise distributions), in units of the standard deviation. Equal variances/covariances For two univariate distributions a and b with the same standard deviation, it is denoted by d' ('dee-prime'): : d' = \frac. In higher dimensions, i.e. with two multivariate distributions with the same variance-covariance matrix \mathbf, (whose symmetric square-root, the standard deviation matrix, is \mathbf), this generalizes to the Mahalanobis distance between the two distributions: : d'=\sqrt = \lVert \mathbf^(\boldsymbol_a-\boldsymbol_b) \rVert = \lVert \boldsymbol_a-\boldsymbol_b \rVert /\sigma_, where \sigma_ = 1/ \lVert\mathbf^\boldsymbol\rVert is the 1d slice of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scaling Discriminability Of Two Distributions
Scaling may refer to: Science and technology Mathematics and physics * Scaling (geometry), a linear transformation that enlarges or diminishes objects * Scale invariance, a feature of objects or laws that do not change if scales of length, energy, or other variables are multiplied by a common factor ** Scaling law, a law that describes the scale invariance found in many natural phenomena * The scaling of critical exponents in physics, such as Widom scaling, or scaling of the renormalization group Computing and information technology * Feature scaling, a method used to standardize the range of independent variables or features of data * Image scaling, the resizing of an image * Multidimensional scaling, a means of visualizing the level of similarity of individual cases of a dataset * Scalability, a computer or network's ability to function as the amount of data or number of users increases * Scaling along the Z axis, a technique used in computer graphics for a pseudo-3D effect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Detection Theory
Detection theory or signal detection theory is a means to measure the ability to differentiate between information-bearing patterns (called stimulus in living organisms, signal in machines) and random patterns that distract from the information (called noise, consisting of background stimuli and random activity of the detection machine and of the nervous system of the operator). In the field of electronics, signal recovery is the separation of such patterns from a disguising background. According to the theory, there are a number of determiners of how a detecting system will detect a signal, and where its threshold levels will be. The theory can explain how changing the threshold will affect the ability to discern, often exposing how adapted the system is to the task, purpose or goal at which it is aimed. When the detecting system is a human being, characteristics such as experience, expectations, physiological state (e.g. fatigue) and other factors can affect the threshold app ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
External Links
An internal link is a type of hyperlink on a web page to another page or resource, such as an image or document, on the same website or domain. It is the opposite of an external link, a link that directs a user to content that is outside its domain. Hyperlinks are considered either "external" or "internal" depending on their target or destination. Generally, a link to a page outside the same domain or website is considered external, whereas one that points at another section of the same web page or to another page of the same website or domain is considered internal. Both internal and external links allow users of the website to navigate to another web page or resource. These definitions become clouded, however, when the same organization operates multiple domains functioning as a single web experience, e.g. when a secure commerce website is used for purchasing things displayed on a non-secure website. In these cases, links that are "external" by the above definition can conce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effect Size
In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the value of one parameter for a hypothetical population, or to the equation that operationalizes how statistics or parameters lead to the effect size value. Examples of effect sizes include the correlation between two variables, the regression coefficient in a regression, the mean difference, or the risk of a particular event (such as a heart attack) happening. Effect sizes are a complement tool for statistical hypothesis testing, and play an important role in power analyses to assess the sample size required for new experiments. Effect size are fundamental in meta-analyses which aim to provide the combined effect size based on data from multiple studies. The cluster of data-analysis methods concerning effect sizes is referred to as estima ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Summary Statistics
In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as simply as possible. Statisticians commonly try to describe the observations in * a measure of location, or central tendency, such as the arithmetic mean * a measure of statistical dispersion like the standard mean absolute deviation * a measure of the shape of the distribution like skewness or kurtosis * if more than one variable is measured, a measure of statistical dependence such as a correlation coefficient A common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot. Entries in an analysis of variance table can also be regarded as summary statistics. Examples Location Common measures of location, or central tendency, are the arithmetic mean, median, mode, and interquartile mean. Spread Common measures ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Receiver Operating Characteristic
A receiver operating characteristic curve, or ROC curve, is a graph of a function, graphical plot that illustrates the performance of a binary classifier model (can be used for multi class classification as well) at varying threshold values. ROC analysis is commonly applied in the assessment of diagnostic test performance in clinical epidemiology. The ROC curve is the plot of the true positive rate (TPR) against the false positive rate (FPR) at each threshold setting. The ROC can also be thought of as a plot of the statistical power as a function of the Type I Error of the decision rule (when the performance is calculated from just a sample of the population, it can be thought of as estimators of these quantities). The ROC curve is thus the sensitivity as a function of false positive rate. Given that the probability distributions for both true positive and false positive are known, the ROC curve is obtained as the cumulative distribution function (CDF, area under the probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covariance Matrix
In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector. Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions. As an example, the variation in a collection of random points in two-dimensional space cannot be characterized fully by a single number, nor would the variances in the x and y directions contain all of the necessary information; a 2 \times 2 matrix would be necessary to fully characterize the two-dimensional variation. Any covariance matrix is symmetric and positive semi-definite and its main diagonal contains variances (i.e., the covariance of each element with itself). The covariance matrix of a random vector \mathbf is typically denoted by \operatorname_, \Sigma or S. Definition Throughout this article, boldfaced u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Mean
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean of numbers is the Nth root, th root of their product (mathematics), product, i.e., for a collection of numbers , the geometric mean is defined as : \sqrt[n]. When the collection of numbers and their geometric mean are plotted in logarithmic scale, the geometric mean is transformed into an arithmetic mean, so the geometric mean can equivalently be calculated by taking the natural logarithm of each number, finding the arithmetic mean of the logarithms, and then returning the result to linear scale using the exponential function , :\sqrt[n] = \exp \left( \frac \right). The geometric mean of two numbers is the square root of their product, for example with numbers and the geometric mean is \textstyle \sqrt = The geometric mean o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistic
A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis. The average (or mean) of sample values is a statistic. The term statistic is used both for the function (e.g., a calculation method of the average) and for the value of the function on a given sample (e.g., the result of the average calculation). When a statistic is being used for a specific purpose, it may be referred to by a name indicating its purpose. When a statistic is used for estimating a population parameter, the statistic is called an '' estimator''. A population parameter is any characteristic of a population under study, but when it is not feasible to directly measure the value of a population parameter, statistical methods are used to infer the likely value of the parameter on the basis of a statistic computed from a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Chi-squared Distribution
In probability theory and statistics, the generalized chi-squared distribution (or generalized chi-square distribution) is the distribution of a quadratic function of a multivariate normal distribution, multinormal variable (normal vector), or a linear combination of different normal variables and squares of normal variables. Equivalently, it is also a linear sum of independent noncentral chi-squared distribution, noncentral chi-square variables and a normal distribution, normal variable. There are several other such generalizations for which the same term is sometimes used; some of them are special cases of the family discussed here, for example the gamma distribution. Definition The generalized chi-squared variable may be described in multiple ways. One is to write it as a weighted sum of independent Noncentral chi-squared distribution, noncentral chi-square variables ^2 and a standard normal variable z: :\tilde(\boldsymbol, \boldsymbol, \boldsymbol,s,m)=\sum_i w_i ^2 (k_i,\la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
