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In mathematics, discrepancy theory describes the deviation of a situation from the state one would like it to be in. It is also called the theory of irregularities of distribution . This refers to the theme of classical discrepancy theory, namely distributing points in some space such that they are evenly distributed with respect to some ...
In statistics, deviance is a goodness-of-fit statistic for a statistical model; it is often used for statistical hypothesis testing.It is a generalization of the idea of using the sum of squares of residuals (SSR) in ordinary least squares to cases where model-fitting is achieved by maximum likelihood.
In addition to "distance", similar terms include deviance, deviation, discrepancy, discrimination, and divergence, as well as others such as contrast function and metric. Terms from information theory include cross entropy, relative entropy, discrimination information, and information gain.
Least absolute deviation (LAD) is a statistical method used in regression analysis to estimate the coefficients of a linear model. Unlike the more common least squares method, which minimizes the sum of squared vertical distances (residuals) between the observed and predicted values, the LAD method minimizes the sum of the absolute vertical ...
If the linear model is applicable, a scatterplot of residuals plotted against the independent variable should be random about zero with no trend to the residuals. [5] If the data exhibit a trend, the regression model is likely incorrect; for example, the true function may be a quadratic or higher order polynomial.
They are zero only if the fit is perfect, i.e., if the model and parameter estimates perfectly reproduce the observed data. The discrepancy function is a continuous function of the elements of S, the sample covariance matrix, and Σ(θ), the "reproduced" estimate of S obtained by using the parameter estimates and the structural model.
Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered. On the other hand, when the variance is small, the data in the set is clustered.
Given some experimental measurements of a system and some computer simulation results from its mathematical model, inverse uncertainty quantification estimates the discrepancy between the experiment and the mathematical model (which is called bias correction), and estimates the values of unknown parameters in the model if there are any (which ...