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The RMSD of predicted values ^ for times t of a regression's dependent variable, with variables observed over T times, is computed for T different predictions as the square root of the mean of the squares of the deviations:
Furthermore, the mean square difference between a model and the data can be calculated by adding in quadrature the bias and the standard deviation of the errors. The code for these "modified" Taylor diagrams was developed, and is available in, Python [ 13 ] .
Physical scientists often use the term root mean square as a synonym for standard deviation when it can be assumed the input signal has zero mean, that is, referring to the square root of the mean squared deviation of a signal from a given baseline or fit. [8] [9] This is useful for electrical engineers in calculating the "AC only" RMS of a signal.
The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled).
However, under certain conditions, SSIM may be converted to a normalized root MSE measure, which is a distance function. [5] The square of such a function is not convex, but is locally convex and quasiconvex , [ 5 ] making SSIM a feasible target for optimization.
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In mathematics, the QM-AM-GM-HM inequalities, also known as the mean inequality chain, state the relationship between the harmonic mean, geometric mean, arithmetic mean, and quadratic mean (also known as root mean square). Suppose that ,, …, are positive real numbers. Then
There are associated concepts, such as the DRMS (distance root mean square), which is the square root of the average squared distance error, a form of the standard deviation. Another is the R95, which is the radius of the circle where 95% of the values would fall, a 95% confidence interval .