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In the simulation of energy consumption of buildings, the RMSE and CV(RMSE) are used to calibrate models to measured building performance. [9] In X-ray crystallography, RMSD (and RMSZ) is used to measure the deviation of the molecular internal coordinates deviate from the restraints library values.
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).
When the model has been estimated over all available data with none held back, the MSPE of the model over the entire population of mostly unobserved data can be estimated as follows.
For color images with three RGB values per pixel, the definition of PSNR is the same except that the MSE is the sum over all squared value differences (now for each color, i.e. three times as many differences as in a monochrome image) divided by image size and by three.
For random vectors, since the MSE for estimation of a random vector is the sum of the MSEs of the coordinates, finding the MMSE estimator of a random vector decomposes into finding the MMSE estimators of the coordinates of X separately: {(()) ()} =, for all i and j
"MSE is also sometimes called the variance; RMSE is also sometimes called the standard deviation." Well, the MSE is a random variable itself that needs to be estimated. It's not just a number. If it has been estimated, it gives a measures of the variation of an estimator with repect to a known parameter.
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The difference between the height of each man in the sample and the observable sample mean is a residual. Note that, because of the definition of the sample mean, the sum of the residuals within a random sample is necessarily zero, and thus the residuals are necessarily not independent .