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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.
It is an inverse measure of the explanatory power of ^, and can be used in the process of cross-validation of an estimated model. Knowledge of g would be required in order to calculate the MSPE exactly; in practice, MSPE is estimated.
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).
The term RMS power is sometimes erroneously used (e.g., in the audio industry) as a synonym for mean power or average power (it is proportional to the square of the RMS voltage or RMS current in a resistive load). For a discussion of audio power measurements and their shortcomings, see Audio power.
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.
Standard method like Gauss elimination can be used to solve the matrix equation for .A more numerically stable method is provided by QR decomposition method. Since the matrix is a symmetric positive definite matrix, can be solved twice as fast with the Cholesky decomposition, while for large sparse systems conjugate gradient method is more effective.
According to their research, SSIM has been found to correlate as well as MSE-based methods on subjective databases other than the databases from SSIM's creators. As an example, they cite Reibman and Poole, who found that MSE outperformed SSIM on a database containing packet-loss–impaired video. [ 27 ]
The earliest reference to a similar formula appears to be Armstrong (1985, p. 348), where it is called "adjusted MAPE" and is defined without the absolute values in the denominator. It was later discussed, modified, and re-proposed by Flores (1986).