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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:
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.
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).
If a main application of the forecast is to predict when certain thresholds will be crossed, one possible way of assessing the forecast is to use the timing-error—the difference in time between when the outcome crosses the threshold and when the forecast does so.
The sample Taylor diagram shown in Figure 1 [16] provides a summary of the relative skill with which several global climate models simulate the spatial pattern of annual mean precipitation. Eight models, each represented by a different letter on the diagram, are compared, and the distance between each model and the point labeled “observed ...
Weather forecast skill is often presented in the form of seasonal geographical maps. Forecasting skill for single-value forecasts (i.e., time series of a scalar quantity) is commonly represented in terms of metrics such as correlation, root mean squared error, mean absolute error, relative mean absolute error, bias, and the Brier score, among ...
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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.