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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).
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
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The BCIS "Standard Form of Cost Analysis" (SFCA) remained an industry staple, largely unchanged, until the late 2000s. In 2012 the "New Rules of Measurement" for cost management throughout the construction process were accompanied by a modernised version of the SFCA. [1] In 2022, the BCIS was spun out of RICS. [2]
The Brier score can be thought of as a cost function. More precisely, across all items in a set of N predictions, the Brier score measures the mean squared difference between: The predicted probability assigned to the possible outcomes for item i; The actual outcome