Statistical Parameters for Describing Model Accuracy
Rept. for Mar 1988-Mar 1989
RADEX INC BEDFORD MA
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Methods of probability theory are applied to determine parameters for describing the accuracy of a model, given a data base of measurements with which the predictions of the model are compared. From such comparisons it is customary to determine the mean and standard deviation of the measured-model difference or ratio. In the idealized case that the error distribution is Gaussian, we show that a single parameter, the root mean square rms of the mean and the standard deviation, approximately characterizes the accuracy of the model, since the width of the confidence interval whose center is at zero error can be represented as the product of the rms and the factor which is approximately independent of both the mean and the standard deviation. Using a modified version of Chebyshevs inequality, a similar result is obtained for the upper bound of the confidence interval width for any distribution of specified mean and standard deviation. Furthermore, for any error distribution given by a function which monotonically decreases with increasing distance from its mean, we show that the confidence that the error lies within a specified interval centered about zero decreases monotonically with increasing magnitude of the mean.
- Statistics and Probability