Root mean square noise Measurement of spectrophotometric noise of NIR instruments by measuring a reference (usually a ceramic or spectralon) repeatedly and calculate the root mean square error. [Pg.484]

So far we have said nothing about the conditions needed before this reduction in mean squared error can be attained. The chief requirement is that the error e in the i-th measurement (i.e., the i-th reading of the spring balance or optical detector) be independent of the quantity being measured, for i = l,2,, n. In the weighing problem this implies that the objects to be weighed should be light in comparison with the mass of the balance, and in the optical problem that the noise in the detector be independent of the... [Pg.50]

Maximum likelihood (ML) estimation can be performed if the statistics of the measurement noise Ej are known. This estimate is the value of the parameters for which the observation of the vector, yj, is the most probable. If we assume the probability density function (pdf) of to be normal, with zero mean and uniform variance, ML estimation reduces to ordinary least squares estimation. An estimate, 0, of the true yth individual parameters (pj can be obtained through optimization of some objective function, 0 (0 ). ModeP is assumed to be a natural choice if each measurement is assumed to be equally precise for all values of yj. This is usually the case in concentration-effect modeling. Considering the multiplicative log-normal error model, the observed concentration y is given by ... [Pg.2948]

Suppose a given data set consisting of 20 measurements of the yield y, at different pressures (p) and temperatures (7 ) is available. Fit the model (5.1) to the data this results in a fit error SSEi, where SSE stands for sum of squared residuals (e ). If the same data set is fitted to model (5.2), then this results in a fit error SSE2. Then SSE2 < SSEi, because model (5.2) will always contain model (5.1). Model (5.1) is a constrained version of model (5.2), hence, there is a relationship between the fit errors of both models. This does not mean, however, that model (5.2) is better than model (5.1). If model (5.1) can describe the data well, the increased complexity of model (5.2) will only lead to overfitting, i.e., fitting of noise. [Pg.96]

In this simulated-data example, a twelve-story shear building is considered. It is assumed that this building has uniformly distributed floor mass and uniform stiffness across the height. The mass per floor is taken to be 100 metric tons, while the interstory stiffness is chosen to be k = 202.767 MN/m so that the first five modal frequencies are 0.900,2.686,4.429,6.103 and 7.680 Hz. The covariance matrix is diagonal with the variances corresponding to a 1.0% coefficient of variation of the measurement error of the squared modal frequencies and mode shapes for all modes, a reasonable value based on typical modal test results. For the simulated modal data, a sample of zero-mean Gaussian noise with covariance matrix was added to the exact modal frequencies and mode shapes. [Pg.202]

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