Goodness-of-fit criteria

GLYOXYLA.TE AMINOTRANSFERASE GLYOXYLA.TE REDUCTASE GMP SYNTHETASE GOLDMAN EQUATION GOODNESS-OF-FIT CRITERIA GLOBAL ANALYSIS STATISTICS (A Primer)... 

Wyszecki (13) proposed a "goodness-of-fit" criteria for the CIE in an effort to establish a better method for testing light sources with respect to their suitability to serve as a standard daylight source for colorimetry. While his method... 

The goodness of fit criteria that are used in CURFIT are as follows (1) If the data are not described by selected equation, CURFIT returns the conclusion that the data is described by two or more equations (of the selected form) with overlapping domains. In this case the domains, parameters, and the associated maximum errors for each equation are given. (2) If the data are described by the selected equation, CURFIT computes its parameters and their associated maximum errors. Bad data points are automatically rejected. Thus the number of equations returned by CURFIT determines whether or not the data is described by the proposed reaction model. In those cases where the model is not described by all the data, the information returned by CURFIT can be used to specify what subset (s) of the data fits the reaction model. 

A common approach to deal with model uncertainty is model set expansion (Zio and Apostolakis, 1996). According to this approach, the characteristics of the system under consideration are analyzed and models are created in an attempt to emulate the system based on goodness-of-fit criteria (Reinert and Apostolakis, 2006). The models may use different assumptions and require different inputs. These models are then combined to produce a meta-model of the system. Several methods have been proposed regarding the construction of the meta-model. AU rely on expert opinion. In the Bayesian approach, the combination of the individual models is carried out using Bayes theorem (Droguett and Mosleh, 2008). This method is theoretically very attractive dne to its mathematical rigor and ability to incorporate both objective and subjective information in a probabilistic representation. 

Using this relation we can conduct a linear fit to the resulting F-f plot and apply well accepted goodness of fit criteria, and likely versus unlikely ranges of values for Ko can be readily tested against the data within error limits. Kq and Kq values... 

Equation 7 provides the formal error bars on estimates of the relative travel time and, through Eq. 4, velocity changes. However, in addition to formal error bars, goodness-of-fit criteria must be taken into accotmt as well (Press et al. 1986). In the implementation of CWI at Okmok, two goodness-of-fit criteria are required to be met in order to accept an estimate of relative travel time, irrespective of the error estimate in Eq. 7. It must be that either (a) the standard deviation in Eq. 6 is less than one time sample or (b) the Pearson linear correlation coefficient given by... 

Different tests for estimation the accuracy of fit and prediction capability of the retention models were investigated in this work. Distribution of the residuals with taking into account their statistical weights chai acterizes the goodness of fit. For the application of statistical weights the scedastic functions of retention factor were constmcted. Was established that random errors of the retention factor k ai e distributed normally that permits to use the statistical criteria for prediction capability and goodness of fit correctly. 

Data may be fitted to this equation by the method of least squares in order to determine values of the constants log /c, fiA, / B, etc. The goodness of fit may be shown in graphical form by using the values of determined in this manner to calculate (Cf). A plot of the reaction rate versus this function should then meet the criteria of the general method outlined above. 

The following criteria could be used to ensure an acceptable goodness-of-fit ... 

The form of the equation is specified in advance, and the best correspnding values of any constants are found by least squares. The goodness of fit of several assumed equations are compared by statistical criteria such as the correlation coefficient or the F-test. When the number of sets of data equals the number of unknown constants in the equation, the constants are found by simultaneous solution. Otherwise a least squares regression is used. 

Deconvolution Algorithms. The correlation function for broad distributions is a sum of single exponentials. This ill-conditioned mathematical problem is not subject to the usual criteria for goodness-of-fit. Size resolution is ultimately limited by the noise on the measured correlation function, and measurements for several hours (13) are required to obtain accurate widths. Peaks closer than about 2 1 are unlikely to be resolved unless a-priori assumptions are invoked to constrain the possible solutions. Such constraints should be stated explicitly otherwise, the results are misleading. Constraints that work well with one type of distribution and one set of data often fail with others. Thus, artifacts including nonexistent bi-, tri-, and quadramodals abound. Many particle size distributions are inherently nonsmooth, and attempts to smooth the data prior to deconvolution have not been particularly successful. 

In addition to the usual, statistical criteria for goodness of fit, an even more fundamental requirement for a suitable function is that the constants uniformly increase or decrease with the temperature of aging. 

The kinetic traces are obtained from stopped-flow experiments and fit to a single-exponential or to a sum-of-exponentials model. Strictly speaking, one does not know beforehand how many exponentials will be required to describe adequately a particular kinetic curve, so that one has to perform several separate fits, each using a different number of such terms. We therefore need criteria to use in choosing which model best describes the data. The standard ones are the form of (i) the residuals (ii) the autocorrelation function values and (iii) the value (statistical goodness-of-fit parameter). 

Validation Criteria. QSARs should include a measure of the goodness of fit as well as results from external validation of the QSAR, using independent data beyond the training set. The uncertainty and variability of underlying test data limits the precision, accuracy, and reliability of many QSAR predictions. Hence, large uncertainty factors are commonly applied to QSAR predictions requiring comparisons to protective human health benchmarks. 

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