Metrics variance-based

A diversity metric is a function to aid the quantification of the diversity of a set of compounds in some predefined chemical space. Diversity metrics fall into three main classes (1) Distance-based methods, which express diversity as a function of the pairwise molecular dissimilarities defined through measurement. (2) Cell-based methods, which define diversity in terms of occupancy of a finite number of cells that represent disjoint regions of chemical space. (3) Variance-based methods, which quantify diversity based on the degree of correlation between a compound s important features. 

Overall sampling quality — quantitative analysis. For dynamical trajectories, the "structural decorrelation time" analysis [10] can estimate the slowest timescale affecting significant configuration-space populations and hence yield the effective sample size. For non-dynamical simulations, a variance analysis based on multiple runs is called for [1]. Analyzing the variance in populations of approximate physical states appears to be promising as a benchmark metric. 

Typically the pred block will be used to code all elements of the model. However, use of PREDPP and the associated ADVAN subroutines is possible, particularly when a combined PK/PD model is desired (e.g., see Ref. 4). For this discussion, a model for exposure-response based on the Poisson distribution is assumed and area under the concentration-time curve (AUC) is the exposure metric. The first part of the model provides for definition of the mean and variance of the Poisson distribution. 

More recent proposals discussed for evaluating bioequivalence are based on approaches termed Individual Bioequivalence and Population Bioequivalence. The average bioequivalence approach focuses only on the comparison of population averages (p, p ) of a bioequivalence metric of interest and not on the variances of the metric for the T and R products. The individual bioequivalence approach not only compares the population averages (pj, p ), but also assesses the within-subject variability (o t, o r ) as well as the subject-by-formulation interaction (Od ). The population bioequivalence approach is designed to assess the total variability, i.e., within- and between-subject variability (o, Oxr ) of the pharmacokinetic parameter (metric) in the population. The individual and population bioequivalence... 

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. 

Since nearest neighbor methods are based on similarity measured by some distance metric then variable scaling and the units used to characterize the data can influence results. Variables with the largest amount of scatter (greatest variance) will contribute most strongly to the Euclidean distance and in practice it may be advisable to standardize variables before performing classification analysis. 

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