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The integrated intensities obtained for the individual atomic columns were classified as a histogram, and the data fitting procedure was performed by the use of multiple normal distributions according to the GMM [16].
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On the assumption that the probability variable X i is subjected to a multiple normal distribution, each conditional function in equation (1) is obtained by linear regression for the measured data of the constituent nodes (molecules) measured at m points, i.e., (2) where x ik is the measured value of X i, at the k-th point, and n i is the number of variables corresponding to the parents of V i.
Normal scores are expected values of ordered multiple identical normal distributions.
We also show that the presence of these multiple log-normal distributions of gene expression levels is a universal characteristic of gene expression in eurkaryotes.
We confirmed the finding of multiple log-normal distributions of gene expression in humans with a data set from an RNAseq analysis (data was provided by TGen; high throughput sequencing was performed by Agencourt Bioscience Corporation, Beverly, MA).
Because power law-like behavior is universal for gene expression levels measured by microarrays including examination our data, we hypothesized that the finding that the distributions of gene expression levels could be described by multiple log-normal distributions might also be universal.
One-way ANOVA and pairwise comparison with Student Newman Keuls test were performed to compare multiple independent datasets with normal distributions, whereas Kruskal Wallis one-way ANOVA on ranks were performed to compare datasets without normal distributions.
We assessed the estimates and 95% CI of the effects of each of the predictors on Se and Sp. If warranted by the results of these analyses and the amount of studies available, we planned to consider developing this model further using multiple predictors or assuming separate bivariate normal distributions in different subgroups of studies.
One-way ANOVAs with LSDs were used for continuous variables with normal distributions for comparisons across multiple groups.
This approach does not require normal distributions and controls for the multiple comparisons.
If scaled and centered data are not well-approximated by a multivariate normal distribution (multiple clusters within the data can also violate the normality assumption), rotated axes are more likely to pass through the centre of the multivariate data cloud when obtained using robust covariance estimators to identify the most variable traits using alternative metrics [ 35].
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CEO of Professional Science Editing for Scientists @ prosciediting.com