The authors provide a didactic treatment of nonlinear (categorical) principal components analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated principal components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal variables and that it can handle and discover n...

The Hilbert and Fourier transforms are tools used for signal analysis in the time/frequency domains. The Hilbert transform is applied to casual continuous signals. The majority of the practical signals are discrete signals and they are limited in time. It appeared therefore the need to create numeric algorithms for the Hilbert transform. Such an algorithm is a numeric operator, named the Discre...

Model sensitivity analysis variance reduction ( ) ( ), where ( ) ∑ ( )[ ( )] , ( ) ∑ ( )[ ( )] , ( ) ∑ ( ) , where is the numeric real value of state q, ( ) is the expected real value of Q before applying new findings, ( ) is the expected real value of Q after applying new findings f for variable F, and ( ) is the variance of the real value of Q before any new findings [0,infinity], the greater...

BACKGROUND Confidence intervals (or associated standard errors) facilitate assessment of the practical importance of the findings of a health study, and their incorporation into a meta-analysis. For paired design studies, these items are often not reported. Since the descriptive statistics for such studies are usually presented in the same way as for unpaired designs, direct computation of the ...

A new nonparametric test of independence between the components of bivariate random vectors .X; Y / is motivated and evaluated in practice. The test statistics is based on the fact that under independence, every quantile of Y given X D x is constant. This is in contrast to the most commonly used basis that the joint probability density or distribution function ofX and Y , equals to the product ...