Principal Component Analysis error statistics

Correlations are inherent in chemical processes even where it can be assumed that there is no correlation among the data. Principal component analysis (PCA) transforms a set of correlated variables into a new set of uncorrelated ones, known as principal components, and is an effective tool in multivariate data analysis. In the last section we describe a method that combines PCA and the steady-state data reconciliation model to provide sharper, and less confounding, statistical tests for gross errors. 

Finally, a method for dealing with the inherent correlation existing in chemical processes was discussed. This method combines principal component analysis (PCA) and the steady-state data reconciliation model to provide sharper and less confounding statistical tests for gross errors. 

Principal Component Analysis (PCA) is performed on a human monitoring data base to assess its ability to identify relationships between variables and to assess the overall quality of the data. The analysis uncovers two unusual events that led to further investigation of the data. One, unusually high levels of chlordane related compounds were observed at one specific collection site. Two, a programming error is uncovered. Both events had gone unnoticed after conventional univariate statistical techniques were applied. These results Illustrate the usefulness of PCA in the reduction of multi-dimensioned data bases to allow for the visual inspection of data in a two dimensional plot. 

Principal component analysis (PCA) and principal component regression (PCR) were used to analyze the data [39,40]. PCR was used to construct calibration models to predict Ang II dose from spectra of the aortas. A cross-validation routine was used with NIR spectra to assess the statistical significance of the prediction of Ang II dose and collagen/elastin in mice aortas. The accuracy of the PCR method in predicting Ang II dose from NIR spectra was determined by the F test and the standard error of performance (SEP) calculated from the validation samples. 

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