The use of Monte Carlo methods in factor analysis

Abstract

Monte Carlo techniques are introduced in target transformation factor analysis (TTFA), in combination with the concept of the principal factor model, in order to account for local variances in the data set and to estimate the uncertainties in the obtained source profiles. The new method is validated using several types of artificial data sets. It was found that application of the Monte Carlo method leads to a significant improvement of the accuracy of the derived source profiles in comparison with standard TTFA. From the introduction of (known) error sources to the artificial data sets it was found that the source-profile reproduction quality is optimal if the magnitudes of the Monte Carlo variations are chosen equal to the magnitudes of the introduced errors.