Multivariate Fitting and the Error Matrix in Global Analysis of Data

When a large body of data from diverse experiments is analyzed using a theoretical model with many parameters, the standard error matrix method and the general tools for evaluating the error may become inadequate. We present an iterative method that significantly improves the reliability, and hence the applicability, of the error matrix calculation. Also, to obtain more accurate estimates of the uncertainties on predictions of physical observables, we present a Lagrange multiplier method that explores the entire parameter space and avoids the linear approximations assumed in conventional error propagation calculations. These methods are illustrated by an example involving the global analysis of parton distribution functions.