The problem of identifying the provenance of unknown nuclear material in the environment by multivariate statistical analysis of its uranium and/or plutonium isotopic composition is considered. Such material can be introduced into the environment as a result of nuclear accidents, inadvertent processing losses, illegal dumping of waste, or deliberate trafficking in nuclear materials. Various combinations of reactor type and fuel composition were analyzed using Principal Components Analysis (PCA) and Partial Least Squares Discriminant Analysis (PLSDA) of the concentrations of nine U and Pu isotopes in fuel as a function of burnup. Real-world variation in the concentrations of 234 U and 236 U in the fresh (unirradiated) fuel was incorporated. The U and Pu were also analyzed separately, with results that suggest that, even after reprocessing or environmental fractionation, Pu isotopes can be used to determine both the source reactor type and the initial fuel composition with good discrimination.