  We propose a novel multivariate Monte Carlo method as an efficient and
flexible approach to analyzing extended X-ray sources with the Reflection
Grating Spectrometer (RGS) on XMM Newton. A multi-dimensional interpolation
method is used to efficiently calculate the response function for the RGS in
conjunction with an arbitrary spatially-varying spectral model. Several methods
of event comparison that effectively compare the multivariate RGS data are
discussed. The use of a multi-dimensional instrument Monte Carlo also creates
many opportunities for the use of complex astrophysical Monte Carlo
calculations in diffuse X-ray spectroscopy. The methods presented here could be
generalized to other X-ray instruments as well.
