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We propose a novel multivariate Monte Carlo method as an efficient andflexible approach to analyzing extended X-ray sources with the ReflectionGrating Spectrometer (RGS) on XMM Newton. A multi-dimensional interpolationmethod is used to efficiently calculate the response function for the RGS inconjunction with an arbitrary spatially-varying spectral model. Several methodsof event comparison that effectively compare the multivariate RGS data arediscussed. The use of a multi-dimensional instrument Monte Carlo also createsmany opportunities for the use of complex astrophysical Monte Carlocalculations in diffuse X-ray spectroscopy. The methods presented here could begeneralized to other X-ray instruments as well.Comment: 36 pages, 14 figures, Accepted for publication in Ap

Multivariate Monte Carlo Methods for the Reflection Grating Spectrometers onXMM‐Newton