Quantification of multivariate datasets, such as XPS images, is a major area of research due to the impressive capability of modern instruments. It can, however, present challenges in terms of signal-to-noise and long acquisition times. A very simple but computationally-intensive Bayesian chemometric method@footnote 2@ for addressing this problem was published around ten years ago. With increasing personal computer speeds this has become not just more practical, but even very rapid today. This approach to electron counting statistics results in a novel quantification method that halves acquisition time, or equivalently, results in an increase in signal-to-noise of roughly a factor of 1.4, rising to 1.7 for the shortest acquisition time, noisiest images. This is not a ``black box'' statistical method, but a relatively simple way of building-in the assumption that the primary beam is fairly stable from pixel-to-pixel, which is certainly the case for modern XPS instruments. The method is potentially valuable in depth-profiling too. We show that combining this method with rapid Monte Carlo methods@footnote 3,4@ (whose routine use has also become much more practical recently) leads to several important new chemometric methods for count-limited, multivariate surface analytical data in general. @FootnoteText@ @footnote 1@ K Artyushkova and J E Fulghum in "Surface Analysis by Auger and X-ray Photoelectron Spectroscopy", Ed. D Briggs and J T Grant (IM Publications, Chichester UK, 2004).@footnote 2@ P J Cumpson and M P Seah, Surface and Interface Analysis, 18 (1992) 361.@footnote 3@ P J Cumpson, Surface and Interface Analysis 20 (1993) 727.@footnote 4@ D Ze-jun and R Shimizu in "Surface Analysis by Auger and X-ray Photoelectron Spectroscopy", Ed. D Briggs and J T Grant (IM Publications, Chichester UK, 2004). .