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The analysis of photometric large-scale structure data is often complicatedby the need to account for many observational and astrophysical systematics.The elaborate models needed to describe them often introduce many ``nuisanceparameters'', which can be a major inhibitor of an efficient parameterinference. In this paper we introduce an approximate method to analyticallymarginalise over a large number of nuisance parameters based on the Laplaceapproximation. We discuss the mathematics of the method, its relation toconcepts such as volume effects and profile likelihood, and show that it can befurther simplified for calibratable systematics by linearising the dependenceof the theory on the associated parameters. We quantify the accuracy of thisapproach by comparing it with traditional sampling methods in the context ofexisting data from the Dark Energy Survey, as well as futuristic Stage-IVphotometric data. The linearised version of the method is able to obtainparameter constraints that are virtually equivalent to those found by exploringthe full parameter space for a large number of calibratable nuisanceparameters, while reducing the computation time by a factor 3-10. Furthermore,the non-linearised approach is able to analytically marginalise over a largenumber of parameters, returning constraints that are virtuallyindistinguishable from the brute-force method in most cases, accuratelyreproducing both the marginalised uncertainty on cosmological parameters, andthe impact of volume effects associated with this marginalisation. We providesimple recipes to diagnose when the approximations made by the method fail andone should thus resort to traditional methods. The gains in sampling efficiencyassociated with this method enable the joint analysis of multiple surveys,typically hindered by the large number of nuisance parameters needed todescribe them.

Cosmology with 6 parameters in the Stage-IV era: efficient marginalisation over nuisance parameters