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Computing averages over a target probability density by statisticalre-weighting of a set of samples with a different distribution is a strategywhich is commonly adopted in fields as diverse as atomistic simulation andfinance. Here we present a very general analysis of the accuracy and efficiencyof this approach, highlighting some of its weaknesses. We then give an exampleof how our results can be used, specifically to assess the feasibility ofhigh-order path integral methods. We demonstrate that the most promising ofthese techniques -- which is based on re-weighted sampling -- is bound to failas the size of the system is increased, because of the exponential growth ofthe statistical uncertainty in the re-weighted average.

The inefficiency of re-weighted sampling and the curse of system size in high order path integration