The inefficiency of reweighted sampling and the curse of system size in highorder path integration
Abstract
Computing averages over a target probability density by statistical reweighting of a set of samples with a different distribution is a strategy which is commonly adopted in fields as diverse as atomistic simulation and finance. Here we present a very general analysis of the accuracy and efficiency of this approach, highlighting some of its weaknesses. We then give an example of how our results can be used, specifically to assess the feasibility of highorder path integral methods. We demonstrate that the most promising of these techniques  which is based on reweighted sampling  is bound to fail as the size of the system is increased, because of the exponential growth of the statistical uncertainty in the reweighted average.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 January 2012
 DOI:
 10.1098/rspa.2011.0413
 arXiv:
 arXiv:1107.1908
 Bibcode:
 2012RSPSA.468....2C
 Keywords:

 Physics  Chemical Physics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 Proc. R. Soc. A 8 January 2012 vol. 468 no. 2137 217