Editing Importance sampling (section)

=== Evaluation of importance sampling ===

In order to identify successful importance sampling techniques, it is useful to be able to quantify the run-time savings due to the use of the importance sampling approach. The performance measure commonly used is <math>\sigma^2_{MC} / \sigma^2_{IS} \,</math>, and this can be interpreted as the speed-up factor by which the importance sampling estimator achieves the same precision as the MC estimator. This has to be computed empirically since the estimator variances are not likely to be analytically possible when their mean is intractable. Other useful concepts in quantifying an importance sampling estimator are the variance bounds and the notion of asymptotic efficiency. One related measure is the so-called '''Effective Sample Size''' '''(ESS)'''.<ref>{{Cite journal|last1=Martino|first1=Luca|last2=Elvira|first2=Víctor|last3=Louzada|first3=Francisco|title=Effective sample size for importance sampling based on discrepancy measures|journal=Signal Processing|volume=131|pages=386–401|doi=10.1016/j.sigpro.2016.08.025|arxiv=1602.03572|year=2017|s2cid=26317735 }}</ref>