Editing Importance sampling (section)

=== Variance cost function ===

Variance is not the only possible [[Loss function|cost function]] for a simulation, and other cost functions, such as the mean absolute deviation, are used in various statistical applications. Nevertheless, the variance is the primary cost function addressed in the literature, probably due to the use of variances in [[confidence interval]]s and in the performance measure <math>\sigma^2_{MC} / \sigma^2_{IS} \,</math>.

An associated issue is the fact that the ratio <math>\sigma^2_{MC} / \sigma^2_{IS} \,</math> overestimates the run-time savings due to importance sampling since it does not include the extra computing time required to compute the weight function. Hence, some people evaluate the net run-time improvement by various means. Perhaps a more serious overhead to importance sampling is the time taken to devise and program the technique and analytically derive the desired weight function.