Applying Importance Sampling to a Stochastic Element

For risk analyses, it is frequently necessary to evaluate the low-probability, high-consequence end of the distribution of the performance of the system. Because the models for such systems are often complex (and hence need significant computer time to simulate), it can be difficult to use the conventional Monte Carlo approach to evaluate these low-probability, high-consequence outcomes, as this may require excessive numbers of realizations.

To facilitate these type of analyses, GoldSim allows you to utilize an importance sampling algorithm to modify the conventional Monte Carlo approach so that the tails of distributions (which could correspond to high-consequence, low-probability outcomes) are sampled with an enhanced frequency. During the analysis of the results that are generated, the biasing effects of the importance sampling are reversed. The result is high-resolution development of the high-consequence, low-probability "tails" of the consequences, without paying a high computational price.

Importance sampling is specified by selecting an option from the Importance Sampling button (the default is “None”):

If you select “High-End”, GoldSim will preferentially bias toward the high end of the distribution; if you select “Low-End”, it will preferentially bias toward the low end of the distribution.

It is important to understand that you should use importance sampling sparingly (i.e., only for those elements that really need it). This is because the degree of biasing for distribution tails that GoldSim can apply decreases with the number of elements for which importance sampling is applied.

The importance sampling algorithm is discussed in detail in Appendix B of the GoldSim User’s Guide).

Note: Importance sampling cannot be applied if the Stochastic is resampled during a realization.

Note: In addition to the importance sampling method described here (in which you can choose to force importance sampling on either the low end or high end of a Stochastic element’s range), GoldSim also provides an advanced feature that supports custom importance sampling that can be applied over user-defined regions of the Stochastic element’s range.