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Using Importance Sampling to Model High-Consequence, Low-Probability Outcomes

Rick Kossik
Principal
GoldSim Technology Group
rkossik@goldsim.com

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.

GoldSim has provided a mechanism to carry out importance sampling of parameters in your model (probability distributions) since its earliest version. In particular, you can instruct GoldSim to over-sample either the high-end or the low-end of a distribution.  You will find this feature by expanding the Stochastic dialog. In Version 9.6, it looks like this:

In Version 10, it looks like this:

(The importance sampling algorithm was modified in Version 10 so that it is no longer necessary to specify a Magnification factor).

GoldSim Version 10 introduces an even more powerful feature: the ability to apply importance sampling not only to parameters, but to events.  This allows you to artificially increase the rate of occurrence of rare events in GoldSim (e.g., failures, accidents). The result is high-resolution development of the high-consequence, low-probability "tails" of the consequences resulting from these low-probability events.  This kind of sampling is particularly powerful for risk analyses that involve rare events that can have disastrous (e.g., fatal) consequences.

Version 10 provides importance sampling for Timed Event, Random Choice and Function and Action Reliability elements. It is specified by selecting the checkbox for Use Importance Sampling for this element:

One important note on importance sampling: it should be used very sparingly (typically for only 2 or 3 parameters and/or events at the most). This is because the degree of biasing that GoldSim can provide decreases with the number of elements for which importance sampling is applied.

The mathematical details of the importance sampling algorithm utilized by GoldSim are discussed in detail in Appendix B of the GoldSim User’s Guide.

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