Adaptive Importance Sampling

The Adaptive Importance Sampling method (Wu, 1994) mainly samples in the failure region to compute the probability of failure.

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In adaptive importance sampling the failure region is approximated by a second-order polynomial using principle curvatures like SORM (see Second Order Reliability Method (SORM). The curvature values are updated iteratively to cover the failure region based on the number of sample points actually in the failure region (see the figure below).