1Blurb:: 2Gaussian Process Adaptive Importance Sampling 3Description:: 4\c gpais is recommended for problems that have a relatively small 5number of input variables (e.g. less than 10-20). This method, Gaussian 6Process Adaptive Importance Sampling, 7is outlined in the paper \cite Dalbey2012. 8 9This method starts with an initial set of LHS samples and adds samples 10one at a time, with the goal of adaptively improving the estimate of 11the ideal importance density during the process. The approach uses a 12mixture of component densities. An iterative process is used 13to construct the sequence of improving component densities. At each 14iteration, a Gaussian process (GP) surrogate is used to help identify areas 15in the space where failure is likely to occur. The GPs are not used to 16directly calculate the failure probability; they are only used to approximate 17the importance density. Thus, the Gaussian process adaptive importance 18sampling algorithm overcomes limitations involving using a potentially 19inaccurate surrogate model directly in importance sampling calculations. 20 21Topics:: uncertainty_quantification 22Examples:: 23Theory:: 24Faq:: 25See_Also:: method-adaptive_sampling, method-local_reliability, method-global_reliability, method-sampling, method-importance_sampling, method-polynomial_chaos, method-stoch_collocation 26