Blurb::
Gaussian Process Adaptive Importance Sampling
Description::
\c gpais is recommended for problems that have a relatively small 
number of input variables (e.g. less than 10-20). This method, Gaussian 
Process Adaptive Importance Sampling, 
is outlined in the paper \cite Dalbey2012. 

This method starts with an initial set of LHS samples and adds samples 
one at a time, with the goal of adaptively improving the estimate of 
the ideal importance density during the process. The approach uses a 
mixture of component densities. An iterative process is used
to construct the sequence of improving component densities. At each
iteration, a Gaussian process (GP) surrogate is used to help identify areas
in the space where failure is likely to occur. The GPs are not used to
directly calculate the failure probability; they are only used to approximate
the importance density. Thus, the Gaussian process adaptive importance
sampling algorithm overcomes limitations involving using a potentially
inaccurate surrogate model directly in importance sampling calculations. 

Topics::        uncertainty_quantification	
Examples::
Theory::
Faq::
See_Also::	method-adaptive_sampling, method-local_reliability, method-global_reliability, method-sampling, method-importance_sampling, method-polynomial_chaos, method-stoch_collocation
