Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Importance sampling
This keyword is related to the topics:
Alias: nond_importance_sampling
Argument(s): none
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Optional  samples  Number of samples for samplingbased methods  
Optional  seed  Seed of the random number generator  
Required (Choose One)  Group 1  import  Sampling option  
adapt_import  Importance sampling option  
mm_adapt_import  Sampling option  
Optional  refinement_samples  Number of samples used to refine a probabilty estimate or sampling design.  
Optional  response_levels  Values at which to estimate desired statistics for each response  
Optional  max_iterations  Stopping criterion based on number of iterations  
Optional  convergence_tolerance  Stopping criterion based on convergence of the objective function or statistics  
Optional  distribution  Selection of cumulative or complementary cumulative functions  
Optional  probability_levels  Specify probability levels at which to estimate the corresponding response value  
Optional  gen_reliability_levels  Specify generalized relability levels at which to estimate the corresponding response value  
Optional  rng  Selection of a random number generator  
Optional  model_pointer  Identifier for model block to be used by a method 
The importance_sampling
method is based on ideas in reliability modeling.
An initial Latin Hypercube sampling is performed to generate an initial set of samples. These initial samples are augmented with samples from an importance density as follows:
Options
Choose one of the importance sampling options:
import
adapt_import
mm_adapt_import
The options for importance sampling are as follows: import
centers a sampling density at one of the initial LHS samples identified in the failure region. It then generates the importance samples, weights them by their probability of occurence given the original density, and calculates the required probability (CDF or CCDF level). adapt_import
is the same as import
but is performed iteratively until the failure probability estimate converges. mm_adapt_import
starts with all of the samples located in the failure region to build a multimodal sampling density. First, it uses a small number of samples around each of the initial samples in the failure region. Note that these samples are allocated to the different points based on their relative probabilities of occurrence: more probable points get more samples. This early part of the approach is done to search for "representative" points. Once these are located, the multimodal sampling density is set and then mm_adapt_import
proceeds similarly to adapt_import
(sample until convergence).
Importance sampling is a method that allows one to estimate statistical quantities such as failure probabilities (e.g. the probability that a response quantity will exceed a threshold or fall below a threshold value) in a way that is more efficient than Monte Carlo sampling. The core idea in importance sampling is that one generates samples that preferentially samples important regions in the space (e.g. in or near the failure region or userdefined region of interest), and then appropriately weights the samples to obtain an unbiased estimate of the failure probability [76]. In importance sampling, the samples are generated from a density which is called the importance density: it is not the original probability density of the input distributions. The importance density should be centered near the failure region of interest. For blackbox simulations such as those commonly interfaced with Dakota, it is difficult to specify the importance density a priori: the user often does not know where the failure region lies, especially in a highdimensional space.[78]. We have developed two importance sampling approaches which do not rely on the user explicitly specifying an importance density.
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