Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Number of samples for random sampling using Wilks statistics
Alias: none
Argument(s): none
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Optional  order  The order of the statistics to use when determining sample sizes for random sampling using Wilks order statistics.  
Optional  confidence_level  The confidence level to be used when determining sample sizes for random sampling using Wilks order statistics.  
Optional  one_sided  Specifies onesided order statistics to be used when determining sample sizes for random sampling using Wilks order statistics.  
Optional  two_sided  Specifies twosided order statistics (an interval) to be used when determining sample sizes for random sampling using Wilks order statistics. 
The wilks
keyword is used to compute the number of samples to execute for a random sampling study using Wilks statistics. In contrast to most sampling studies where the user specifies the number of samples in advance, Wilks determines the number of samples to run to achieve a particular objective. Specifically, Wilks statistics specify a probability level, alpha, and confidence level, beta, and determines the minimum number of samples required such that there is beta% confidence that the alpha*100 percentile of the uncertain distribution on model output will fall below the actual alpha*100 percentile given by the sample when outputs are ordered from smallest to largest. Statistics can also be either one_side or two_sided with the former reflecting a statement about uppermost sample output and the latter reflecting both the smallest and largest sample outputs. Finally, the order of the statistics can be increased to higher order such that the statement concerning probability level and confidence level applies to the uppermost M outputs (for onesided Morder Wilks) or the lowest M and uppermost M outputs (for twosided Morder Wilks).
Default Behavior
By default, Wilks statistics are computed using onesided firstorder order statistics with a 95% confidence interval (beta) and 95% probability (alpha). This results in a sample size of 59.
Usage Tips
Wilks sample sizes apply to model outputs considered oneatatime. Joint variation among multiple outputs requires a generalization of the Wilks approach and is not supported in Dakota at this time.
When more than one probability level is specified, the largest sample size will be used.
method sampling sample_type random wilks probability_levels = 0.75 0.8 0.95 0.99 confidence_level 0.99 two_sided order 2