Dakota Reference Manual  Version 6.4 Large-Scale Engineering Optimization and Uncertainty Analysis
wilks

Number of samples for random sampling using Wilks statistics

## Specification

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 one-sided order statistics to be used when determining sample sizes for random sampling using Wilks order statistics.

Optional two_sided

Specifies two-sided order statistics (an interval) to be used when determining sample sizes for random sampling using Wilks order statistics.

## Description

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 one-sided M-order Wilks) or the lowest M and uppermost M outputs (for two-sided M-order Wilks).

Default Behavior

By default, Wilks statistics are computed using one-sided first-order 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 one-at-a-time. 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.

## Examples

```method
sampling
sample_type random
wilks
probability_levels = 0.75 0.8 0.95 0.99
confidence_level 0.99
two_sided
order 2
```