Dakota Reference Manual: sampling

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sampling

Randomly samples variables according to their distributions

## Topics

This keyword is related to the topics:

- uncertainty_quantification
- sampling

## Specification

Alias: nond_sampling

Argument(s): none

Child Keywords:

| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description
--- | --- | --- | --- | ---
| Optional | samples | Number of samples for sampling-based methods
| Optional | seed | Seed of the random number generator
| Optional | fixed_seed | Reuses the same seed value for multiple random sampling sets
| Optional | sample_type | Selection of sampling strategy
| Optional | refinement_samples | Performs an incremental Latin Hypercube Sampling (LHS) study
| Optional | d_optimal | Generate a D-optimal sampling design
| Optional | variance_based_decomp | Activates global sensitivity analysis based on decomposition of response variance into contributions from variables
| Optional | backfill | Ensures that the samples of discrete variables with finite support are unique
| Optional | principal_components | Activates principal components analysis of the response matrix of N samples * L responses.
| Optional | wilks | Number of samples for random sampling using Wilks statistics
| Optional | final_moments | Output moments of the specified type and include them within the set of final statistics.
| Optional | response_levels | Values at which to estimate desired statistics for each response
| Optional | probability_levels | Specify probability levels at which to estimate the corresponding response value
| Optional | reliability_levels | Specify reliability levels at which the response values will be estimated
| Optional | gen_reliability_levels | Specify generalized relability levels at which to estimate the corresponding response value
| Optional | distribution | Selection of cumulative or complementary cumulative functions
| Optional | rng | Selection of a random number generator
| Optional | model_pointer | Identifier for model block to be used by a method

## Description

This method generates parameter values by drawing samples from the specified uncertain variable probability distributions. The computational model is executed over all generated parameter values to compute the responses for which statistics are computed. The statistics support sensitivity analysis and uncertainty quantification.

Default Behavior

By default, `sampling` methods operate on aleatory and epistemic uncertain variables. The types of variables can be restricted or expanded (to include design or state variables) through use of the `active` keyword in the variables block in the Dakota input file. If continuous design and/or state variables are designated as active, the sampling algorithm will treat them as parameters with uniform probability distributions between their upper and lower bounds. Refer to variable_support for additional information on supported variable types, with and without correlation.

The following keywords change how the samples are selected:

- sample_type
- fixed_seed
- rng
- samples
- seed
- variance_based_decomp

Expected Outputs

As a default, Dakota provides correlation analyses when running LHS. Correlation tables are printed with the simple, partial, and rank correlations between inputs and outputs. These can be useful to get a quick sense of how correlated the inputs are to each other, and how correlated various outputs are to inputs. `variance_based_decomp` is used to request more sensitivity information, with additional cost.

Additional statistics can be computed from the samples using the following keywords:

- `response_levels`
- `reliability_levels`
- `probability_levels`
- `gen_reliability_levels`

`response_levels` computes statistics at the specified response value. The other three allow the specification of the statistic value, and will estimate the corresponding response value.

`distribution` is used to specify whether the statistic values are from cumulative or complementary cumulative functions.

Expected HDF5 Output

If Dakota was built with HDF5 support and run with the hdf5 keyword, this method writes the following results to HDF5:

- When variance_based_decomp is enabled
  - Variance-Based Decomposition (Sobol' Indices)
- For aleatory UQ studies
  - Probability Density
  - Level Mappings
  - Sampling Moments
  - Correlations
- For epistemic UQ studies
  - Extreme Responses
  - Correlations

Usage Tips

`sampling` is a robust approach to doing sensitivity analysis and uncertainty quantification that can be applied to any problem. It requires more simulations than newer, advanced methods. Thus, an alternative may be preferable if the simulation is computationally expensive.

## Examples

    # tested on Dakota 6.0 on 140501

    environment
      tabular_data
        tabular_data_file = 'Sampling_basic.dat'

    method
      sampling
        sample_type lhs
        samples = 20

    model
      single

    variables
      active uncertain
      uniform_uncertain = 2
        descriptors  =   'input1'     'input2'
        lower_bounds =  -2.0     -2.0
        upper_bounds =   2.0      2.0
      continuous_state = 1
        descriptors =   'constant1'
        initial_state = 100

    interface
      analysis_drivers 'text_book'
        fork

    responses
      response_functions = 1
      no_gradients
      no_hessians

This example illustrates a basic sampling Dakota input file.

- LHS is used instead of purely random sampling.
- The default random number generator is used.
- Without a `seed` specified, this will not be reproducable
- In the `variables` block, two types of variables are used
- Only the uncertain variables are varied, this is the default behavior, and is also specified by the `active` keyword, w/ the `uncertain` option

## See Also

These keywords may also be of interest:

- active

## FAQ

Q: Do I need to keep the LHS* and S4 files? A: No