Blurb::
Use the pick-and-freeze variance-based decomposition method 
Description::
Uses structured samples to compute main and total
effect sensitivity indices.

**Default Behavior**

If the user specified a number of samples, :math:`N`, and a number of
nondeterministic variables, :math:`M`, pick-and-freeze variance-based 
decomposition requires the evaluation of :math:`N*(M+2)` samples.

.. warning::
    Specifying this keyword will increase the number of function 
    evaluations above the number requested with the ``samples`` keyword 
    since replicated sets of sample values are evaluated.

**Expected Output**

When ``pick_and_freeze`` is specified as the ``vbd_sampling_method``,
sensitivity indices for main effects and total effects will be 
reported.  Main effects (roughly) represent the percent 
contribution of each individual variable to the variance 
in the model response.  Total effects represent the percent 
contribution of each individual variable in combination with 
all other variables to the variance in the model response.

Examples::

.. code-block::

    method,
      sampling
        sample_type lhs
        samples = 100
        variance_based_decomp
          vbd_sampling_method pick_and_freeze

Theory::
Pick-and-freeze methods 
are currently the most popular approach for varianced-based sensitivity
index computation, but they incur significant computational cost. These
approaches rely on structured sampling wherein two independent random
sample sets of the input variables are generated, then the random samples
of the variable whose sensitivity index is being computed are substituted
from one sample set into the other. Specifically, if the user specified a 
number of samples, :math:`N`, and a number of nondeterministic variables, :math:`M`, 
pick-and-freeze variance-based decomposition requires the evaluation of 
:math:`N*(M+2)` samples.

Faq::

See_Also::
