Blurb::
Number of bins used to compute the variance-based 
decomposition

Description::
Allows the user to specify the number of bins to be used
in the variance-based decomposition.

**Default Behavior**
Default number of bins is the square root of the number
of samples rounded down to the nearest integer.

Examples::

.. code-block::

    method,
      sampling
        sample_type lhs
        samples = 100
        variance_based_decomp
          vbd_method binned
            num_bins = 10

Theory::
The binned approach to computing Sobol' main effect indices is 
introduced in :cite:p:`Li16`. As opposed to pick-and-freeze 
approaches like :cite:p:`Sal04`, it does not require a specific
sampling structure. Given a set of randomly-generated input-output 
samples, it computes the main effect index by binning samples, 
computing a sample statistic for each bin, then computing another
sample statistic over the bins. 

The number of bins recommended in :cite:p:`Li16` is the square 
root of the number of input-output samples. This is the default
number of bins used for the method in Dakota. However, if the
user wishes to specify a different number of bins, they can do 
so using ``num_bins``.

Faq::

See_Also::
