Blurb::
Use the binned Sobol' main effect index computation
Description::
Uses unstructured input-output samples to estimate
main effect indices. It cannot compute total indices.

**Expected Output**
Sensitivity indices for main effects *only* will be reported.  
Main effects (roughly) represent the percent contribution of 
each individual variable to the variance in the model response. 

Examples::

.. code-block::

    method,
      sampling
        sample_type lhs
        samples = 100
        variance_based_decomp
          vbd_sampling_method binned

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. 

Two algorithms are detailed in :cite:p:`Li16`: computing a 
sample expectation for each bin, then a sample variance, or 
computing a sample variance for each bin, then an expectation.
The second algorithm is implemented in Dakota.

Faq::

See_Also::
