.. _method-fsu_quasi_mc-variance_based_decomp-vbd_sampling_method-binned-num_bins:

""""""""
num_bins
""""""""


Number of bins used to compute the variance-based 
decomposition



.. toctree::
   :hidden:
   :maxdepth: 1



**Specification**

- *Alias:* None

- *Arguments:* INTEGER

- *Default:* -1


**Description**


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

**Default Behavior**
For continuous variables, the default number of 
bins is the square root of the number of samples rounded 
down to the nearest integer. For discrete and categorical
variables, the number of bins is equal to the number of 
unique values the variable takes in the sample set.




**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``.



