.. _method-multilevel_sampling-allocation_target-scalarization:

"""""""""""""
scalarization
"""""""""""""


Fit MLMC sample allocation to a mixture of terms of means and standard deviations.


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

   method-multilevel_sampling-allocation_target-scalarization-scalarization_response_mapping
   method-multilevel_sampling-allocation_target-scalarization-optimization


**Specification**

- *Alias:* None

- *Arguments:* None


**Child Keywords:**

+-------------------------+--------------------+------------------------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword                     | Dakota Keyword Description                    |
|                         | Group              |                                    |                                               |
+=========================+====================+====================================+===============================================+
| Optional                                     | `scalarization_response_mapping`__ | Coefficients for linear scalarization         |
|                                              |                                    | (combination) of responses                    |
+----------------------------------------------+------------------------------------+-----------------------------------------------+
| Optional                                     | `optimization`__                   | Solve the optimization problem for the sample |
|                                              |                                    | allocation by numerical optimization in the   |
|                                              |                                    | case of sampling estimator targeting the      |
|                                              |                                    | scalarization.                                |
+----------------------------------------------+------------------------------------+-----------------------------------------------+

.. __: method-multilevel_sampling-allocation_target-scalarization-scalarization_response_mapping.html
__ method-multilevel_sampling-allocation_target-scalarization-optimization.html



**Description**


Fit MLMC sample allocation to control the variance of the estimator for a mixture of terms of means and standard deviations. The exact scalarized formulation is given by the keyword ``scalarization_response_mapping``.



**Examples**


The following method block

.. code-block::

    method,
     model_pointer = 'HIERARCH'
            multilevel_sampling
       pilot_samples = 20 seed = 1237
       convergence_tolerance = .01
       allocation_target = scalarization
        scalarization_response_mapping = 1 0 0 0
                                                     0 0 1 3


uses the standard_deviation as sample allocation target by computing its variance. In this example, we assume a problem with two responses where the first line in scalarization_response_mapping refers to the first response, the second line to the second response. In the first line we only use 1 times the mean as quantity of interest. For the second response, we use 1 time the mean plus 3 times the standard devitation of the second quantity of interested. This behavior mimics the keywords :dakkw:`model-nested-sub_method_pointer-primary_response_mapping` and :dakkw:`model-nested-sub_method_pointer-secondary_response_mapping`.


