.. _method-bayes_calibration-calibrate_error_multipliers:

"""""""""""""""""""""""""""
calibrate_error_multipliers
"""""""""""""""""""""""""""


Calibrate hyper-parameter multipliers on the observation error covariance


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

   method-bayes_calibration-calibrate_error_multipliers-one
   method-bayes_calibration-calibrate_error_multipliers-per_experiment
   method-bayes_calibration-calibrate_error_multipliers-per_response
   method-bayes_calibration-calibrate_error_multipliers-both
   method-bayes_calibration-calibrate_error_multipliers-hyperprior_alphas


**Specification**

- *Alias:* None

- *Arguments:* None

- *Default:* none


**Child Keywords:**

+-------------------------+--------------------+-----------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword        | Dakota Keyword Description                    |
|                         | Group              |                       |                                               |
+=========================+====================+=======================+===============================================+
| Required (Choose One)   | Calibrate Error    | `one`__               | Calibrate one hyper-parameter multiplier      |
|                         | Multipliers        |                       | across all responses/experiments              |
|                         |                    +-----------------------+-----------------------------------------------+
|                         |                    | `per_experiment`__    | Calibrate one hyper-parameter multiplier per  |
|                         |                    |                       | experiment                                    |
|                         |                    +-----------------------+-----------------------------------------------+
|                         |                    | `per_response`__      | Calibrate one hyper-parameter multiplier per  |
|                         |                    |                       | response                                      |
|                         |                    +-----------------------+-----------------------------------------------+
|                         |                    | `both`__              | Calibrate one hyper-parameter multiplier for  |
|                         |                    |                       | each response/experiment pair                 |
+-------------------------+--------------------+-----------------------+-----------------------------------------------+
| Optional                                     | `hyperprior_alphas`__ | Shape (alpha) of the inverse gamma            |
|                                              |                       | hyper-parameter prior                         |
+----------------------------------------------+-----------------------+-----------------------------------------------+

.. __: method-bayes_calibration-calibrate_error_multipliers-one.html
__ method-bayes_calibration-calibrate_error_multipliers-per_experiment.html
__ method-bayes_calibration-calibrate_error_multipliers-per_response.html
__ method-bayes_calibration-calibrate_error_multipliers-both.html
__ method-bayes_calibration-calibrate_error_multipliers-hyperprior_alphas.html



**Description**


Calibrate one or more multipliers on the user-provided
observation error covariance (
:dakkw:`responses-calibration_terms-calibration_data-experiment_variance_type`).  Options
include ``one`` multiplier on the whole block-diagonal covariance
structure, one multiplier ``per_experiment`` covariance block, one
multiplier ``per_response`` covariance block, or separate multipliers
for each response/experiment pair (for a total of number experiments X
number response groups).

*Default Behavior:* No hyper-parameter calibration.  When
hyper-parameter calibration is enabled, the default prior on the
multiplier is a diffuse inverse gamma, with mean and mode
approximately 1.0.

*Expected Output:* Final calibration results will include both
inference parameters and one or more calibrated hyper-parameters.

*Usage Tips:* The per_response option can be useful when each
response has its own measurement error process, but all experiments
were gathered with the same equipment and conditions.  The
per_experiment option might be used when working with data from
multiple independent laboratories.



**Examples**


Perform Bayesian calibration with 2 calibration variables
and two hyper-parameter multipliers, one per each of two responses.
The multipliers are assumed the same across the 10 experiments.  The
priors on the multipliers are specified using the
:dakkw:`method-bayes_calibration-calibrate_error_multipliers-hyperprior_alphas`
and
:dakkw:`method-bayes_calibration-calibrate_error_multipliers-hyperprior_alphas-hyperprior_betas`
keywords.


.. code-block::

    bayes_calibration queso
      samples = 1000 seed = 348
      dram
      calibrate_error_multipliers per_response
        hyperprior_alphas = 27.0
        hyperprior_betas  = 26.0
    
    variables
      uniform_uncertain 2
        upper_bounds  1.e8 10.0
        lower_bounds 1.e6 0.1
        initial_point 2.85e7 2.5
        descriptors 'E' 'w'
    
    responses
     calibration_terms = 2
        calibration_data_file = 'expdata.withsigma.dat'
          freeform
          num_experiments = 10
         experiment_variance_type = 'scalar'