.. _method-bayes_calibration-dream-emulator-ml_pce:

""""""
ml_pce
""""""


Multilevel Polynomial Chaos Expansion as an emulator model.


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

   method-bayes_calibration-dream-emulator-ml_pce-allocation_control
   method-bayes_calibration-dream-emulator-ml_pce-discrepancy_emulation
   method-bayes_calibration-dream-emulator-ml_pce-expansion_order_sequence
   method-bayes_calibration-dream-emulator-ml_pce-orthogonal_least_interpolation
   method-bayes_calibration-dream-emulator-ml_pce-askey
   method-bayes_calibration-dream-emulator-ml_pce-wiener
   method-bayes_calibration-dream-emulator-ml_pce-normalized
   method-bayes_calibration-dream-emulator-ml_pce-export_expansion_file
   method-bayes_calibration-dream-emulator-ml_pce-diagonal_covariance
   method-bayes_calibration-dream-emulator-ml_pce-full_covariance


**Specification**

- *Alias:* None

- *Arguments:* None


**Child Keywords:**

+-------------------------+--------------------+------------------------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword                     | Dakota Keyword Description                    |
|                         | Group              |                                    |                                               |
+=========================+====================+====================================+===============================================+
| Optional                                     | `allocation_control`__             | Sample allocation approach for multilevel     |
|                                              |                                    | expansions                                    |
+----------------------------------------------+------------------------------------+-----------------------------------------------+
| Optional                                     | `discrepancy_emulation`__          | Formulation for emulation of model            |
|                                              |                                    | discrepancies.                                |
+-------------------------+--------------------+------------------------------------+-----------------------------------------------+
| Required (Choose One)   | Required (Choose   | `expansion_order_sequence`__       | Sequence of expansion orders used in a        |
|                         | One)               |                                    | multi-stage expansion                         |
|                         |                    +------------------------------------+-----------------------------------------------+
|                         |                    | `orthogonal_least_interpolation`__ | Build a polynomial chaos expansion from       |
|                         |                    |                                    | simulation samples using orthogonal least     |
|                         |                    |                                    | interpolation.                                |
+-------------------------+--------------------+------------------------------------+-----------------------------------------------+
| Optional (Choose One)   | Basis Polynomial   | `askey`__                          | Select the standardized random variables (and |
|                         | Family             |                                    | associated basis polynomials) from the Askey  |
|                         |                    |                                    | family that best match the user-specified     |
|                         |                    |                                    | random variables.                             |
|                         |                    +------------------------------------+-----------------------------------------------+
|                         |                    | `wiener`__                         | Use standard normal random variables (along   |
|                         |                    |                                    | with Hermite orthogonal basis polynomials)    |
|                         |                    |                                    | when transforming to a standardized           |
|                         |                    |                                    | probability space.                            |
+-------------------------+--------------------+------------------------------------+-----------------------------------------------+
| Optional                                     | `normalized`__                     | The normalized specification requests output  |
|                                              |                                    | of PCE coefficients that correspond to        |
|                                              |                                    | normalized orthogonal basis polynomials       |
+----------------------------------------------+------------------------------------+-----------------------------------------------+
| Optional                                     | `export_expansion_file`__          | Export the coefficients and multi-index of a  |
|                                              |                                    | Polynomial Chaos Expansion (PCE) to a file    |
+-------------------------+--------------------+------------------------------------+-----------------------------------------------+
| Optional (Choose One)   | Covariance Type    | `diagonal_covariance`__            | Display only the diagonal terms of the        |
|                         |                    |                                    | covariance matrix                             |
|                         |                    +------------------------------------+-----------------------------------------------+
|                         |                    | `full_covariance`__                | Display the full covariance matrix            |
+-------------------------+--------------------+------------------------------------+-----------------------------------------------+

.. __: method-bayes_calibration-dream-emulator-ml_pce-allocation_control.html
__ method-bayes_calibration-dream-emulator-ml_pce-discrepancy_emulation.html
__ method-bayes_calibration-dream-emulator-ml_pce-expansion_order_sequence.html
__ method-bayes_calibration-dream-emulator-ml_pce-orthogonal_least_interpolation.html
__ method-bayes_calibration-dream-emulator-ml_pce-askey.html
__ method-bayes_calibration-dream-emulator-ml_pce-wiener.html
__ method-bayes_calibration-dream-emulator-ml_pce-normalized.html
__ method-bayes_calibration-dream-emulator-ml_pce-export_expansion_file.html
__ method-bayes_calibration-dream-emulator-ml_pce-diagonal_covariance.html
__ method-bayes_calibration-dream-emulator-ml_pce-full_covariance.html



**Description**


Selects a multilevel polynomial chaos expansion (ML PCE) surrogate model
to use in the Bayesian likelihood calculations.  Most specification options are
carried over for using ML PCE as a surrogate within the Bayesian framework.


