.. _method-bayes_calibration-muq-proposal_covariance:

"""""""""""""""""""
proposal_covariance
"""""""""""""""""""


Defines the technique used to generate the MCMC proposal covariance.



**Topics**


bayesian_calibration


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

   method-bayes_calibration-muq-proposal_covariance-prior
   method-bayes_calibration-muq-proposal_covariance-derivatives
   method-bayes_calibration-muq-proposal_covariance-values
   method-bayes_calibration-muq-proposal_covariance-filename


**Specification**

- *Alias:* None

- *Arguments:* None


**Child Keywords:**

+-------------------------+--------------------+--------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword     | Dakota Keyword Description                    |
|                         | Group              |                    |                                               |
+=========================+====================+====================+===============================================+
| Required (Choose One)   | Proposal           | `prior`__          | Uses the covariance of the prior              |
|                         | Covariance Source  |                    | distributions to define the MCMC proposal     |
|                         |                    |                    | covariance.                                   |
|                         |                    +--------------------+-----------------------------------------------+
|                         |                    | `derivatives`__    | Use derivatives to inform the MCMC proposal   |
|                         |                    |                    | covariance.                                   |
|                         |                    +--------------------+-----------------------------------------------+
|                         |                    | `values`__         | Specifies matrix values to use as the MCMC    |
|                         |                    |                    | proposal covariance.                          |
|                         |                    +--------------------+-----------------------------------------------+
|                         |                    | `filename`__       | Uses a file to import a user-specified MCMC   |
|                         |                    |                    | proposal covariance.                          |
+-------------------------+--------------------+--------------------+-----------------------------------------------+

.. __: method-bayes_calibration-muq-proposal_covariance-prior.html
__ method-bayes_calibration-muq-proposal_covariance-derivatives.html
__ method-bayes_calibration-muq-proposal_covariance-values.html
__ method-bayes_calibration-muq-proposal_covariance-filename.html



**Description**


The proposal covariance is used to define a multivariate normal (MVN)
jumping distribution used to create new points within a Markov chain.
That is, a new point in the chain is determined by sampling within a
MVN probability density with prescribed covariance that is centered at
the current chain point.  The accuracy of the proposal covariance has
a significant effect on rejection rates and the efficiency of chain mixing.

*Default Behavior*

The default proposal covariance is ``prior`` when no emulator is
present; ``derivatives`` when an emulator is present.

*Expected Output*

The effect of the proposal covariance is reflected in the MCMC chain
values and the rejection rates, which can be seen in the diagnostic
outputs from the QUESO solver within the ``QuesoDiagnostics``
directory.

*Usage Tips*

When derivative information is available inexpensively (e.g., from an
emulator model), the derived-based proposal covariance forms a more
accurate proposal distribution, resulting in lower rejection rates and
faster chain mixing.


