Blurb::
Compute surrogate quality metrics
Description::
Diagnostic metrics assess the goodness of fit of a global surrogate to
its training data.

The default diagnostics are:

- ``root_mean_squared``
- ``mean_abs``
- ``rsquared``

Additional available diagnostics include

- ``sum_squared``
- ``mean_squared``
- ``sum_abs``
- ``max_abs``

The keywords ``press`` and ``cross_validation`` further specify
leave-one-out or k-fold cross validation, respectively, for all of the
active metrics from above.

*Usage Tips*
When specified, the ``metrics`` keyword must be followed by a list of
quoted strings, each of which activates a metric.
Topics::
surrogate_models
Examples::
This example input fragment constructs a quadratic polynomial
surrogate and computes four metrics on the fit, both with and without
5-fold cross validation. (Also see
dakota/share/dakota/test/dakota_surrogate_import.in for additional
examples.)


.. code-block::

    model
      surrogate global
        polynomial quadratic
        metrics = "root_mean_squared" "sum_abs" "mean_abs" "max_abs"
        cross_validation folds = 5


Theory::
Most of these diagnostics refer to some operation on the
residuals (the difference between the surrogate model and the truth
model at the data points upon which the surrogate is built).

For example, ``sum_squared`` refers to the sum of the squared
residuals, and ``mean_abs`` refers to the mean of the absolute value of
the residuals. ``rsquared`` refers to the R-squared value typically
used in regression analysis (the proportion of the variability in the
response that can be accounted for by the surrogate model). Care
should be taken when interpreting metrics, for example, errors may be
near zero for interpolatory models or rsquared may not be applicable
for non-polynomial models.
Faq::

See_Also::
