Blurb::
Add context to data: specify the type of experimental error
Description::
There are four options for specifying the experimental error (e.g. the
measurement error in the data you provide for calibration purposes):
'none' (default), 'scalar', 'diagonal', or 'matrix.'

If the user specifies scalar, they can provide a scalar variance per
calibration term.  Note that for scalar calibration terms, only 'none'
or 'scalar' are options for the measurement variance.  However, for
field calibration terms, there are two additional options.  'diagonal'
allows the user to provide a vector of measurement variances (one for
each term in the calibration field).  This vector corresponds to the
diagonal of the full covariance matrix of measurement errors.  If the
user specifies 'matrix', they can provide a full covariance matrix
(not just the diagonal terms), where each element (i,j) of the
covariance matrix represents the covariance of the measurement error
between the i-th and j-th field values.

*Usage Tips*

Variance information is specified on a per-response group
(descriptor), per-experiment basis.  Off-diagonal covariance between
response groups or between experiments is not supported.
Topics::

Examples::
The figure below shows an observation vector with 5 responses; 2
scalar + 3 field (each field of length > 1).  The
corresponding covariance matrix has scalar variances :math:`\sigma_1^2,
\sigma_2^2`  for each of the scalars :math:`s1, s2` , diagonal
covariance :math:`D_3`  for field :math:`f3` , scalar covariance
:math:`\sigma_4^2`  for field :math:`f4` , and full matrix covariance
:math:`C_5`  for field :math:`f5` .  In total, Dakota supports block
diagonal covariance :math:`\Sigma`  across the responses, with blocks
:math:`\Sigma_i` , which could be fully dense within a given field
response group.  Covariance across the highest-level responses
(off-diagonal blocks) is not supported, nor is covariance between
experiments.

\image html ObsErrorCovariance.png "An example of scalar and field response data, with associated block-diagonal observation error covariance."
Theory::

Faq::

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