Blurb:: Calibrate hyper-parameter multipliers on the observation error covariance

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

<b>Default Behavior:</b> 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.

<b>Expected Output:</b> Final calibration results will include both
inference parameters and one or more calibrated hyper-parameters.

<b>Usage Tips:</b> 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.

Topics::

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 \ref
method-bayes_calibration-calibrate_error_multipliers-hyperprior_alphas
and \ref
method-bayes_calibration-calibrate_error_multipliers-hyperprior_alphas-hyperprior_betas
keywords.

\verbatim
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'
\endverbatim

Theory::
Faq::
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