Blurb:: (Experimental) Gaussian Process Models for Simulation Analysis
(GPMSA) Bayesian calibration


Description::
GPMSA (Gaussian Process Models for Simulation Analysis) is a
surrogate-based Markov Chain Monte Carlo Bayesian calibration
method. Dakota's GPMSA is an experimental capability and not ready for
production use at this time.

Central to GPMSA is the construction of a Gaussian Process emulator
from simulation runs collected at various settings of input
parameters. The emulator is a statistical model of the system
response, and it is used to incorporate the observational data to
improve system predictions and constrain or calibrate the unknown
parameters. The GPMSA code draws heavily on the theory developed in
the seminal Bayesian calibration paper by Kennedy and O'Hagan 
\cite Kenn01.  The particular approach in GPMSA was developed by the Los
Alamos National Labortory statistics group and documented in \cite Hig08.
Dakota's GPMSA capability comes from the QUESO package developed at UT Austin.

<b> Usage Tips: </b>

Configuring GPMSA essentially involves identifying the simulation
build data, the experiment data, the calibration and configuration
(state) variables, and any necessary algorithm controls.  The GP
surrogate model is automatically constructed internal to the algorithm
and need not be specified through Dakota input.

Dakota's GPMSA implementation is not intended for production use.
There are a number of known limitations, including:

<ul>
<li>Only works for scalar and multivariate responses, not field
responses.  Field responses will be treated as a single multi-variate
response set.  Consequently, simulation and experiment data must have
the same dimensions.</li>

<li>When build data is not imported a design of experiments will be
conducted over all calibration and scenario variables present.</li>

<li>Experiment data is required (one cannot pose the simulation data
as a set of residuals with the assumption of 0-valued
experiments).</li>

<li>Output and diagnostics are limited.  Advanced users will need to
examine QUESO output files (potentially written in a transformed
scaled space) in the QuesoDiagnostic directory</li>
</ul>

Topics::	package_queso, bayesian_calibration

Examples::

The following input file fragment illustrates GPMSA-based Bayesian
calibration of 3 \f$\beta\f$ variables with a uniform prior, with 3
configuration (scenario) variables \f$x\f$.  A total of 60 simulation
build points are provided in <tt>sim_data.dat</tt>, which contains
columns for each \f$\beta\f$, followed by each \f$x\f$, and then the
simulation response 'lin'.  Each row of the experiment data file
<tt>y_exp_with_var.dat</tt> contains the values of the 3 \f$x\f$
variables, followed by the value of 'lin' and its observation error
(variance).

\verbatim

method
  bayes_calibration gpmsa
    chain_samples 1000
    seed 2460
    build_samples 60
    import_build_points_file  'sim_data.dat'  freeform
    export_chain_points_file  'posterior.dat'
      burn_in_samples = 100  sub_sampling_period = 2
    posterior_stats kl

variables
  uniform_uncertain  3
    upper_bounds   0.4500   -0.1000    0.4000
    initial_point  0.2750   -0.3000    0.1000
    lower_bounds  -0.1000   -0.5000   -0.2000
    descriptors   'beta0'   'beta1'   'beta2' 

  continuous_state  3
    upper_bounds   3 * 1.0
    initial_state  3 * 0.5
    lower_bounds   3 * 0.0
    descriptors    'x0'  'x1'  'x2'

responses
  descriptors 'lin'
  calibration_terms   1
  calibration_data_file 'y_exp_with_var.dat'
    freeform
    num_experiments  5
      num_config_variables   3
    experiment_variance_type 'scalar'
  no_gradients
  no_hessians

\endverbatim

Theory::
Faq::
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