1Blurb:: (Experimental) Gaussian Process Models for Simulation Analysis
2(GPMSA) Bayesian calibration
3
4
5Description::
6GPMSA (Gaussian Process Models for Simulation Analysis) is a
7surrogate-based Markov Chain Monte Carlo Bayesian calibration
8method. Dakota's GPMSA is an experimental capability and not ready for
9production use at this time.
10
11Central to GPMSA is the construction of a Gaussian Process emulator
12from simulation runs collected at various settings of input
13parameters. The emulator is a statistical model of the system
14response, and it is used to incorporate the observational data to
15improve system predictions and constrain or calibrate the unknown
16parameters. The GPMSA code draws heavily on the theory developed in
17the seminal Bayesian calibration paper by Kennedy and O'Hagan
18\cite Kenn01.  The particular approach in GPMSA was developed by the Los
19Alamos National Labortory statistics group and documented in \cite Hig08.
20Dakota's GPMSA capability comes from the QUESO package developed at UT Austin.
21
22<b> Usage Tips: </b>
23
24Configuring GPMSA essentially involves identifying the simulation
25build data, the experiment data, the calibration and configuration
26(state) variables, and any necessary algorithm controls.  The GP
27surrogate model is automatically constructed internal to the algorithm
28and need not be specified through Dakota input.
29
30Dakota's GPMSA implementation is not intended for production use.
31There are a number of known limitations, including:
32
33<ul>
34<li>Only works for scalar and multivariate responses, not field
35responses.  Field responses will be treated as a single multi-variate
36response set.  Consequently, simulation and experiment data must have
37the same dimensions.</li>
38
39<li>When build data is not imported a design of experiments will be
40conducted over all calibration and scenario variables present.</li>
41
42<li>Experiment data is required (one cannot pose the simulation data
43as a set of residuals with the assumption of 0-valued
44experiments).</li>
45
46<li>Output and diagnostics are limited.  Advanced users will need to
47examine QUESO output files (potentially written in a transformed
48scaled space) in the QuesoDiagnostic directory</li>
49</ul>
50
51Topics::	package_queso, bayesian_calibration
52
53Examples::
54
55The following input file fragment illustrates GPMSA-based Bayesian
56calibration of 3 \f$\beta\f$ variables with a uniform prior, with 3
57configuration (scenario) variables \f$x\f$.  A total of 60 simulation
58build points are provided in <tt>sim_data.dat</tt>, which contains
59columns for each \f$\beta\f$, followed by each \f$x\f$, and then the
60simulation response 'lin'.  Each row of the experiment data file
61<tt>y_exp_with_var.dat</tt> contains the values of the 3 \f$x\f$
62variables, followed by the value of 'lin' and its observation error
63(variance).
64
65\verbatim
66
67method
68  bayes_calibration gpmsa
69    chain_samples 1000
70    seed 2460
71    build_samples 60
72    import_build_points_file  'sim_data.dat'  freeform
73    export_chain_points_file  'posterior.dat'
74      burn_in_samples = 100  sub_sampling_period = 2
75    posterior_stats kl
76
77variables
78  uniform_uncertain  3
79    upper_bounds   0.4500   -0.1000    0.4000
80    initial_point  0.2750   -0.3000    0.1000
81    lower_bounds  -0.1000   -0.5000   -0.2000
82    descriptors   'beta0'   'beta1'   'beta2'
83
84  continuous_state  3
85    upper_bounds   3 * 1.0
86    initial_state  3 * 0.5
87    lower_bounds   3 * 0.0
88    descriptors    'x0'  'x1'  'x2'
89
90responses
91  descriptors 'lin'
92  calibration_terms   1
93  calibration_data_file 'y_exp_with_var.dat'
94    freeform
95    num_experiments  5
96      num_config_variables   3
97    experiment_variance_type 'scalar'
98  no_gradients
99  no_hessians
100
101\endverbatim
102
103Theory::
104Faq::
105See_Also::
106