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