Dakota Reference Manual
Version 6.12
Explore and Predict with Confidence

(Experimental) Gaussian Process Models for Simulation Analysis (GPMSA) Bayesian calibration
This keyword is related to the topics:
Alias: none
Argument(s): none
Child Keywords:
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Required  chain_samples  Number of Markov Chain Monte Carlo posterior samples  
Optional  seed  Seed of the random number generator  
Optional  rng  Selection of a random number generator  
Required  build_samples  Number of initial model evaluations used in build phase  
Optional  import_build_points_file  File containing points you wish to use to build a surrogate  
Optional  standardized_space  Perform Bayesian inference in standardized probability space  
Optional  logit_transform  Utilize the logit transformation to reduce sample rejection for bounded domains  
Optional  gpmsa_normalize  Enable GPMSAinternal normalization  
Optional  export_chain_points_file  Export the MCMC chain to the specified filename  
Optional (Choose One)  MCMC Algorithm (Group 1)  dram  Use the DRAM MCMC algorithm  
delayed_rejection  Use the Delayed Rejection MCMC algorithm  
adaptive_metropolis  Use the Adaptive Metropolis MCMC algorithm  
metropolis_hastings  Use the MetropolisHastings MCMC algorithm  
Optional  proposal_covariance  Defines the technique used to generate the MCMC proposal covariance.  
Optional  options_file  File containing advanced QUESO options 
GPMSA (Gaussian Process Models for Simulation Analysis) is a surrogatebased 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 [54]. The particular approach in GPMSA was developed by the Los Alamos National Labortory statistics group and documented in[47]. Dakota's GPMSA capability comes from the QUESO package developed at UT Austin.
Usage Tips:
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:
Only works for scalar and multivariate responses, not field responses. Field responses will be treated as a single multivariate response set. Consequently, simulation and experiment data must have the same dimensions.
When build data is not imported a design of experiments will be conducted over all calibration and scenario variables present.
Experiment data is required (one cannot pose the simulation data as a set of residuals with the assumption of 0valued experiments).
The following input file fragment illustrates GPMSAbased Bayesian calibration of 3 variables with a uniform prior, with 3 configuration (scenario) variables . A total of 60 simulation build points are provided in sim_data.dat
, which contains columns for each , followed by each , and then the simulation response 'lin'. Each row of the experiment data file y_exp_with_var.dat
contains the values of the 3 variables, followed by the value of 'lin' and its observation error (variance).
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