Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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bayes_calibration


Bayesian calibration

Topics

This keyword is related to the topics:

Specification

Alias: nond_bayes_calibration

Argument(s): none

Required/Optional Description of Group Dakota Keyword Dakota Keyword Description
Required
(Choose One)
Group 1 queso Markov Chain Monte Carlo algorithms from the QUESO package
gpmsa (Experimental) Gaussian Process Models for Simulation Analysis (GPMSA) Markov Chain Monte Carlo algorithm with Gaussian Process Surrogate
wasabi

(Experimental Method) Non-MCMC Bayesian inference using interval analysis

dream DREAM (DiffeRential Evolution Adaptive Metropolis)
Optional standardized_space

Perform Bayesian inference in standardized probability space

Optional calibrate_error_multipliers

Calibrate hyper-parameter multipliers on the observation error covariance

Optional burn_in_samples

Manually specify the burn in period for the MCMC chain.

Optional sub_sampling_period

Specify a sub-sampling of the MCMC chain

Optional probability_levels

Specify probability levels at which to compute credible and prediction intervals

Optional convergence_tolerance

Stopping criterion based on convergence of the objective function or statistics

Optional max_iterations

Stopping criterion based on number of iterations

Optional model_pointer

Identifier for model block to be used by a method

Description

Bayesian calibration methods take prior information on parameter values (in the form of prior distributions) and observational data (e.g. from experiments) and produce posterior distributions on the parameter values. When the computational simulation is then executed with samples from the posterior parameter distributions, the results that are produced are consistent with ("agree with") the experimental data. Calibrating parameters from a computational simulation model requires a "likelihood function" that specifies the likelihood of observing a particular observation given the model and its associated parameterization; Dakota assumes a Gaussian likelihood function currently. The algorithms that produce the posterior distributions on model parameters are most commonly Monte Carlo Markov Chain (MCMC) sampling algorithms. MCMC methods require many samples, often tens of thousands, so in the case of model calibration, often emulators of the computational simulation are used. For more details on the algorithms underlying the methods, see the Dakota User's manual.

Dakota has three Bayesian calibration methods: QUESO, DREAM, and GPMSA, specified with bayes_calibration queso, bayes_calibration dream, or bayes_calibration gpmsa, respectively. The QUESO method uses components from the QUESO library (Quantification of Uncertainty for Estimation, Simulation, and Optimization) developed at The University of Texas at Austin. Dakota uses its DRAM (Delayed Rejected Adaptive Metropolis) algorithm, and variants, for the MCMC sampling. DREAM (DiffeRential Evolution Adaptive Metropolis) is a method that runs multiple different chains simultaneously for global exploration, and automatically tunes the proposal covariance during the process by a self-adaptive randomized subspace sampling.[86]. GPMSA (Gaussian Process Models for Simulation Analysis) is an approach developed at Los Alamos National Laboratory. It constructs Gaussian process models to emulate the expensive computational simulation as well as model discrepancy. GPMSA also has extensive features for calibration, such as the capability to include a "model discrepancy" term and the capability to model functional data such as time series data.

The Bayesian capabilities are under active development. At this stage, the QUESO methods in Dakota are the most advanced and robust, followed by DREAM, followed by GPMSA, which is in prototype form at this time. Dakota also has an experimental WASABI capability for non-MCMC Bayesian inference; it is not yet ready for production use. Note that as of Dakota 6.2, the field responses and associated field data may be used with QUESO and DREAM. That is, the user can specify field simulation data and field experiment data, and Dakota will interpolate and provide the proper residuals to the Bayesian calibration.