bayes_calibration

Bayesian calibration

Topics

bayesian_calibration, package_queso

Specification

• Alias: nond_bayes_calibration

• Arguments: None

Child Keywords:

Required/Optional	Description of Group	Dakota Keyword	Dakota Keyword Description
Required (Choose One)	Bayesian Calibration Method	queso	Markov Chain Monte Carlo algorithms from the QUESO package
		gpmsa	(Experimental) Gaussian Process Models for Simulation Analysis (GPMSA) Bayesian calibration
		wasabi	(Experimental Method) Non-MCMC Bayesian inference using interval analysis
		dream	DREAM (DiffeRential Evolution Adaptive Metropolis)
		muq	Markov Chain Monte Carlo algorithms from the MUQ package
Optional		experimental_design	(Experimental) Adaptively select experimental designs for iterative Bayesian updating
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		posterior_stats	Compute information-theoretic metrics on posterior parameter distribution
Optional		chain_diagnostics	Compute diagnostic metrics for Markov chain
Optional		model_evidence	Calculate model evidence (marginal likelihood of model) when using Bayesian methods
Optional		model_discrepancy	(Experimental) Post-calibration calculation of model discrepancy correction
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 objective function or statistics convergence
Optional		max_iterations	Number of iterations allowed for optimizers and adaptive UQ methods
Optional		model_pointer	Identifier for model block to be used by a method
Optional		scaling	Turn on scaling for variables, responses, and constraints

Description

Bayesian calibration methods take prior information on parameter values (in the form of prior distributions) and observational data (e.g. from experiments) and infer 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. 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 four classes of Bayesian calibration methods: QUESO/DRAM, GPMSA, DREAM, and WASABI.

1. The QUESO methods use 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.

2. GPMSA (Gaussian Process Models for Simulation Analysis) is an approach developed at Los Alamos National Laboratory and Dakota currently uses the QUESO implementation. 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. This is an experimental capability and not all features are available in Dakota yet.

3. 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. [VtBD+09].

4. WASABI: Non-MCMC Bayesian inference via interval analysis

Usage Tips

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 and WASABI which are not yet ready for production use.

The prior distribution is characterized by the properties of the uncertain variables. Correlated priors are only supported for unbounded normal, untruncated lognormal, uniform, exponential, gumbel, frechet, and weibull distributions and require specification of standardized_space, for example, for QUESO standardized_space

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.