Markov Chain Monte Carlo algorithms from the QUESO package


bayesian_calibration, package_queso


  • Alias: None

  • Arguments: None

Child Keywords:


Description of Group

Dakota Keyword

Dakota Keyword Description



Number of Markov Chain Monte Carlo posterior samples



Seed of the random number generator



Selection of a random number generator



Use an emulator or surrogate model to evaluate the likelihood function



Perform Bayesian inference in standardized probability space



Utilize the logit transformation to reduce sample rejection for bounded domains



Export the MCMC chain to the specified filename

Optional (Choose One)

MCMC Algorithm


Use the DRAM MCMC algorithm


Use the Delayed Rejection MCMC algorithm


Use the Adaptive Metropolis MCMC algorithm


Use the Metropolis-Hastings MCMC algorithm


Use the multilevel MCMC algorithm.



Perform deterministic optimization for MAP before Bayesian calibration



Defines the technique used to generate the MCMC proposal covariance.



File containing advanced QUESO options


The queso method supports the following MCMC algorithms: DRAM (Delayed Rejection Adaptive Metropolis), delayed rejection (DR) only, adaptive metropolis (AM) only, pure Metropolis Hasting (MH)s, and multilevel (ML).

When calibrating fast-running simulation models, use of an emulator is not typically warranted. For slower models, using an emulator model in the MCMC sampling will greatly improve the speed, since the Monte Carlo Markov Chain will generate thousands of samples on the emulator instead of the real simulation code. An emulator may be specified with the keyword emulator, followed by a gaussian_process emulator, a pce emulator (polynomial chaos expansion), or a sc emulator (stochastic collocation). For the gaussian_process emulator, the user must specify whether to use the surfpack or dakota version of the Gaussian process. The user can define the number of samples build_samples from which the emulator should be built. It is also possible to build the Gaussian process from points read in from the import_points_file and to export approximation-based sample evaluations using export_points_file. For pce or sc, the user can define a sparse_grid_level.

There are a variety of ways the user can specify the proposal covariance matrix which is very important in governing the samples generated in the chain. The proposal covariance specifies the covariance structure of a multivariate normal distribution. The user can specify proposal_covariance, followed by derivatives, prior, values, or filename. The derivative specification involves forming the Hessian of the misfit function (the negative log likelihood). When derivative information is available inexpensively (e.g. from an emulator), the derived-based proposal covariance forms a more accurate proposal distribution, resulting in lower rejection rates and faster chain mixing. The prior setting involves constructing the proposal from the variance of the prior distributions of the parameters being calibrated. When specifying the proposal covariance with values or from a file, the user can choose to specify only the diagonals of the covariance matrix with diagonal or to specify the full covariance matrix with matrix.

There are two other controls for QUESO. The pre_solve option enables the user to start the chain at an optimal point, the Maximum A Posteriori (MAP) point. This is the point in parameter space that maximizes the log posterior, (defined as the log-likelihood minus the log_prior). A deterministic optimization method is used to obtain the MAP point, and the MCMC chain is then started at the best point found in the optimization. The second factor is a logit_transform, which performs an internal variable transformation from bounded domains to unbounded domains in order to reduce sample rejection due to an out-of-bounds condition.

Note that as of Dakota 6.2, the field data capability may be used with QUESO. 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.