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


Markov Chain Monte Carlo algorithms from the QUESO package

Topics

This keyword is related to the topics:

Specification

Alias: none

Argument(s): none

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 emulator

Use an emulator or surrogate model to evaluate the likelihood function

Optional logit_transform

Utilize the logit transformation to reduce sample rejection for bounded domains

Optional export_chain_points_file

Export the MCMC chain to the specified filename

Optional
(Choose One)
MCMC algorithm type (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 Metropolis-Hastings MCMC algorithm

multilevel

Use the multilevel MCMC algorithm.

Optional rng

Selection of a random number generator

Optional pre_solve

Perform deterministic optimization for MAP before Bayesian calibration

Optional proposal_covariance

Defines the technique used to generate the MCMC proposal covariance.

Description

For the QUESO method, one can use an emulator in the MCMC sampling. This 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. However, in the case of fast running evaluations, we recommend the use of no emulator. 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.

In terms of the MCMC sampling, one can specify one of the following MCMC algorithms to use: dram for DRAM (Delayed Rejection Adaptive Metropolis), delayed_rejection for delayed_rejection only, adaptive_metropolis for adaptive metropolis only, metropolis_hastings for Metropolis Hastings, and multilevel for the multilevel MCMC algorithm.

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.