Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Markov Chain Monte Carlo algorithms from the QUESO package
This keyword is related to the topics:
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 MetropolisHastings 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. 
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 approximationbased 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 derivedbased 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 loglikelihood 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 outofbounds 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.