Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Perform deterministic optimization for MAP before Bayesian calibration
Alias: none
Argument(s): none
Default: nip presolve for emulators
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Required (Choose One)  Group 1  sqp  Uses a sequential quadratic programming method for underlying optimization  
nip  Uses a nonlinear interior point method for underlying optimization  
none  Deactivates MAP presolve prior to initiating the MCMC process. 
When specified, Dakota will perform a deterministic derivativebased optimization to maximize the log posterior (minimize the negative log posterior = misfit  log_prior + constant normalization factors). The Markov chain in Bayesian calibration will subsequently be started at the best point found in the optimization (the MAP point), which can eliminate the need for "burn in" of the chain in which some initial portion of the chain is discarded. Note that both optimization methods available (sqp
and nip
) require derivatives of the negative log posterior, either firstorder in the case of SQP (with quasiNewton Hessians from secant updates) or secondorder in the case of fullNewton NIP (with explicit Hessian use). The derivatives will be computed from the same model used for the MCMC process; e.g. if an emulator is used, the emulator derivatives will be used, otherwise they will be based on the user's model specification for the model.
It is important to clarify that the use of the Hessian of the negative log posterior within a full Newton solver does not strictly require Hessians from the model response quantities of interest (QoIs). Rather, the Hessian of the negative log posterior is formed from an exact Hessian of the negative log prior and a misfit Hessian that can be either exact or approximated: the full misfit Hessian can be formed using QoI residuals, gradients, and Hessians or the GaussNewton approximate misfit Hessian can be formed using only QoI gradients [4]. This Hessian composition is configured automatically based on MAP solver selection and the emulator's or simulation model's support for derivatives.
Default Behavior The default MAP presolve behavior depends on the use of an emulator model within the inference process.
If there is an emulator (for which derivatives are easily computed), then the MAP presolve is active by default and a full Newton NIP formulation is selected if OPT++ is available. The default use of a MAP presolve can be overridden using "pre_solve none" and the default selection of OPT++ full Newton NIP can be replaced with NPSOL SQP using "pre_solve sqp." Depending on the emulator's support for derivatives of the simulated QoI (gradients for dakota GP and stochastic collocation; gradients and Hessians for surfpack GP and polynomial chaos), the contribution of the misfit Hessian to the Hessian of the negative log posterior will be computed either using the full misfit Hessian or its GaussNewton approximation (refer to Bayesian chapter in[4]).
If no emulator model is specified, then the presolve is bypassed by default and the MCMC chain is initiated from userspecified (or default) initial value for the prior distributions of the random variables. This default can be overridden by specifying "pre_solve nip" for a full Newton NIP solution or "pre_solve sqp" for an NPSOL SQP solution. Both MAP presolve approaches require QoI gradients from the simulation model, and the full Newton approach can further leverage QoI Hessians when available (though not required due to the GaussNewton approximation, as explained previously).
Expected Output When presolve is enabled, the output will include a deterministic optimization, followed by a Bayesian calibration. The final results will include the MAP point as well as posterior statistics from the MCMC chain. The MAP point that is reported is the point with highest posterior probability spanning both the presolve and the subsequent MCMC chain; it will most commonly reflect the end state of the presolve, although it can reflect subsequent improvements from the chain evolution, should they occur.
method bayes_calibration queso samples = 2000 seed = 348 delayed_rejection emulator pce sparse_grid_level = 2 pre_solve nip # default for emulators