derivatives
Use derivatives to inform the MCMC proposal covariance.
Topics
bayesian_calibration
Specification
Alias: None
Arguments: None
Child Keywords:
Required/Optional |
Description of Group |
Dakota Keyword |
Dakota Keyword Description |
---|---|---|---|
Optional |
Period at which to update derivative-based proposal covariance |
Description
This keyword selection results in definition of the MCMC proposal covariance from the Hessian of the misfit function (negative log likelihood), where this Hessian is defined from either a Gauss-Newton approximation (using only first derivatives of the calibration terms) or a full Hessian (using values, first derivatives, and second derivatives of the calibration terms). If this Hessian is indeterminate, it will be corrected as described in Bayesian Methods.
Default Behavior
The default is prior
based proposal covariance. This is a more
advanced option that exploits structure in the form of the likelihood.
Expected Output
When derivatives are specified for defining the proposal covariance, the misfit Hessian and its inverse (the MVN proposal covariance) will be output to the standard output stream.
Usage Tips
The full Hessian of the misfit is used when either supported by the emulator in use (for PCE and surfpack GP, but not SC or dakota GP) or by the user’s response specification (Hessian type is not “no_hessians”), in the case of no emulator. When this full Hessian is indefinite and cannot be inverted to form the proposal covariance, fallback to the positive semi-definite Gauss-Newton Hessian is employed.
Since this proposal covariance is locally accurate, it should be
updated periodically using the update_period
option. While the
adaptive metropolis option can be used in combination with
derivative-based preconditioning, it is generally preferable to
instead decrease the proposal update period due to the improved local
accuracy of this approach.
Examples
Generate a 2000 sample posterior chain, using derivatives to initialize the proposal covariance at the start of the chain.
method,
bayes_calibration queso
samples = 2000 seed = 348
delayed_rejection
emulator pce sparse_grid_level = 2
proposal_covariance derivatives