Dakota Reference Manual: derivatives

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derivatives

Use derivatives to inform the MCMC proposal covariance.

## Topics

This keyword is related to the topics:

- bayesian_calibration

## Specification

Alias: none

Argument(s): none

Child Keywords:

| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description
--- | --- | --- | --- | ---
| Optional | update_period | 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[15]

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