Dakota Reference Manual: calibrate_error_multipliers

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calibrate_error_multipliers

Calibrate hyper-parameter multipliers on the observation error covariance

## Specification

Alias: none

Argument(s): none

Default: none

Child Keywords:

| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description
--- | --- | --- | --- | ---
| Required (Choose One) | Calibrate Error Multipliers (Group 1) | one | Calibrate one hyper-parameter multiplier across all responses/experiments
per_experiment | Calibrate one hyper-parameter multiplier per experiment
per_response | Calibrate one hyper-parameter multiplier per response
both | Calibrate one hyper-parameter multiplier for each response/experiment pair
| Optional | hyperprior_alphas | Shape (alpha) of the inverse gamma hyper-parameter prior

## Description

Calibrate one or more multipliers on the user-provided observation error covariance (experiment_variance_type). Options include `one` multiplier on the whole block-diagonal covariance structure, one multiplier `per_experiment` covariance block, one multiplier `per_response` covariance block, or separate multipliers for each response/experiment pair (for a total of number experiments X number response groups).

Default Behavior: No hyper-parameter calibration. When hyper-parameter calibration is enabled, the default prior on the multiplier is a diffuse inverse gamma, with mean and mode approximately 1.0.

Expected Output: Final calibration results will include both inference parameters and one or more calibrated hyper-parameters.

Usage Tips: The per_response option can be useful when each response has its own measurement error process, but all experiments were gathered with the same equipment and conditions. The per_experiment option might be used when working with data from multiple independent laboratories.

## Examples

Perform Bayesian calibration with 2 calibration variables and two hyper-parameter multipliers, one per each of two responses. The multipliers are assumed the same across the 10 experiments. The priors on the multipliers are specified using the hyperprior_alphas and hyperprior_betas keywords.

    bayes_calibration queso
      samples = 1000 seed = 348
      dram
      calibrate_error_multipliers per_response
        hyperprior_alphas = 27.0
        hyperprior_betas  = 26.0

    variables
      uniform_uncertain 2
        upper_bounds  1.e8 10.0
        lower_bounds 1.e6 0.1
        initial_point 2.85e7 2.5
        descriptors 'E' 'w'

    responses
        calibration_terms = 2
        calibration_data_file = 'expdata.withsigma.dat'
          freeform
          num_experiments = 10
            experiment_variance_type = 'scalar'