Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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calibrate_error_multipliers


Calibrate hyper-parameter multipliers on the observation error covariance

Specification

Alias: none

Argument(s): none

Default: none

Required/Optional Description of Group Dakota Keyword Dakota Keyword Description
Required
(Choose One)
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 (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
        variance_type = 'scalar'