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Dakota Reference Manual
Version 6.15
Explore and Predict with Confidence
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Specify probability levels at which to compute credible and prediction intervals
Alias: none
Argument(s): REALLIST
Default: No CDF/CCDF response levels to compute
Child Keywords:
Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description | |
---|---|---|---|---|
Optional | num_probability_levels | This capability is currently inactive |
Credible and prediction intervals of model responses are computed for specified probabilities. Credible intervals are calculated from the response function values corresponding to the final MCMC chain. Calculation of prediction intervals consider these response values as well as the experimental uncertainty, which is specified by the user via the experiment_variance_type
command.
Expected Output
If probability_levels
is specified, Dakota will create a table containing the credibile intervals for each response function. The corresponding table containing the prediction intervals will also be created if a experiment_variance_type
has been specified. This information is output to the screen and to a file. In addition, the output file contains the means and standard deviations of each response function and Gaussian approximations of the 5/95 credible and prediction intervals, in which the lower bound is two standard deviations below the mean and the upper bound is two standard deviations above the mean.
Usage Tips
Only one probability level needs to be specified for each desired interval. Both corresponding end points of the intervals are automatically calculated. For example, if 0.05 is specified, both the 0.05 and 0.95 probability levels are output to the screen and output file.
Additional Discussion
Credible intervals propagate uncertainties in parameter density information to the quantity of interest and quantify how well the model fits the provided data. Prediction intervals propagate both parameter and experimental measurement uncertainties and contain the next experimental or simulated observation with the specified probability.
Below is a Dakota input file specifying the calculation of credible and prediction intervals
method, bayes_calibration queso chain_samples = 1000 seed = 348 dram proposal_covariance diagonal values 1.0e6 1.0e-1 probability_levels 0.05 0.1 0.075 0.1 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' continuous_state 4 initial_state 3 40000 500 1000 descriptors 't' 'R' 'X' 'Y' interface, direct analysis_driver = 'mod_cantilever' responses, calibration_terms = 2 calibration_data_file = 'dakota_cantilever_queso.withsigma.dat' freeform num_experiments = 10 experiment_variance_type = 'scalar' descriptors = 'stress' 'displacement' no_gradients no_hessians
The resulting screen output below shows the table of credible and prediction intervals.
Credibility Intervals for stress Response Level Probability Level ----------------- ----------------- 2.4764049695e+03 5.0000000000e-02 2.8242874802e+03 9.5000000000e-01 2.4990608791e+03 1.0000000000e-01 2.7952985803e+03 9.0000000000e-01 Credibility Intervals for displacement Response Level Probability Level ----------------- ----------------- 2.7409870925e-01 7.5000000000e-02 3.0991296255e-01 9.2500000000e-01 2.7538816802e-01 1.0000000000e-01 3.0889319332e-01 9.0000000000e-01 Prediction Intervals for stress Response Level Probability Level ----------------- ----------------- 2.0964882850e+03 5.0000000000e-02 3.1993026765e+03 9.5000000000e-01 2.1822183238e+03 1.0000000000e-01 3.1099058450e+03 9.0000000000e-01 Prediction Intervals for displacement Response Level Probability Level ----------------- ----------------- 2.3559036055e-01 7.5000000000e-02 3.5097481218e-01 9.2500000000e-01 2.4016170870e-01 1.0000000000e-01 3.4701712866e-01 9.0000000000e-01