Results
Four tables are generated in an inverse uncertainty quantification study and added to the result output table group for inverse uncertainty quantification:
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A MCMC samples table. It contains the samples of all calibration parameters from their posterior distributions, the samples of the standard deviation of the added discrepancy between the surrogate model and experimental data, the log-likelihood of the posterior and the acceptance rate of the Markov chain. From a converged Markov chain, the log-posterior should be smoothly varying and close to its maximum value. The acceptance rate measures the percentage of random samples accepted by the Markov chain iteration. A small acceptance rate close to 0 indicates that the step size might be too large where the new samples are mostly rejected by the Markov chain; a large acceptance rate close to 1 indicates that the step size might be too small where the new samples does not cover enough space from parameter space defined by the prior distributions.
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A Calibrated confidence interval table. It contains one row per calibrated parameter, with columns for the mean, standard deviation (STD), potential scale reduction factor (Rhat) and number of efficient samples (Neff), minimum, and maximum, followed by confidence intervals for 90%, 95%, and 99% likelihood. The potential scale reduction factor measures the ratio of the variance of samples within a Markov chain to the variance of the samples across chains computed with different starting points. The potential scale reduction factor should decline to 1 when the sample size approaches infinity and the chain converges. The number of efficient samples measures the effectiveness of a Markov chain, it estimates the number of samples as if they are independent random draws from the posterior distribution. The number of efficient samples should be at least 20 for each calibration parameter to be considered a converged Markov chain.
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A Posterior mean around experimental data table. It contains the experimental data, the mean and the standard deviation of the predicted QoIs computed with the calibrated parameters from the Markov chain in the MCMC samples table. The experimental data of the QoIs at the experimental data points should be contained within the bound of the predicted QoIs mean and standard deviation.
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Finally, a Maximum entropy table. It contains the maximum relative standard deviation from the GP surrogate model, one per QoI.
When an adaptive GP surrogate model is used, an Adaptive maximum entropy table is also added to the output table group. It contains the maximum relative standard deviation, one per QoI for all the adaption steps.