randomly select quadruples from this overall pool. The first batch uses only four measurements, that is, four stress values each associated with a triplet of control parameter values. The second batch is generated by randomly selecting eight measurements. The number of measurements that form the next measurement is increased, each time, by four. The 15th and last batch counts a total of 60 data points. Through a series of comparisons of PTW model predictions against experimental stress measurements conducted at varying settings of control parameters, we obtain the true values for discrepancy term at discrete settings. These discrete discrepancy values at these settings are then used to train the GPM emulator, which represents the discrepancy bias of the PTW simulations within the entire domain of applicability. Next, the calibrated and bias corrected PTW model is executed to forecast at some randomly selected hold-out experiment settings. The number of hold-out experiments is kept four experiments larger than those used in calibration to ensure that, in this random process, at least eight experiments are true forecasting predictions. A PTW model calibrated with four randomly selected measurements is used to forecast eight randomly selected hold-out experiments, while a PTW model calibrated with eight measurements is used to forecast twelve hold-out experiments, and so-on. Since we are specifically interested in the trends of the forecasting errors as the number of experiments initially selected for the calibration is gradually increased, this procedure is repeated for each one of these 15 batches; for each batch the probability distribution of the forecasting error is determined. The forecasts of hold-out experiments are done with 2000 random draws from the 10,000 accepted random walks of MCMC. For these 2000 draws, the forecasting error is calculated as the difference between each of the stress values predicted by the calibrated and bias corrected PTW model and the measured stress value of that particular hold-out experiment. If the experimental settings are decided solely based upon expert, yet arbitrary judgments, the obvious question to be determined involves the dependency of the forecasting errors to the sequence of selected experiments (i.e. path-dependency). Independent of the sequence in which the experiments are selected, we expect to see a consistent and monotonic reduction in the forecasting errors. However, it is plausible that the rate of this reduction may exhibit dependency to which experiments are selected from the pool. To reiterate, a lucky experimentalist may conduct the experiments in the optimum sequence and observe a very rapid reduction in forecasting error. An unlucky experimentalist may conduct the experiments in the least optimum sequence and observe a slow reduction in the forecasting error. Our approach at addressing the ‘luck factor’ is to treat the procedure as a random process and repeat both the 442
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