Inverse and Direct Prediction and Its Effect on Measurement Uncertainty in Polynomial Comparative Calibration

In measurement science and its applications, calibration is a standard operation to establish a relation between the measurement standards (stimuli), possibly affected by the measurement uncertainties, and the corresponding indications registered by the measurement device (responses), which are typically affected by more prominent measurement uncertainties. The calibration function estimated from the calibration experiment is further used for predicting the value of the unobservable stimulus from the future indication (measured response) received by using the calibrated measurement device, together with its associated measurement uncertainty. In this contribution, we present a brief overview of results known for linear and polynomial comparative calibration and raise a natural question about the effect of using inverse relationship in modeling the calibration function, i.e., by changing the standard roles of the stimulus and the response in the considered calibration function.