Propagating input uncertainties into parameter uncertainties and model prediction uncertainties—A review

Abstract

A review of uncertainty quantification techniques is provided for a variety of situations involving uncertainties in model inputs (independent variables). The situations of interest are divided into three categories: (i) when model prediction uncertainties are quantified based on uncertainties in uncertain inputs, (ii) when parameter estimate uncertainties are calculated by propagation of uncertainties from measured inputs and outputs, and (iii) when model prediction uncertainties are quantified based on corresponding uncertainties in measured inputs and uncertain parameter estimates. For all three situations, linearization‐based and Monte Carlo‐based techniques are reviewed and details for their corresponding algorithms are presented. Recommendations are provided on which uncertainty quantification techniques are best for different types of chemical engineering models based on the amount of input uncertainty and nonlinearity over the range of plausible input and parameter values.

Parameter estimation and prediction uncertainties for multi‐response kinetic models with uncertain inputs

“…1,[17][18][19] However, the literature on quantifying parameter uncertainty when inputs are not perfectly known is quite limited. 7,[20][21][22] In a recent study, we extended a parametric bootstrap technique for models with perfectly-known independent variables 23 so that it can be used for parameter uncertainty quantification in EVM. 10 Synthetic data sets are generated multiple times, using typical input and output uncertainties, and parameters are estimated for each synthetic data set.…”

“…Recently, we reviewed methods for quantifying prediction uncertainties when inputs are uncertain. 20 We learned that past researchers T A B L E 1 Procedure for error-in-variables model (EVM) parameter estimation using pseudo-replicate data. 10 1.…”

“…The literature contains many studies concerned with uncertainty in model parameters when the inputs are perfectly known 1,17–19 . However, the literature on quantifying parameter uncertainty when inputs are not perfectly known is quite limited 7,20–22 . In a recent study, we extended a parametric bootstrap technique for models with perfectly‐known independent variables 23 so that it can be used for parameter uncertainty quantification in EVM 10 .…”

“…Recently, we reviewed methods for quantifying prediction uncertainties when inputs are uncertain 20 . We learned that past researchers assumed that they knew the uncertainty distributions of their parameter estimates a priori 24–31 .…”

“…The results from Table 2 provide 95% confidence intervals for noise‐free values of the dependent variables at the condition of interest. If the modeler is interested instead in a 95% confidence interval on noisy measured values that might be obtained from a future experiment, then, additive measurement errors in the dependent variables must also be considered 20 . Both types of prediction uncertainties are computed in the case study in Section 4.…”