Assessing the precision of model predictions and other functions of model parameters

Models fitted to data are used extensively in chemical engineering for a va riety of purposes, including simulation, design and control. In any of thes e contexts it is important to assess the uncertainties in the estimated par ameters and in any functions of these parameters, including predictions fro m the fitted model. Profiling is a likelihood ratio approach to estimating uncertainties in parameters and functions of parameters. A comparison is ma de between the optimization and reparameterization approaches to determinin g likelihood intervals for functions of parameters. The merits and limitati ons of generalized profiling are discussed in relation to the linearization approach commonly used in engineering. The benefits of generalized profili ng are illustrated with two examples. A geometric interpretation of profili ng is used to elucidate its value, and cases are identified for which the n umerical algorithm fails. An alternative approach is suggested for these ca ses.