| Abstract: | Models fitted to data are used extensively in chemical engineering for a variety of purposes, including simulation, design and control. In any of these contexts it is important to assess the uncertainties in the estimated parameters and in any functions of these parameters, including predictions from the fitted model. Profiling is a likelihood ratio approach to estimating uncertainties in parameters and functions of parameters. A comparison is made between the optimization and reparameterization approaches to determining likelihood intervals for functions of parameters. The merits and limitations of generalized profiling are discussed in relation to the linearization approach commonly used in engineering. The benefits of generalized profiling are illustrated with two examples. A geometric interpretation of profiling is used to elucidate its value, and cases are identified for which the numerical algorithm fails. An alternative approach is suggested for these cases. |
