Determining confidence intervals for parameters derived from analysis of equilibrium analytical ultracentrifugation data

In the above discussion, we have introduced the profiling approach of Bates and Watts. It is an easy to implement, empirical approach to the determination of confidence intervals for parameters in nonlinear models. We have applied the approach to the analysis of equilibrium sedimentation data and have demonstrated that, although models for analyzing such data are formally nonlinear they are functionally linear. As such, linear approximation confidence intervals for the parameters are adequate for these models and data sets. Further, we have been able to examine the effect of implementing a multiple independent variable approach (in this case, using multiple rotor speeds) on the precision of the analysis. We found that the standard errors of the parameters were reduced and that this is accounted for by either the increase in the number of data points or the decreases in parameter correlation. In this case, profiling helped to visualize the effect on the sum of squares surface of reducing parameter correlation, making the effect of the small decreases in the correlation of some parameters more evident. Using profiling, it should be easy to explore other methods for the improvement of the analysis of ultracentrifugation data and to be able to quantitate the improvement. With the above discussion as an example, it is likely that the profiling approach should be quite useful and broadly applicable in the analysis of data in terms of nonlinear models.