Formation constants of molecular complexes from spectrophotometric data. Experimental design for concurrent models discrimination and optimal determination of the parameters

Abstract

A typical experimental procedure as is now established collects all the data together at the beginning of the study, before the true model is known. The resulting design (i.e. all the available experimental points) may not be very effective for discriminating between the tentative models initially assumed, and/or not very appropriate for the optimal determination of the parameters of the model finally chosen. Furthermore, in a non-linear situation, as in our case, the experiment cannot be optimally designed a priori, even if the model is known. An alternative experimental procedure is proposed, in which the observations are added sequentially, chosen on the basis of the task currently requested. The first and central part of the experiment is mainly devoted to the discrimination among the initial competing models. In the final phase, when hopefully only the correct model remains, the observations are added (still sequentially) to maximize the determinant of the information matrix |X′X|, until the parameter variances are sufficiently low to stop the experiment.