Non-linear least-squares and chemical kinetics. An improved method to analyse monomer-excimer decay data

The least squares fitting of experimental results with a non-linear model can result in a serious loss of accuracy in the model parameters estimation if the statistical nature of the method is not correctly considered. This occurs when the experimental data is fitted to a set of functional parameters that depend in the model parameters to be estimated in the end. A realistic example can be found in the two state model of monomer-excimer kinetics. The decay curves of the monomer and excimer are a sum and a difference of two exponentials, respectively. It is usual to fit the experimental decays in order to obtain the pre-exponential factors and decay constants, thus using a reparametrization that is non-linear with respect to the model parameters. This procedure is thoroughly discussed and a new method to analyse the decay curves that circumvents the problem of reparametrization is presented. The proposed method yields improved results with less than 7% bias in the recovered rate constants. Monte Carlo simulations have been performed in order to obtain confidence intervals for the fitting and model parameters.