Maximum likelihood decay curve fits by the simplex method

Abstract

Abstract A multicomponent decay curve analysis technique has been developed and incorporated into the decay curve fitting computer code, MLDS (maximum likelihood decay by the simplex method). The fitting criteria are based on the maximum likelihood technique for decay curves made up of time binned events. The probabilities used in the likelihood functions are based on the Poisson distribution, so decay curves constructed from a small number of events are treated correctly. A simple utility is included which allows the use of discrete event times, rather than time-binned data, to make maximum use of the decay information. The search for the maximum in the multidimensional likelihood surface for multi-component fits is performed by the simplex method, which makes the success of the iterative fits extremely insensitive to the initial values of the fit parameters and eliminates the problems of divergence. The simplex method also avoids the problem of programming the partial derivatives of the decay curves with respect to all the variable parameters, which makes the implementation of new types of decay curves straightforward. Any of the decay curve parameters can be fixed or allowed to vary. Asymmetric error limits for each of the free parameters, which do not consider the covariance of the other free parameters, are determined. A procedure is presented for determining the error limits which contain the associated covariances. The curve fitting procedure in MLDS can easily be adapted for fits to other curves with any functional form.