A new procedure for estimating the parameters of a scientific model is described, and the method is applied and illustrated for the class of experiments with multinominal data structure. The procedure is referred to as the method of population-parameter mapping, and it has a number of novel and advantageous features. The method is a variation of a standard Bayesian analysis. However, instead of directly developing a posterior distribution for the model parameters, this procedure first characterizes the population proportions for the multinomial cells. Random samples are then drawn from the posterior distribution for these proportions, and these samples are mapped to the parameters of the scientific model. This method leads naturally to a definition of model identifiability, and leads to a direct probability estimate of the coherence of the scientific model. Moreover, the new procedure can circumvent the problem of dealing with computationally difficult integrals that frequently occur with Bayesian analyses of complex multinomial models. The method is illustrated by means of several memory measurement models as well as a signal-detection model. Copyright 1998 Academic Press.