We propose a general formulation of the Bayesian method for assigning individuals to a population among a predetermined set of reference populations using molecular marker information. Compared to previously published methods, ours allows us to consider different types of prior information about allele frequencies by using a Dirichlet prior probability distribution. It also makes it possible to assign a set of individuals assumed to belong to the same population with increased accuracy using their pooled genotype data. The efficiency of the method is illustrated by application to a group of closely related coconut populations. An interesting feature of the Bayesian procedure is the way it handles imprecise information. With a poor or even incomplete dataset, assignment is still be possible and gives valid results: poor data quality is reflected in an ambiguous result rather than in a false conclusion.