The problem of determining the unknown number of components in mixtures is of considerable interest to researchers in many areas. This paper generalizes a Bayesian testing method based on the Kullback-Leibler distance proposed by Mengersen and Robert (1996). An alternative, weighted Kullback-Leibler distance is proposed as testing criterion. Explicit formulas for this distance are given for a number of mixture distributions. A step-wise testing procedure is proposed to select the minimum number of components adequate for the data. A fast, collapsing approach is proposed for reducing the number of components which does not require full refitting at each step. The method, using both distances, is compared to the Bayes factor approach. The method is easy to implement and is illustrated using \texttt{BUGS} (a general purpose software for Bayesian analysis).
normal mixture
gamma mixture