This article presents Bayesian inference for exponential mixtures, includin
g the choice of a noninformative prior based on a location-scale reparamete
rization of the mixture. Adapted control sheets are proposed for studying t
he convergence of the associated Gibbs sampler. They exhibit a strong lock
of stability in the allocations of the observations to the different compon
ents of the mixture, The setup is extended to the case when the number of c
omponents in the mixture is unknown and a reversible jump MCMC technique is
implemented. The results are illustrated on simulations and a real dataset
.