David Valls-Gabaud CFHT Different cosmological scenarios predict widely different integrated rates of star formation in galaxies. At sub-galactic scales, star formation may preferentially produce clusters of stars, in bursts of intense activity superimposed on a more quiescent mode. If this is indeed the case, it should be reflected in the colour-magnitude diagrams of volume-limited samples of stars. Here we present a new maximum likelihood technique, based on standard variational calculus associated with Bayesian statistics, to infer --in a non-parametric way-- the past history of the star formation rate in a variety of such volumes. We use WFPC2 observations of five nearby dwarf satellites and a sub-sample of the Hipparcos catalogue to reconstruct in unprecedented detail the variation of the star formation history in these environments. Extensions of this method will also be discussed, and in particular on how to lift the age- metallicity degeneracy in single stellar populations.