  We present a probabilistic formulation of the classical problem of
synthesizing spectral properties of a galaxy using a base of star clusters. The
problem consists of estimating the population vector x, composed by the
contributions of n_star base elements to the integrated spectrum of a galaxy,
and the extinction A_V, given a set of absorption line equivalent widths and
continuum colors. The formalism is applied to the n_star = 12 base defined by
Schmidt etal and subsequently used in several studies. The 13-D parameter space
is explored with a Markov chain Monte Carlo sampling scheme based on the
Metropolis algorithm, which produces a smooth and efficient mapping of the
P(x,A_V) probability distribution.
  This version of Empirical Population Synthesis is used to investigate the
ability to recover the detailed history of star-formation and chemical
evolution using this spectral base. This is studied as a function of (1) the
magnitude of the measurement errors and (2) the set of observables used in the
synthesis. Only for extremely high S/N all 12 base proportions can be
accurately recovered, though the observables are very precisely reproduced for
any S/N. Furthermore, the individual mean x components are biased in the sense
that components which carry a large fraction of the light tend to share their
contribution preferably among components of same age. This compensation effect
is linked to noise-induced linear dependences in the base, which very
effectively redistribute the likelihood in x-space. The age distribution,
however, can be satisfactorily recovered for realistic data quality. (abridged)
