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Star clusters are studied widely both as benchmarks for stellar evolutionmodels and in their own right. Cluster age and mass distributions withingalaxies are probes of star formation histories, and of cluster formation anddisruption processes. The vast majority of clusters in the Universe is small,and it is well known that the integrated fluxes and colors have broadprobability distributions, due to small numbers of bright stars. This papergoes beyond the description of predicted probability distributions, andpresents results of the analysis of cluster energy distributions in anexplicitly stochastic context. The method developed is Bayesian. It providesposterior probability distributions in the age-mass-extinction space, usingmulti-wavelength photometric observations and a large collection of Monte-Carlosimulations of clusters of finite stellar masses. Both UBVI and UBVIK datasetsare considered, and the study conducted in this paper is restricted to thesolar metallicity. We first reassess and explain errors arising from the use ofstandard analysis methods, which are based on continuous population synthesismodels: systematic errors on ages and random errors on masses are large, whilesystematic errors on masses tend to be smaller. The age-mass distributionsobtained after analysis of a synthetic sample are very similar to those foundfor real galaxies in the literature. The Bayesian approach on the other hand,is very successful in recovering the input ages and masses. Taking stochasticeffects into account is important, more important for instance than the choiceof adding or removing near-IR data in many cases. We found no immediatelyobvious reason to reject priors inspired by previous (standard) analyses ofcluster populations in galaxies, i.e. cluster distributions that scale withmass as M^-2 and are uniform on a logarithmic age scale.

Accounting for Stochastic Fluctuations when Analysing Integrated Light of Star Clusters. I: First Systematics