  We used broad-band imaging data for 10 cool-core brightest cluster galaxies
(BCGs) and conducted a Bayesian analysis using stellar population synthesis to
determine the likely properties of the constituent stellar populations.
Determination of ongoing star formation rates (SFRs), in particular, has a
direct impact on our understanding of the cooling of the intracluster medium
(ICM), star formation and AGN-regulated feedback. Our model consists of an old
stellar population and a series of young stellar components. We calculated
marginalized posterior probability distributions for various model parameters
and obtained 68% plausible intervals from them. The 68% plausible interval on
the SFRs is broad, owing to a wide range of models that are capable of fitting
the data, which also explains the wide dispersion in the star formation rates
available in the literature. The ranges of possible SFRs are robust and
highlight the strength in such a Bayesian analysis. The SFRs are correlated
with the X-ray mass deposition rates (the former are factors of 4 to 50 lower
than the latter), implying a picture where the cooling of the ICM is a
contributing factor to star formation in cool-core BCGs. We find that 9 out of
10 BCGs have been experiencing starbursts since 6 Gyr ago. While four out of 9
BCGs seem to require continuous SFRs, 5 out of 9 seem to require periodic star
formation on intervals ranging from 20 Myr to 200 Myr. This time scale is
similar to the cooling-time of the ICM in the central (< 5 kpc) regions.
