  The universality of the stellar initial mass function (IMF) is tested using
Bayesian statistics with a sample of eight young Galactic stellar clusters (IC
348, ONC, NGC 2024, NGC 6611, NGC 2264, $\rho$ Ophiuchi, Chameleon I, and
Taurus). We infer the posterior probability distribution function (pPDF) of the
IMF parameters when the likelihood function is described by a tapered power law
function, a lognormal distribution at low masses coupled to a power law at
higher masses, and a multi-component power law function. The inter-cluster
comparison of the pPDFs of the IMF parameters for each likelihood function
shows that these distributions do not overlap within the $1\sigma$ uncertainty
level. Furthermore, the most probable values of the IMF parameters for most of
the clusters deviate substantially from their values for the Galactic field
stellar IMF. We also quantify the effects of taking into account the
completeness correction as well as the uncertainties on the measured masses.
The inclusion of the former affects the inferred pPDFs of the slope of the IMF
at the low mass end while considering the latter affects the pPDFs of the slope
of the IMF in the intermediate- to high mass regime. As variations are observed
in all of the IMF parameters at once and for each of the considered likelihood
functions, even for completeness corrected samples, we argue that the observed
variations are real and significant, at least for the sample of eight clusters
considered in this work. The results presented here clearly show that the IMF
is not universal.
