Multicomponent driven equilibrium single pulse observation of T1 and T2 (mcDESPOT) has been proposed as a rapid approach for multicomponent relaxometry. However, even for the simplest two-pool signal model consisting of myelin-associated and non-myelin-associated water, the dimensionality of the parameter space for obtaining MWF estimates remains high. This renders parameter estimation difficult, especially at low-to-moderate signal-to-noise ratios (SNRs), due to the presence of local minima and the flatness of the fit residual energy surface used for parameter determination using conventional nonlinear least squares (NLLS)-based algorithms. We have introduced Bayesian approaches for analysis of the mcDESPOT signal model to stabilize the analysis. Given the high-dimensional nature of the mcDESPOT signal model, and, therefore the high-dimensional marginalizations over nuisance parameters needed to derive the posterior probability distribution of the MWF, the Bayesian analyses introduced here use different approaches to reduce the dimensionality of the parameter space. The first approach uses normalization by average signal amplitude, and assumes that noise can be accurately estimated from signal-free regions of the image. The second approach likewise uses average amplitude normalization, but incorporates a full treatment of noise as an unknown variable through marginalization. The third approach does not use amplitude normalization and incorporates marginalization over both noise and signal amplitude. Through extensive Monte Carlo numerical simulations and analysis, we demonstrated markedly improved accuracy and precision in the estimation of MWF using these Bayesian methods as compared to the stochastic region contraction (SRC) implementation of NLLS. These methods are general and have been applied to mapping proteoglycan content in the human knee in vivo.