  Being able to rigorously quantify the uncertainties in reaction models is
crucial to moving this field forward. Even though Bayesian methods are becoming
increasingly popular in nuclear theory, they are yet to be implemented and
applied in reaction theory problems. The purpose of this work is to
investigate, using Bayesian methods, the uncertainties in the optical
potentials generated from fits to elastic scattering data and the subsequent
uncertainties in the transfer predictions. We also study the differences in two
reaction models where the parameters are constrained in a similar manner, as
well as the impact of reducing the experimental error bars on the data used to
constrain the parameters. We use Bayes' Theorem combined with a Markov Chain
Monte Carlo to determine posterior distributions for the parameters of the
optical model, constrained by neutron-, proton-, and/or deuteron-target elastic
scattering. These potentials are then used to predict transfer cross sections
within the adiabatic wave approximation or the distorted-wave Born
approximation. We study a number of reactions involving deuteron projectiles
with energies in the range of $10-25$ MeV/u on targets with mass $A=48-208$.
The case of $^{48}$Ca(d,p)$^{49}$Ca transfer to the ground state is described
in detail. A comparative study of the effect of the size of experimental errors
is also performed. Five transfer reactions are studied, and their results
compiled in order to systematically identify trends. Uncertainties in transfer
cross sections can vary significantly (25-100\%) depending on the reaction.
While these uncertainties are reduced when smaller experimental error bars are
used to constrain the potentials, this reduction is not trivially related to
the error reduction. We also find smaller uncertainties when using the
adiabatic formulation than when using distorted-wave Born approximation.
