Using the $^{70}$Zn(d,$^3$He)$^{69}$Cu reaction as a case-study, we developed a new Markov Chain Monte Carlo method to analyze Distorted Wave Born Approximation models of particle transfer measurements. Not only are we able to assign uncertainties to our extracted physical parameters (spectroscopic factors), but this framework provides us with a method to assign probabilities to angular momentum transfer ambiguities.