With the detection of Shapiro delay and precise mass measurement of the millisecond pulsar (MSP) J0740+6620, strong constraints can be put on neutron stars’ equation of state (Cromartie et al. 2020). The measurement of MSPs' timing parameters are typically estimated by a generalized-least-squares method that maximizes the likelihood of the timing model. Any remaining timing residuals are then assumed to be characterized by linear corrections to the original timing solutions. In this study, we use the Bayesian methods in the pulsar timing analysis code enterprise to examine the full non-linear parameterization of pulsar timing models in tandem with noise and dispersion measure (DM) modeling. This may better model timing parameters not well approximated in the linear regime in addition to allowing robust comparison between DM models. We apply these techniques to J0740+6620 and examine changes to the noise and timing parameter posteriors and their subsequent effects on the MSP’s mass.