InSAR and GPS observations of Earth's surface displacements are used to infer earthquake source parameters. Bayesian estimation of the source parameters produces the probability densities of the plausible parameters that are consistent with the observations. This facilitates analysis of the model parameters uncertainties and trade-offs regardless of the complexities (e.g., non-linearity, non-uniqueness, under- or over- parametrization, etc.) of the problem. In this thesis, I show various approaches, e.g., use of a priori information and innovative parameterization schemes, to study the effect of fault geometry in the fault slip estimation. During the Bayesian inference of fault parameters for the 2005 Mw6.6 Fukuoka (Japan) earthquake from InSAR and GPS data, the offshore location of the earthquake makes the fault parameter estimation challenging with geodetic data coverage mostly to the southeast of the earthquake. We use a priori constraints on the moment magnitude and fault location with respect to the aftershock distribution to alleviate the bias in fault slip estimation. Propagating the uncertainties of the improved source parameters in the calculation of Coulomb failure stress changes shows that the mainshock strongly increased failure stresses on a nearby fault below Fukuoka city. Biased discrepancies between the observations and the forward model predictions during fault source estimation of large earthquakes occur while using pre-assumed simple planar fault geometries. For this, we parametrize complex non-planar fault geometries using a few polynomial parameters. The fault geometry parametrization allows the fault surface to have any desired curvature in both the down-dip and the along-strike directions. Using Bayesian inference to estimate the fault geometrical parameters simultaneously with the spatially-variable slip, we demonstrate the precise estimation of the location and value of the slip and their uncertainties. This robust approach is exemplied using a synthetic test considering a checkerboard-like slip pattern on a listric non-planar fault. This fault parametrization is then used to infer the non-planar fault geometry simultaneously with the spatially-variable slip for the 2011 Mw 9.1 megathrust Tohoku-Oki (Japan) earthquake. A priori information like the trench and seismicity locations are utilized during the Bayesian estimation. Fault geometry estimated for the earthquake shows variation in fault dip in both along-strike and down-dip directions, while the slip distribution estimated is comparable to those of the previously reported studies. The fault geometry and its uncertainties are then compared with Hayes' slab1.0 model.