Mitral valve orifice area is a key functional metric that depends on complex geometric features, motivating a systematic assessment of the relative influence of these parameters. In this study, the mitral valve geometry is parameterized using twelve geometric variables, and a global sensitivity analysis based on Sobol indices is performed to quantify their relative importance. Because global sensitivity analysis requires many simulations, a Gaussian Process regressor is developed to efficiently predict the orifice area from the geometric inputs. Structural simulations of the mitral valve are carried out in Abaqus, focusing exclusively on the valve mechanics. The predicted distribution of orifice areas obtained from the Gaussian Process shows strong agreement with the ground-truth simulation results, and similar agreement is observed when only the most influential geometric parameters are varied. The analysis identifies a subset of geometric parameters that dominantly govern the mitral valve orifice area and can be reliably extracted from medical imaging modalities such as echocardiography. These findings establish a direct link between echocardiographic measurements and physics-based simulations and provide a framework for patient-specific assessment of mitral valve mechanics, with potential applications in guiding interventional strategies such as MitraClip placement.