Over two decades of astrometric and radial velocity data of short period stars at the Galactic center has the potential to provide unprecedented tests of General Relativity and insight into the astrophysics of the super-massive black hole. Fundamental to this is understanding the underlying statistical issues of fitting stellar orbits. Unintended prior effects can obscure actual physical effects from General Relativity and underlying extended mass distribution. At the heart of this is dealing with large parameter spaces inherent to multi-star fitting and ensuring acceptable coverage properties of the resulting confidence intervals in the Bayesian framework. This proceeding will detail some of the UCLA group's analysis and work in addressing these statistical issues.