The FARO Focus laser scanner produces 3D point cloud data sets. Most scan projects require the combination of multiple scans from different locations to sufficiently capture their complexity. However, all individual scans have their own local coordinate system. Registration is the process of aligning multiple scans in a common frame. Target based registration uses salient objects that can be identified and matched in multiple scans and uses them as reference points for alignment. The difficulty in registration lies in the inevitable measurement errors that lead to contradictory target information. Hence, all targets cannot be perfectly aligned. As a solution, an error model is used that defines the optimality criterion according to which the most likely alignment is computed. This work develops an advanced error model for target based registration based on Bayesian statistics that approximates the optimal transformation and non-parametric uncertainty measures using statistical inference. The developed approach allows the modeling of target errors and previous knowledge using the probabilistic programming language Stan. Scanned data sets and simulations are used for evaluation. The registration quality and influence of prior knowledge is investigated. This includes uncertainty estimates based on scan point metrics, target accuracy estimates and external references. An alternative robust error model based on an L1 error is investigated that is more robust to outliers.