Motion based wave inference allows the estimation of the directional sea spectrum from the measured motions of a vessel. Solving the resulting inverse problem is challenging as it is often ill-posed; as a matter of fact, statistical errors of the estimated platform response functions (RAOs) may lead to misleading estimations of the sea states as many noise values are severely amplified in the mathematical process. Hence, in order to obtain reliable estimations of the sea conditions some hypothesis must be included by means of regularization parameters. This work discusses how these errors affect the regularization parameters and the accuracy of the sea state estimations. For this purpose, a statistical quantification of the errors associated to the estimated transfer functions has been included in an expanded Bayesian inference approach. Then, the resulting statistical inference model has been verified by means of a comparison between the outputs of this approach and those obtained without considering the statistical errors in the Bayesian inference. The assessment of the impact on the accuracy of the estimations is based on the results of a dedicated model-scale experimental campaign, which includes more than 150 different test conditions.