Abstract: We propose a Bayesian approximation to a deep learning architecture for 3D hand pose estimation. Through this framework, we explore and analyse the two types of uncertainties that are influenced either by data or by the learning capability. Furthermore, we draw comparisons against the standard estimator over three popular benchmarks. The first contribution lies in outperforming the baseline while in the second part we address the active learning application. We also show that with a newly proposed acquisition function, our Bayesian 3D hand pose estimator obtains lowest errors with the least amount of data. The underlying code is publicly available at https://github.com/razvancaramalau/al_bhpe.