Abstract-We introduce Bayesian Eigenobjects (BEOs), a novel object representation that is the first technique able to perform joint classification, pose estimation, and 3D geometric completion on previously unencountered and partially observed query objects. BEOs employ Variational Bayesian Principal Component Analysis (VBPCA) directly on 3D object representations to create generative and compact probabilistic models for classes of 3D objects. Using only depth information, we significantly outperform the current state-of-the-art method for joint classification and 3D completion in both accuracy and query time. Additionally, we show that BEOs are well suited for the extremely challenging task of joint classification, completion, and pose estimation on a large dataset of household objects.