Quadrics are a compact mathematical formulation for a range of primitive surfaces. A problem arises when there are not enough data points to compute the model but knowledge of the shape is available. This paper presents a method for fitting a quadric with a Bayesian prior. We use a matrix normal prior in order to favour ellipsoids when fitting to ambiguous data. The results show the algorithm copes well when there are few points in the point cloud, competing with contemporary techniques in the area.