A lot of computer vision applications have to deal with occlusions. In such settings only a subset of the features of interest can be observed, i.e.~only incomplete or partial measurements are available. In this article we show how a learned statistical model can be used to make a prediction of the unknown (occluded) features. The probabilistic nature of the framework also allows to compute the remaining uncertainty given an incomplete observation. The resulting posterior probability distribution can then be used for inference. Additional unknowns such as alignment or scale are easily incorporated into the framework. Instead of computing the alignment in a preprocessing step, it is left as an additional uncertainty, similar to the uncertainty introduced by the missing values of the measurement. It is shown how the technique can be applied to the analysis of human locomotion, when body parts are occluded. Experiments show how the unobserved body locations are predicted and how it can be inferred whether the measurements come from a running or walking sequence.