In the field of Graph Signal Processing (GSP), a common task is to recover a complete signal defined over the nodes of a graph or network given only a partial observation. For example, consider predicting the annual income of each individual in an online social network given that the true value is known for a subset of the individuals only. In this seminar we discuss how tools from GSP can be used to build statistical models describing the likelihood of different underlying distributions for the true graph signal. In particular, we are concerned with the reconstruction of tensor-valued signals that exist on the nodes of a Cartesian product graph. Such models are a natural extension of standard signal reconstruction tasks, and can be used in situations that naturally present multiple independent graph-like axes, such as network time series, fMRI scans and hyperspectral imaging. We cover reconstruction of real-valued, as well as binary and categorical signals, and discuss how filtering operations can be generalised to an arbitrary number of graph-like axes. We also look at case studies of these methods in pollutant monitoring and bond yield prediction.