I am reading this paper on Generalised Wishart Process (GWP). It is about modelling covariance matrix of D - dimensional gaussian processes (GP) as GWP. I fail to understand interpretation of "degrees of freedom" $\nu$ for a GP.
There are quiet a few mention of degree of freedom in the paper. In section 4, they define GWP as sum of outer product of $\nu$ D-dimensional gaussian processes. Based on this definition $\nu$ seemed to be no. of observations for the gaussian processes. But then in the same section, they also mention about real-valued degrees of freedom, which rules out previous explanation that $\nu$ = no. of observations/data points.
Moving on, Section 5 Bayesian Inference says, degrees of freedom control how concentrated the prior is around the expected value $\Sigma(t)$ (This generic statement does make sense). Also, in section 5.1, they sample from posterior distribution over the gaussian processes with different degrees of freedom (which I fail to understand again). In section 5, they set $\nu$ to its minimum value D + 1 (so that the wishart distribution does not become degenerate).
I'd appreciate if you can provide me with answers or any other resources which can help me understand this.