Q: Does this have anything to do with the degrees of freedom of the Wishart?

A: I set it equal to 200. The dimension of the Wishart is going to be 192, so I just wanted to set something that was just over that so it's defined - you know, I went back and looked at what's the implications of the prior in terms of prior density and prior density matched up with something that looked like it had some weight over smaller values and some weight over higher values. Because if you set the degrees of freedom of the Wishart too high then it just collapses too quickly. I really want my prior to reflect that I'm not exactly sure of where - how to spread out these things.

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