Inverse Wishart distribution


I have a question with regards to specifying an inverse Wishart distribution as a prior in my Stan model. I already know all the downsides of using this specific prior, but regardless of that, I need to try something out.

It seems that the inverse Wishart distribution in Stan requires two parameters: degrees of freedom and a scale matrix S. I was wondering which values should I supply for these parameters if I want a weakly informative prior? I am also confused as to what the matrix S should look like and how can I build this matrix in Stan? Any help would be appreciated, thanks!

Assuming the correlation of the parameters are unknown, I would use a scaled diagonal matrix S, 0.01 on the diagonals corresponds to a Variance of 100. As degree of freedom either set to 4 or create a Stan parameter and use gamma(2.0, 0.1) as prior.

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