I need to have a sigma that is both symmetric and positive definite that I can use to pass in the multi_student_t_lpdf function. Also, I think it needs to have a valid prior.
I tried many ways but I was not able to get all the requirement satisfied.
Can someone please help me by giving me some simple sample code?
Thank you very very much.
Take a look at the multivariate normal examples in the manual, they’re really thorough and should work with the team distribution as well.
You can sample covariance matrices from an inverse wishart distribution.
You need to define hyperpriors for v_0 and W_0.
See https://github.com/stan-dev/stan/wiki/Prior-Choice-Recommendations for some advice. And as sakrejda said, the manual.
sigma ~ inv_wishart(v_0,W_0)
The manual chapter on regression has examples as @sakrejda points out. But they recommend using a Cholesky factor for a correlation matrix with an LKJ prior then scaling with a scale vector with its own independent priors.