Non-centered parameterization of the multivariate student-t distribution


#1

In the multivariate normal case, we have

mu + L * z

where mu is the mean vector, L is the cholesky factor of the covariance matrix and z are independent standard normal variables. My question is how to correctly incorporate the degrees of freedom parameter nu into the above formula to create multivariate-t random variables? I remember having seens this somewhere already, but I can’t find it right now…


#2

https://groups.google.com/d/msg/stan-users/nk03n8hX4Us/-pTN5IGjCQAJ

One may optimize it using the inv_chi_square and turn the division in a multiplication.


#3

Thanks, that’s what I was looking for! :-)


#4

Hello @paul.buerkner @andre.pfeuffer,

The parameterization: mu+L*z you mentioned for the multivariate normal is valid when the covariance matrix is known (defined in the data block).

Is there any difference when the covariance matrix is unknown (defined in the parameters block)?

Thanks a lot.


#5

It’s still valid.


#6

I think it’s a bit more complicated in my case. I’ll create a new topic.