Where is the scale of the residuals and is their correlation matrix. We like this parameterization (rather than specifying the covariance matrix of the residuals directly) as it’s easier to give informed priors to the scale and correlation of the errors. If we want to use a multivariate Student’s t distribution, we just specify
where is the degrees of freedom parameter to be estimated; small values of this indicate fat tails.
for data of order-of-magnitude around 1. Then we give a prior to the correlation matrix, normally an LKJ prior with degrees of freedom inversely proportional to the degree of endogeneity we think are in the data. If we think there’s a fair bit of endogeneity, then a prior degrees of freedom around 2 might be reasonable.