Hi, @stemangiola! You don’t need a prior with covariance. For example, Andrew Gelman and I didn’t use multivariate priors in our Covid sensitivity and specificity paper because we didn’t have the kind of data required to fit it. But I’d recommend doing it if your data supports it, especially if you don’t have much data and there are strong correlations.
We explain how to code the multivariate priors efficiently following Gelman and Hill’s Red-State/Blue-State example in their original regression book.
Luckily, it doesn’t change the stratification logic at all—MRP still works exactly the same way.