Hello stan users :)

I’d like to fit a mixture of Poisson and Multivariate log-normal, such as

Because the multivariate log-normal is not implemented in stan, I thought about writing my model as

Is this really similar to the former? I think that I might miss a subtility due to the multivariate nature of my model.

However, if I understand the manual correctly, jacobian adjustment would not be necessary if I write the model like this, because I sample the \lambda_{ij} parameter before transforming it.

What do you think would be the right way to implement the Poisson-multivariate log-normal model??

Thank you very much, and have a good day :)

Lucas