How to define two dimensional likelihood in pyro?

I’m trying to implement likelihood for data that is two dimensional. Each dimension follows a Cauchy distribution (with parameters loc as unknown) and is independent. How can I use pyro.sample to define a joint distribution? Also what if one followed a Cauchy and other Normal. How can I get a custom likelihood?

check out the tutorials if you haven’t, most of the examples use some sort of custom likelihood. in your case, you can use pyro.plate and a pyro.sample with a Cauchy of batch_shape 2. You can similarly use two sample statements to get the Cauchy-Normal likelihood.