We were discussing “joint models” here, i.e. estimating a parameter from two different sets of data, accounting for commonalities in the data generating processes.

In a simple example, we could estimate beta from datasets y and y’ using something like:

target += normal_lpdf(y | alpha + beta * x, sigma);

target += normal_lpdf(y_prime | alpha_prime + beta * x_prime, sigma_prime);

It should work, but I wonder how to get the log_lik for further use in loo in this case? Simply using a vector of length sum of the lengths of y and y_prime?