Imagine I have two models, for simplicity say an AR(1) model and a MA(1) model.
I want to construct and sample from a composition of their likelihoods, i.e. a geometric average, where the weight themselves is a parameter with a prior. In addition, I will require the variance of the noise to be common across both models.
I’m not sure how much detail to include in the post, but this comes from the literature on so-called “Composite Likelihood methods”.