Say I have a probability distribution $\theta$. I'm expressing $\theta$ as $\hat\theta(\phi_1,\dots,\phi_k)$, where the $(\phi_i)$ are mutually independent, and $\hat\theta$ is an injective & deterministic function.
This might look like needless complexity, but doing this allows me to model my problem in a slightly nicer way: I'm essentially decomposing my (potentially very complex) distribution into independent parts. My question is: is there a standard word for doing this kind of operation? I'm using "normalization" for now, but I suppose this kind of trick has been already done before, and I'd like to reuse terminology if possible.