A natural latent is, by definition, a latent which satisfies two properties. The first is that the observables are IID conditional on the latent, i.e. the common construction you’re talking about. That property by itself doesn’t buy us much of interest, for our purposes, but in combination with the other property required for a natural latent, it buys quite a lot.
A natural latent is, by definition, a latent which satisfies two properties. The first is that the observables are IID conditional on the latent, i.e. the common construction you’re talking about. That property by itself doesn’t buy us much of interest, for our purposes, but in combination with the other property required for a natural latent, it buys quite a lot.
Wait, I thought the first property was just independence, not also identically distributed.
In principle I could have e.g. two biased coins with their biases different but deterministically dependent.
Oh, you’re right. Man, I was really not paying attention before bed last night! Apologies, you deserve somewhat less tired-brain responses than that.