I am quite confused with the distinction between a latent variable and model parameters.
So say I have two observed variables $x$ and $y$ and they have some unknown relationship between them i.e. $y = f(x)$. Now based on that I have a generative model with $ y = f(x) + e$ where I model $e$ as zero mean independent and identically distributed noise with some variance $\sigma$.
Am I correct in saying that:
1: The relationship $f$ that we try to estimate is the latent variable in this case.
2: $\sigma$ is a model parameter. Now, our estimate of $\sigma$ will also have some uncertainty associated with it. With these model parameters, are we saying that it has a fixed but unknown value that we try and estimate, but due to limited data size our estimates have uncertainty. However, underlying the model is the assumption that the value of a $\sigma$ takes a fixed value or is $\sigma$ also a random variable type entity?