Replace {response_name}_mean with {response_name}_{parent_name}.

[tomicapretto]

Because of historical reasons, Bambi is always calling the parent of all families "mean". Given the flexibility we have now, e.g. distributional models for arbitrary likelihoods, I think it does not make sense to keep using "mean", and actually it can lead to confusion.

I think we can simply use the name of the parameter. For Normal likelihoods, it will be mu, for Bernoulli and Binomial it will be p, etc. etc.

[tomicapretto]

I'm also starting to think it's a good chance to change the dimension name for the observation index.

Right now we use {response_name}_obs and it has two drawbacks:

1. We have to build the name every time we want to use it
2. The name can be something not easy to read such as c(category 1, category 2, cat 3)_obs or p(y, n)_obs or censored(x, value)_obs.

I think we can always use the same name. Something like obs_idx, _obs_idx, __idx, obs_index, etc.

[tomicapretto]

There's more. What if we stop pre-pending the LHS of the formula to the name of the parameter? Right now it leads to something like p(y, n)_mean. If we use the name of the parameter it will be p(y, n)_p. What if we drop whatever we have on the RHS and start using parameter names? Simply mu, sigma, p, alpha, etc. etc.