Specifying hierarchical Binomial model when individuals have varying numbers of trials?

I see what you are doing now. But just to confirm it, you are doing the following:

  1. setting n to be number of trials / individual,
  2. setting observed to be the number of successes / individual,
  3. and removing the brackets, [], around a because the shape and other arguments make sure to not make them universal variables.

But what I did before also does the same thing, despite the syntax having a few key differences?