Notation for a sum over a set of variables I have a vector of variables $y=(y_1, \ldots, y_n)$ whose elements are either zero or one. I would like to express the sum over all variables belonging to a subset $S$. For example, if $n=4$ and $S=\{2, 3\}$, I would like to express
$$
\sum_{y_2\in\{0,1\}}\sum_{y_3\in\{0,1\}} f[y] = f[(y_1, 0, 0, y_3)] + f[(y_1, 1, 0, y_3)] + f[(y_1, 0, 1, y_3)]+ f[(y_1, 1, 1, y_3)]
$$
more concisely. Does standard notation exist? 
For context, I am concerned with marginalisation of a subset of a binary likelihood.

I'm not aware of any conventional method of writing this. That said, if the application is such that it is important that this be able to be written in one expression, I'd suggest doing it in two steps:
First, let $S' \subset \{0,1\}\times S$.  Define $\hat{y}_{S'}$ as the vector whose $i$th component is $y_i$ if $i \not \in S$, and $\pi_i(S')$ if $i\in S$ (where $\pi_i$ denotes the projection onto the $i$-coordinate of $S'$).  In other words, just the resulting vector one gets by replacing the components of $y$ with indices in $S$ with the values in $S'$.  
Then what you're looking for can be written as:
$$\sum_{T \subseteq \{0,1\} \times S} \hat{y}_{T}.$$
