What does a subscript on a probability represent? I've been trying to look this up, but I must not be searching correctly because I think it's a pretty basic question.
What I want to know is what do subscripts mean when talking about the probability (or expectation) of something? For example $P_{\theta}(x|y^{(i)})$. What does the $\theta$ subscript mean here?
I saw someone ask the same question here, but I don't understand the answer.

Abhinav Gupta gave a nice example (+1). The general answer is that you can use the subscript to carry descriptive information about the distribution. For example, the definition of independence can be written as
$$
P_{X,Y}(x,y) = P_X(x) \, P_Y(y)
$$
Or you could define mixture distribution as
$$
P_X(x) =\sum_k \pi_k P_k(x)
$$
where $\sum_k \pi_k = 1$ are the mixing weights and $P_k$ are the individual components, the distributions that are “mixed”.
In all the cases, the subscript carries information that makes more precise what does the distribution represent. As with mathematical notation in general, there is no single way how the subscripts are used, so you always need to verify it from the context.
