I am trying to understand ABC and I there is something fundamental that I'm not quite understanding.
So, the goal can be thought of as sampling from some posterior distribution. But in some cases, the calculation/evaluation of that posterior is difficult of impossible, likely due to an intractable likelihood function. ABC circumnavigates the evaluation of the likelihood function. We're left with an approximate distribution, but what does one do with this? I mean, we have the list of accepted thetas and can make a curve/histogram of it. But if you don't have the pdf for that distribution, in a formula, what can you do with it?
I know I'm just misunderstanding something. Thanks in advance.