You can't fully prove it, but there are usually context clues.
There are and will always be posts that are totally ambiguous. "Sincerity" false negatives are probably common. But if you have enough experience in a certain community, you start to be able to pick up on subtle things. False positives are probably not that high.
It's a bit difficult to explain, but it's basically like distinguishing actually crazy people from people faking it. (And that's often exactly what you're doing on anonymous sites, too.) If you have a large enough set of writing samples of two ostensibly schizophrenic people, where one is faking it and one is real, there are certain patterns that only the most brilliant and dedicated and seasoned of trolls can authentically mimic. Most trolls tend to not be that masterful.
