At least one guy that I know did this for risk scoring in a payment gateway. He had no clue it even had a name, it just seemed the most obvious way to solve the problem.

Loosely speaking, I've seen Bayesian inference described as a way to update your knowledge when you receive new evidence. In that sense, it's been re-invented since the time of the ancient Greeks.

The ancient Greeks -- do you have anything in particular in mind that they did? They certainly knew combinatorics at a level not guessed at until pretty recently (e.g. Schröder–Hipparchus numbers) but I haven't heard of any evidence for probability.

I was only thinking of the generalizations I've read, that Bayesianism is a "way of thinking," not about the math.

OK. Every now and then I hear of some old Greek fragment that was "ahead of its time", and it's gotten to be a hobby to collect them.

I think it's actually interesting to figure out what things the Greeks hadn't figured out in their time -- possibly a much smaller set. They didn't have algebra (e.g., the quadratic formula eluded them), and something must have happened after their time, to bring us modern empirical science.

Still it remains impressive to me what they were able to accomplish without modern tools.