Given several random variables distributed according to different beta distributions, how can I calculate the probability that any one of those random variables is actually the highest?
The application for this is that I have several ads which people can view and possibly click. Over time I collect more and more data about each ad (views and clicks, which I can use to determine a beta distribution), and I'm interested in picking the ad that people most like to click on.
I need to determine when it is safe to select the ad with the highest click-through rate, so I need to know when a particular ad exceeds a threshold probability of being the best.
ps. I'm a software engineer not a mathematician, I would appreciate it if answers could bear this in mind by avoiding any complex notation ;)