I don’t quite understand what your plot means. What’s on the x axis? What is the bayes optimal?
A beta-binomial model like that should show a posterior beta that is Beta(a+successes, b+failures), where a and b are your prior parameters. So you should see beta1_~Beta(5.1+successes, 2+failures)
Unrelated to your question, pymc3 is quite old and no longer maintained. I suggest you update to pymc (v>5) if you intend to use the library seriously.