From prior to posterior
Suppose ? has a Gamma(a,b) prior distribution:
? a–1e–b ? ba/ ?(a), ? > 0
[mean is a/b, SD is ?a/b]
Posterior is proportional to:
? a–1e–b ? ? ? ke–?= ? ? a+ke–(b+1) ? which is Gamma(a+k,b+1).
[Another example of conjugate prior.]