the standard result is that with a uniform prior on p (from 0 to 1) and binomial signals (h H signals and (n-h) L signals from n draws, each with probability p), the posterior mean is (h+1)/(n+2) and the ex-ante probability of observing h H's is 1/(n+1). it's beautifully short formulae.
are there some papers or books or treatises that consider variations thereon for use with undergraduate students?
For example, one can entertain a parameter that increases the accuracy of the signal (e.g., x% of the time, the signal is pure noise, or the signal is drawn with probability p/2 + 1/2, or ...); or a more extreme-loaded prior (a more central prior is easy, because one can start with the posterior after one H and one L signal). All derivable, but it would be good to see a whole lot of variations in one go-to reference place.
