It was shown in (Ross, 2003) that a Bayesian estimate for Bernoulli trials using the beta distribution delivers good credibility intervals 5 , importantly, when sample sizes are small, or when occurrence probabilities are close to 0.
we assume that where the parameters for the two beta distributions are set to Prior information related to p(x) and the conditional probability p(x|y) can be incorporated by setting the hyper-parameters of the betadistribtutions.