x ~ Binomial(N,p) and you wish to estimate p. Here are a whole collection methods for how to estimate p and calculate a confidence interval for it: https://en

x ~ Binomial(N,p) and you wish to estimate p. Here are a whole collection methods for how to estimate p and calculate a confidence interval for it: https://en.wikipedia.org/wiki/Binomial_distribution#Confidence_intervals_for_the_parameter_p https://en.wikipedia.org/wiki/Binomial_distribution#Confiden... One of the methods is Bayesian; the rest are not. Not mentioned in the list, but you can also use likelihood ratio intervals calculated from a likelihood profile: another Frequentist method. None of the methods -- including the Bayesian, requires an informative prior.