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Estimating the difference between two binomial proportions will beinvestigated, where Bayesian, frequentist and fiducial (BFF) methods will beconsidered. Three vague priors will be used, the Jeffreys prior, a divergenceprior and the probability matching prior. A probability matching prior is aprior distribution under which the posterior probabilities of certain regionscoincide with their coverage probabilities. Fiducial inference can be viewed asa procedure that obtains a measure on a parameter space while assuming lessthan what Bayesian inference does, i.e. no prior. Fisher introduced the idea offiducial probability and fiducial inference. In some cases the fiducialdistribution is equivalent to the Jeffreys posterior. The performance of theJeffreys prior, divergence prior and the probability matching prior will becompared to a fiducial method and other classical methods of constructingconfidence intervals for the difference between two independent binomialparameters. These intervals will be compared and evaluated by looking at theircoverage rates and average interval lengths. The probability matching anddivergence priors perform better than the Jeffreys prior.

Bayesian, frequentist and fiducial intervals for the difference between two binomial proportions