# Raubenheimer, Lizanne

## BFF estimation methods for the difference between two binomial proportions

#### School of Mathematical and Statistical Sciences, North-West University, South Africa

Bayesian, frequentist and fiducial (BFF) methods for estimating the difference between two binomial proportions will be considered. Three non-informative priors will be used, the Jeffreys prior, a divergence prior and the probability matching prior. A probability matching prior is a prior distribution under which the posterior probabilities of certain regions coincide with their coverage probabilities. Fiducial inference can be viewed as a procedure that obtains a measure on a parameter space while assuming less than what Bayesian inference does, i.e. no prior. Fisher introduced the idea of fiducial probability and fiducial inference. In some cases the fiducial distribution is equivalent to the Jeffreys posterior. The performance of the Jeffreys prior, divergence prior and the probability matching prior will be compared to a fiducial method and other classical methods for constructing confidence intervals for the difference between two independent binomial parameters.

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