A Probability Matching Prior for the Powered Ratio of Trinomial Proportions

This paper presents a probability matching prior for Bayesian analysis of a powered ratio of two trinomial proportions. The prior is derived by using Tibshirani’s method. A simulation study demonstrates that the posterior probabilities of certain regions, based on the prior, approximately coincide with their coverage probabilities. For the posterior analysis of the powered ratio, this paper considers a Markov chain Monte Carlo method that facilitates the Metropolis-Hastings algorithm. It is shown that this Bayesian computation method is straightforward to specify distributionally and to implement computationally, with output really adapted for required inference summaries. The study also compares the probability matching prior with Jeffreys prior in terms of the coverage probability and the accuracy of the posterior estimate of the ratio.