An Objective Bayesian Analysis of the Powered Ratio of Multinomial Proportions

This paper proposes a probability matching prior for performing objective Bayesian analysis of a powered ratio of multinomial proportions. The prior is derived by using the Tibshirani’s method that facilitates an orthogonal parameterization. Two numerical illustrations demonstrate that the proposed prior has good probability matching property with respect to the frequentist coverage probability. The illustrations also show the better performance of the prior over the Jeffreys prior in terms of the coverage probability and the accuracy in posterior estimation of the ratio. A Markov chain Monte Carlo method that facilitates the Metropolis-Hastings algorithm is considered to implement posterior analysis of the powered ratio. It is shown that the computational method is straightforward to specify distribution and to implement computation whose output is readily adapted for required posterior summaries.