Bayesian and Likelihood Inference for the Generalized Fieller—Creasy Problem
The famous Fieller-Creasy problem involves inference about the ratio of two normal means. It is quite challenging from either a frequentist or a likelihood perspective. Bayesian analysis with noninformative priors usually provides ideal solutions for this problem. In this paper, we find a second order matching prior and a one at a time reference prior which work well for Fieller-Creasy problem in the more general setting of two location-scale models with smooth symmetric density functions. The properties of the posterior distributions are investigated for some particular cases including the normal, t, and the double exponential. The Bayesian procedure is implemented via Markov Chain Monte Carlo (MC 2). Our simulation study indicates that the second order matching priors, in general, perform better than the reference priors in terms of matching the target coverage probabilities in a frequentist sense.
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