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.
KeywordsPosterior Distribution Coverage Probability Probability Match Profile Likelihood Likelihood Inference
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- Berger, J.O. and J.M. Bernardo (1992). On the development of reference priors (with discussion). In J. Bernardo, J. Berger, A. Dawid, and A. Smith (Eds.), Bayesian Statistics IV, pp. 35–60. Oxford University Press.Google Scholar
- Bernardo, J.M. (1977). Inferences about the ratio of normal means: A. Bayesian approach to the Fieller-Creasy problem. In Recent Developments in Statistics, Proceedings of the 1976 European Meeting of Statisticians, pp. 345–350.Google Scholar
- Chib, S. and E. Greenberg (1995). Understanding the Metropolis-Hastings algorithm. Amer. Statist. 49, 327–335.Google Scholar
- Ghosh, M. and R. Mukerjee (1998). Recent developments on probability matching priors. In S. Ahmed, M. Ahsanullah, and B. Sinha (Eds.), Applied Statistical Science III. Nonparametric Statistics and Related Topics, pp. 227–252. Nova Science Publ., Inc.Google Scholar
- Mendoza, M. (1996). A note on the confidence probabilities of reference priors for the calibration model. preprint.Google Scholar
- Phillipe, A. and C.P. Robert (1994). A note on the confidence properties of reference priors for the calibration model, preprint.Google Scholar
- Reid, N. (1995). Likelihood and Bayesian approximation methods (with discussion). In J. Bernardo, J. Berger, A. Dawid, and A. Smith (Eds.), Bayesian Statistics, Volume 5, pp. 611–618. Oxford University Press.Google Scholar