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APPLICATIONS OF LIKELIHOOD RATIO ORDER IN BAYESIAN INFERENCES

Published online by Cambridge University Press:  06 August 2018

Kai Huang  and
Jie Mi
Kai Huang
Affiliation:
Department of Mathematics and Statistics, Florida International University, Miami, FL 33199, USA E-mail: [email protected]; [email protected]
Jie Mi
Affiliation:
Department of Mathematics and Statistics, Florida International University, Miami, FL 33199, USA E-mail: [email protected]; [email protected]
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Abstract

The present paper studies the likelihood ratio order of posterior distributions of parameter when the same order exists between the corresponding prior of the parameter, or when the observed values of the sufficient statistic for the parameter differ. The established likelihood order allows one to compare the Bayesian estimators associated with many common and general error loss functions analytically. It can also enable one to compare the Bayes factor in hypothesis testing without using numerical computation. Moreover, using the likelihood ratio (LR) order of the posterior distributions can yield the LR order between marginal predictive distributions, and posterior predictive distributions.

Keywords

bayesian estimatorsbayes factorlikelihood ratio orderpredictive distributionprior distributionposterior distribution
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 1 , January 2020 , pp. 1 - 13
Copyright
Copyright © Cambridge University Press 2018 

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References

1.Arias-Nicolás, J.P., Ruggeri, F. & Suárez-Llorens, A. (2016). New classes of priors based on stochastic orders and distortion functions. Bayesian Analysis 11(4): 1107–1136.Google Scholar
2.Berger, J.O. (1985). Statistical decision: theory and Bayesian analysis, 2nd ed. New York, USA: Springer-Verlag.Google Scholar
3.Billingsley, P. (1986). Probability and measure, 2nd ed. New York, USA: Wiley.Google Scholar
4.Christensen, R., Johnson, W., Branscum, A. & Hanson, T.E. (2011). Bayesian ideas and data analysis: An introduction for scientists and statisticians. Boca Raton, FL, USA: CRC Press Taylor & Francis Group.Google Scholar
5.Ghosh, J., Delampady, M. & Samanta, T. (2006). An introduction to Bayesian analysis theory and methods. New York, USA: Springer.Google Scholar
6.Ross, S.M. (1983). Stochastic processes. New York: John Williams & Sons.Google Scholar
7.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York, USA: Springer.Google Scholar
8.Spizzichino, F. (2001). Subjective Probability Models for Lifetimes. Boca Raton, FL, USA: Chapman and Hall/CRC.Google Scholar
9.Suen, W. Monotone likelihood ratio property. Available at http://www.sef.hku.hk/wsuen/teaching/uncertainty/mlrp.pdfGoogle Scholar
10.Zacks, S. (1971). The theory of statistical inference. New York, USA: Wiley & Sons, INC.Google Scholar