Institute of Mathematical Statistics Collections
CD posterior – combining prior and data through confidence distributions
This article proposes an alternative approach to incorporate information from observed data with its corresponding prior information using a recipe developed for combining confidence distributions. The outcome function is called a CD posterior, an alternative to Bayes posterior, which is shown here to have the same coverage property as the Bayes posterior. This approach to incorporating a prior distribution has a great advantage that it does not require any prior on nuisance parameters. It also can ease the computational burden which a typical Bayesian analysis endures. An error bound is established on the CD-posterior when there is an error in prior specification.
First available in Project Euclid: 14 March 2012
Permanent link to this document
Digital Object Identifier
Primary: 62A01: Foundations and philosophical topics 62F03: Hypothesis testing 62F12: Asymptotic properties of estimators 62F15: Bayesian inference 62F40: Bootstrap, jackknife and other resampling methods 62G05: Estimation 62G10: Hypothesis testing 62G20: Asymptotic properties
Copyright © 2012, Institute of Mathematical Statistics
Singh, Kesar; Xie, Minge. CD posterior – combining prior and data through confidence distributions. Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festschrift for William E. Strawderman, 200--214, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2012. doi:10.1214/11-IMSCOLL814. https://projecteuclid.org/euclid.imsc/1331731621.
- Bickel D.R. (2006) Incorporation expert knowledge into frequentist inference by combining generalized confidence distributions. Unpublished manuscript.
- Boos, D.D. and Monahan, J.F. (1986). Bootstrap methods using prior information. Biometrika, 73, 77–83.
- Efron, B. (1986). Why isn’t everybody a Bayesian? The American Statistician, 40(1), 1–5.
- Efron, B. (1993). Bayes and likelihood calculations from confidence intervals. Biometrika, 80, 3–26.
- Efron, B. (1998). Fisher in 21st Century (with discussion) Stat. Scie., 13, 95–122.
- Fraser, D.A.S. (1991). Statistical inference: Likelihood to significance. Journal of the American Statistical Association, 86, 258–265.
- Joseph, L., du Berger R., and Belisle P. (1997). Bayesian and mixed Bayesian/likelihood criteria for sample size determination. Statistics in Medicine, 16, 769–781.
- Liu, R.Y. and Singh, K. (1993). A quality index based on data-depth and a multivariate rank test. Journal of the American Statistical Association, 88, 257–260.
- Liu, R.Y., Parelius, J. and Singh, K. (1999). Multivariate analysis by data-depth: Descriptive statistics, graphics and inference. Ann. Stat., 27, 783–856 (with discussions).
- Schweder, T. and Hjort, N.L. (2002). Confidence and Likelihood. Scan. J. Statist., 29, 309–332.
- Singh, K., Xie, M. and Strawderman, W.E. (2005). Combining information from independent sources through confidence distribution. Ann. Stat., 33, 159–183.
- Singh, K., Xie, M. and Strawderman, W.E. (2007). Confidence distributions - Distribution estimator of a parameter. in Complex Datasets and Inverse Problems. IMS Lecture Notes-Monograph Series, No. 54, (R. Liu, et al., Eds.), 132–150. Festschrift in memory of Yehuda Vardi. IMS Lecture Notes Series.
- Wasserman, L. (2007). Why isn’t everyone a Bayesian? in The Science of Bradley Efron. (C.R., Morris and R. Tibshirani, Eds.), 260–261. Springer.
- Xie, M., Singh, K. and Strawderman, W.E. (2009). Confidence distributions and a unifying framework for meta-analysis. Technical Report. Department of Statistics, Rutgers University. Submitted for publication.
- Xie, M., Liu, R.Y., Damaraju, C.V. and Olson, W.H. (2009). Incorporating expert opinions in the analysis of binomial clinical trials. Technical Report. Department of Statistics, Rutgers University. Submitted for publication.