Statistical Science

Weak Informativity and the Information in One Prior Relative to Another

Michael Evans and Gun Ho Jang

Full-text: Open access


A question of some interest is how to characterize the amount of information that a prior puts into a statistical analysis. Rather than a general characterization, we provide an approach to characterizing the amount of information a prior puts into an analysis, when compared to another base prior. The base prior is considered to be the prior that best reflects the current available information. Our purpose then is to characterize priors that can be used as conservative inputs to an analysis relative to the base prior. The characterization that we provide is in terms of a priori measures of prior-data conflict.

Article information

Statist. Sci., Volume 26, Number 3 (2011), 423-439.

First available in Project Euclid: 31 October 2011

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Weak informativity prior-data conflict information noninformativity


Evans, Michael; Jang, Gun Ho. Weak Informativity and the Information in One Prior Relative to Another. Statist. Sci. 26 (2011), no. 3, 423--439. doi:10.1214/11-STS357.

Export citation


  • Bernardo, J.-M. (1979). Reference posterior distributions for Bayesian inference (with discussion). J. Roy. Statist. Soc. Ser. B 41 113–147.
  • Chib, S. and Ergashev, B. (2009). Analysis of multifactor affine yield curve models. J. Amer. Statist. Assoc. 104 1324–1337.
  • Evans, M. and Jang, G. H. (2010). Invariant P-values for model checking. Ann. Statist. 38 312–323.
  • Evans, M. and Jang, G. H. (2011). A limit result for the prior predictive applied to checking for prior-data conflict. Statist. Probab. Lett. 81 1034–1038.
  • Evans, M. and Moshonov, H. (2006). Checking for prior-data conflict. Bayesian Anal. 1 893–914.
  • Evans, M. and Moshonov, H. (2007). Checking for prior-data conflict with hierarchically specified priors. In Bayesian Statistics and Its Applications (A. K. Upadhyay, U. Singh and D. Dey, eds.) 145–159. Anamaya Publishers, New Delhi.
  • Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models. Bayesian Anal. 1 515–533.
  • Gelman, A., Jakulin, A., Pittau, M. G. and Su, Y.-S. (2008). A weakly informative default prior distribution for logistic and other regression models. Ann. Appl. Statist. 2 1360–1383.
  • Kass, R. E. and Wasserman, L. (1995). A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. J. Amer. Statist. Assoc. 90 928–934.
  • Lindley, D. V. (1956). On a measure of the information provided by an experiment. Ann. Math. Statist. 27 986–1005.
  • Racine, A., Grieve, A. P., Flühler, H. and Smith, A. F. M. (1986). Bayesian methods in practice: Experiences in the pharmaceutical industry (with discussion). J. Roy. Statist. Soc. Ser. C 35 93–150.
  • Tjur, T. (1974). Conditional Probability Models. Institute of Mathematical Statistics, Univ. Copenhagen, Copenhagen.