Bayesian Analysis

A quantitative study of quantile based direct prior elicitation from expert opinion

Dipak K. Dey and Junfeng Liu

Full-text: Open access


Eliciting priors from expert opinion enjoys more efficiency and reliability by avoiding the statistician's potential subjectivity. Since elicitation on the predictive prior probability space requires too-simple priors and may be burdened with additional uncertainties arising from the response model, quantitative elicitation of flexible priors on the direct prior probability space deserves much attention. Motivated by precisely acquiring the shape information for the general location-scale-shape family beyond the limited and simple location-scale family, we investigate multiple numerical procedures for a broad class of priors, as well as interactive graphical protocols for more complicated priors. We highlight the quantile based approaches from several aspects, where Taylor's expansion is demonstrated to be an efficient approximate alternative to work on the regions in which the shape parameter is highly sensitive. By observing inherent associations between the scale and shape parameters, we put more weight on practical solutions under a proper sensitivity index (SI) rather than presumability. Our proposed methodology is demonstrated through skew-normal and Gamma hyper-parameter elicitation where the shape parameter is numerically solved in a stable way. The performance comparisons among different elicitation approaches are also provided.

Article information

Bayesian Anal., Volume 2, Number 1 (2007), 137-166.

First available in Project Euclid: 22 June 2012

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: Database Expansion Item

location parameter prior elicitation quantile scale parameter shape parameter skewness Taylor's expansion


Dey, Dipak K.; Liu, Junfeng. A quantitative study of quantile based direct prior elicitation from expert opinion. Bayesian Anal. 2 (2007), no. 1, 137--166. doi:10.1214/07-BA206.

Export citation


  • Aigner, D. J., Lovell, C. K., and Schmidt, P. (1977). "Formulation and estimation of stochastic frontier production function model." Journal of Econometrics, 6(1): 21–37.
  • Al-Awadhi, S. A. and Garthwaite, P. H. (1998). "An elicitation method for multivariate normal distributions." Communications in Statistics: Theory and Methods, 27(5): 1123–1142.
  • Azzalini, A. (1985). "A class of distributions which includes the normal ones." Scandinavian Journal of Statistics, 12(2): 171–178.
  • Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis. New York: Springer-Verlag, 2 edition.
  • Dalal, S. R. and Hall, W. J. (1983). "Approximating priors by mixtures of natural conjugate priors." Journal of the Royal Statistical Society - Series B, 45(2): 278–286.
  • Garthwaite, P. H. (1989). "Fractile assessment for a linear regression model: an experimental study." Organizational Behavior and Human Decision Processes, 43: 188–206.
  • Garthwaite, P. H. and Dickey, J. M. (1985). "Double- and single-bisection methods for subjective probability assessment in a location-scale family." Special Bayesian issue of J. Econometrics, 29: 149–163.
  • –- (1988). "Quantifying expert opinion in linear regression problems." Journal of the Royal Statistical Society - Series B, 50(3): 462–474.
  • Garthwaite, P. H., Kadane, J. B., and O'Hagan, A. (2005). "Statistical methods for elicitating probability distributions." Journal of the American Statistical Association, 100(470): 680–701.
  • Gill, J. and Walker, L. D. (2005). "Elicited priors for Bayesian model specifications in political science research." The Journal of Politics, 67(3): 841–872.
  • Jaynes, E. T. (1968). "Prior probabilities." IEEE Transactions on Systems Science and Cybernetics, SSC-4: 227–241.
  • Kadane, J. B., Dickey, J. M., Winkler, R. L., Smith, W. S., and Peters, S. C. (1980). "Interactive elicitation of opinion for a normal linear model." Journal of the American Statistical Association, 75(372): 845–854.
  • Meeden, G. (1992). "An elicitation procedure using piecewise conjugate priors." In Goel, P. K. and Iyengar, N. S. (eds.), Bayesian analysis in statistics and econometrics. Springer-Verlag.
  • O'Hagan, A. (1998). "Eliciting expert beliefs in substantial practical applications." The Statistician, 47: 21–35.
  • Peterson, C. R. and Miller, A. (1964). "Mode, median and mean as optimal strategies." Journal of Experimental Psychology, 68: 363–367.
  • Sahu, S., Dey, D. K., and Branco, M. (2003). "A new class of multivariate skew distributions with application to Bayesian regression models." The Canadian Journal of Statistics, 31: 129–150.