Advertisement

Abstract

In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge. This has the advantage that prior-data conflict sensitivity can be modelled: Ranges of posterior inferences should be larger when prior and data are in conflict. We propose a new method for generating prior sets which, in addition to prior-data conflict sensitivity, allows to reflect strong prior-data agreement by decreased posterior imprecision.

Keywords

Bayesian inference Strong prior-data agreement Prior-data conflict Imprecise probability Conjugate priors 

Notes

Acknowledgements

Gero Walter was supported by the Dinalog project “Coordinated Advanced Maintenance and Logistics Planning for the Process Industries” (CAMPI).

References

  1. 1.
    Augustin, T., Coolen, F., de Cooman, G., Troffaes, M.: Introduction to Imprecise Probabilities. Wiley, Chichester (2014)CrossRefzbMATHGoogle Scholar
  2. 2.
    Berger, J., et al.: An overview of robust Bayesian analysis. TEST 3, 5–124 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bickis, M.: The geometry of imprecise inference. In: Augustin, T., Doria, S., Miranda, E., Quaeghebeur, E. (eds.) ISIPTA 2015: Proceedings of the Ninth International Symposium on Imprecise Probability: Theories and Applications, pp. 47–56. SIPTA (2015). http://www.sipta.org/isipta15/data/paper/31.pdf
  4. 4.
    Evans, M., Moshonov, H.: Checking for prior-data conflict. Bayesian Analysis 1, 893–914 (2006). http://projecteuclid.org/euclid.ba/1340370946 MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Quaeghebeur, E., de Cooman, G.: Imprecise probability models for inference in exponential families. In: Cozman, F., Nau, R., Seidenfeld, T. (eds.) ISIPTA 2005, Proceedings of the Fourth International Symposium on Imprecise Probabilities and Their Applications, pp. 287–296. SIPTA, Manno (2005)Google Scholar
  6. 6.
    Robert, C.P.: The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation. Springer, New York (2007)zbMATHGoogle Scholar
  7. 7.
    Troffaes, M., Walter, G., Kelly, D.: A robust Bayesian approach to modelling epistemic uncertainty in common-cause failure models. Reliab. Eng. Syst. Saf. 125, 13–21 (2014)CrossRefGoogle Scholar
  8. 8.
    Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London (1991)CrossRefzbMATHGoogle Scholar
  9. 9.
    Walley, P.: Inferences from multinomial data: Learning about a bag of marbles. J. R. Stat. Soc. Ser. B 58(1), 3–34 (1996)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Walter, G.: Generalized Bayesian inference under prior-data conflict. Ph.D. thesis, Ludwig-Maximilians-Universität München (2013). http://nbn-resolving.de/urn:nbn:de:bvb:19-170598
  11. 11.
    Walter, G., Augustin, T.: Imprecision and prior-data conflict in generalized Bayesian inference. J. Stat. Theory Pract. 3, 255–271 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Walter, G., Graham, A., Coolen, F.P.A.: Robust Bayesian estimation of system reliability for scarce and surprising data. In: Podofillini, L., Sudret, B., Stojadinović, B., Zio, E., Kröger, W. (eds.) Safety and Reliability of Complex Engineered Systems: ESREL 2015, pp. 1991–1998. CRC Press, Boca Raton (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of Industrial EngineeringEindhoven University of TechnologyEindhovenNetherlands
  2. 2.Department of Mathematical SciencesDurham UniversityDurhamUK

Personalised recommendations