Skip to main content

Concept Uncertainty in Adversarial Statistical Decision Theory

  • Chapter
  • First Online:
The Mathematics of the Uncertain

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 142))

Abstract

We focus on concept uncertainty which adds a new layer to the traditional risk analysis distinction between aleatory and epistemic uncertainties, when adversaries are present. The idea is illustrated with a problem in adversarial point estimation framed as a specific case of adversarial statistical decision theory.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Banks D, Ríos J, Ríos Insua D (2015) Adversarial risk analysis. CRC Press, Boca Raton

    Book  MATH  Google Scholar 

  2. Bedford T, Cooke RM (2001) Probabilistic risk analysis: foundations and methods. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  3. Clyde M, George EI (2004) Model uncertainty. Stat Sci 19(1):81–94

    Article  MathSciNet  MATH  Google Scholar 

  4. Cooke RM (1991) Experts in uncertainty: opinion and subjective probability in science. Oxford University Press, New York

    Google Scholar 

  5. Dalvi N, Domingos P, Mausam, Sanghai S, Verma D (2004) Adversarial classification. In: Kohavi R, Gehrke J, DuMouchel W, Ghosh J (eds) KDD’04 proceedings of 10th ACM SIGKDD international conference on knowledge discovery and data mining. ACM Press, New York

    Google Scholar 

  6. French S, Ríos Insua D (2000) Statistical decision theory. Wiley, New York

    MATH  Google Scholar 

  7. Gibbons R (1992) Game theory for applied economists. Princeton University Press, Princeton

    Google Scholar 

  8. Gil P (1997) Las matemáticas de lo incierto. Inaugural year address, University of Oviedo, Oviedo. http://digibuo.uniovi.es/dspace/bitstream/10651/28625/1/matematicasincierto.pdf

  9. Hargreaves-Heap S, Varoufakis Y (1995) Game theory: a critical introduction. Routledge, London

    Book  Google Scholar 

  10. Harsanyi JC (1967) Games with incomplete information played by “Bayesian” players, I-III. Part I. The basic model. Manag Sci 14(3):159–182

    Google Scholar 

  11. Hoeting JA, Madigan D, Raftery AE, Volinsky CT (1999) Bayesian model averaging: a tutorial. Stat Sci 14(4):382–417

    Article  MathSciNet  MATH  Google Scholar 

  12. Merrick J, Parnell GS (2011) A comparative analysis of PRA and intelligent adversary methods for counterterrorism management. Risk Anal 31(9):1488–1510

    Article  Google Scholar 

  13. O’Hagan A, Buck CE, Daneshkhah A, Eiser JR, Garthwaite PH, Jenkinson DJ, Oakley JE, Rakow T (2006) Uncertain judgements: eliciting experts’ probabilities. Wiley, Chichester

    Book  MATH  Google Scholar 

  14. Parry GW (1996) The characterization of uncertainty in probabilistic risk assessments of complex systems. Reliab Eng Syst Saf 54(2–3):119–126

    Article  Google Scholar 

  15. Paté-Cornell E, Guikema S (2002) Probabilistic modeling of terrorist threats: a systems analysis approach to setting priorities among countermeasures. Mil Op Res 7(4):5–23

    Article  Google Scholar 

  16. Refsgaard JC, van der Sluijs JP, Højberg AL, Vanrolleghem PA (2007) Uncertainty in the environmental modelling process - a framework and guidance. Environ Model Softw 22(11):1543–1556

    Article  Google Scholar 

  17. Ríos J, Ríos Insua D (2012) Adversarial risk analysis for counterterrorism modeling. Risk Anal 32(5):894–915

    Google Scholar 

  18. Ríos Insua D, Ríos J, Banks D (2009) Adversarial risk analysis. J Am Stat Assoc 104(486):841–854

    Google Scholar 

  19. Stahl DO, Wilson PW (1995) On players’ models of other players: theory and experimental evidence. Games Econ Behav 10(1):218–254

    Article  MathSciNet  MATH  Google Scholar 

  20. Tetlock P, Gardner D (2015) Superforecasting: the art and science of prediction. Random House, New York

    Google Scholar 

  21. Tygar JD (2011) Adversarial machine learning. IEEE Intern Comput 15(5):4–6

    Article  Google Scholar 

  22. Walker WE, Harremoës P, Rotmans J, van der Sluijs JP, van Asselt MB, Janssen P, Krayer von Krauss MP (2003) Defining uncertainty: a conceptual basis for uncertainty management in model-based decision support. Integr Assess 4(1):5–17

    Article  Google Scholar 

Download references

Acknowledgements

The work of DRI is supported by the Spanish Ministry of Economy and Innovation program MTM2014-56949-C3-1-R and the AXA-ICMAT Chair on Adversarial Risk Analysis. JGO’s research is financed by the Spanish Ministry of Economy and Competitiveness under FPI SO grant agreement BES-2015-072892. This work has also been partially supported by the Spanish Ministry of Economy and Competitiveness through the “Severo Ochoa” Program for Centers of Excellence in R&D (SEV-2015-0554) and project MTM2015-72907-EXP.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to David Ríos Insua .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ríos Insua, D., González-Ortega, J., Banks, D., Ríos, J. (2018). Concept Uncertainty in Adversarial Statistical Decision Theory. In: Gil, E., Gil, E., Gil, J., Gil, M. (eds) The Mathematics of the Uncertain. Studies in Systems, Decision and Control, vol 142. Springer, Cham. https://doi.org/10.1007/978-3-319-73848-2_49

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-73848-2_49

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73847-5

  • Online ISBN: 978-3-319-73848-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics