Advertisement

Objective Uncertainty Quantification

  • Edward R. DoughertyEmail author
  • Lori A. Dalton
  • Roozbeh Dehghannasiri
Chapter
Part of the Simulation Foundations, Methods and Applications book series (SFMA)

Abstract

When designing an operator to alter the behavior of a physical system, the standard engineering paradigm is to begin with a scientific model describing the system, mathematically characterize a class of operators, define a performance cost relative to the operational objective, and pick an operator that minimizes the performance cost. Validation ipso facto plays a role because the scientific model needs to be validated. With complex systems, or those for which experiments are costly, there may be insufficient data for system identification, with validation being outside the realm of possibility. Given the resulting model uncertainty, the best one can do is to design a “robust” operator that is optimal relative to both the objective and the uncertainty. This robust optimization paradigm entails optimal experimental design: should one not be satisfied with the performance, choose the experiment that maximally reduces the uncertainty as it pertains to the objective. In this chapter, we address these problems and present examples in the context of gene regulatory network intervention.

Keywords

Bayesian experimental design Robust design Mean absolute cost of uncertainty Uncertainty quantification 

References

  1. Bae, H.-R., Grandhi, R. V., & Canfield, R. A. (2004). An approximation approach for uncertainty quantification using evidence theory. Reliability Engineering & System Safety, 86(3), 215–225.CrossRefGoogle Scholar
  2. Barbieri, M. M., & Berger, J. O. (2004). Optimal predictive model selection. The Annals of Statistics, 32(3), 870–897.MathSciNetzbMATHCrossRefGoogle Scholar
  3. Batchelor, E., Loewer, A., & Lahav, G. (2009). The ups and downs of p53: Understanding protein dynamics in single cells. Nature Reviews Cancer, 9(5), 371–377.CrossRefGoogle Scholar
  4. Bernardo, J. M., & Smith, A. F. (2001). Bayesian theory. Measurement Science and Technology, 12(2), 221.Google Scholar
  5. Boluki, S., Esfahani, M. S., Qian, X., & Dougherty, E. R. (2017). Incorporating biological prior knowledge for Bayesian learning via maximal knowledge-driven information priors. BMC Bioinformatics, 18(Suppl 14), 552.CrossRefGoogle Scholar
  6. Chen, M.-H., Ibrahim, J. G., Shao, Q.-M., & Weiss, R. E. (2003). Prior elicitation for model selection and estimation in generalized linear mixed models. Journal of Statistical Planning and Inference, 111(1–2), 57–76.MathSciNetzbMATHCrossRefGoogle Scholar
  7. Clyde, M., & George, E. I. (2004). Model uncertainty. Statistical Science, 19(1), 81–94.MathSciNetzbMATHCrossRefGoogle Scholar
  8. Dalton, L. A., & Dougherty, E. R. (2013). Optimal classifiers with minimum expected error within a Bayesian framework-Part I: Discrete and Gaussian models. Pattern Recognition, 46(5), 1301–1314.zbMATHCrossRefGoogle Scholar
  9. Dalton, L. A., & Dougherty, E. R. (2014). Intrinsically optimal Bayesian robust filtering. IEEE Transactions on Signal Processing, 62(3), 657–670.MathSciNetzbMATHCrossRefGoogle Scholar
  10. Dehghannasiri, R., Esfahani, M. S., & Dougherty, E. R. (2017). Intrinsically Bayesian robust Kalman filter: An innovation process approach. IEEE Transactions on Signal Processing, 65(10), 2531–2546.MathSciNetzbMATHCrossRefGoogle Scholar
  11. Dehghannasiri, R., Xue, D., Balachandran, P. V., Yousefi, M. R., Dalton, L. A., Lookman, T., et al. (2017). Optimal experimental design for materials discovery. Computational Materials Science, 129, 311–322.CrossRefGoogle Scholar
  12. Dehghannasiri, R., Yoon, B.-J., & Dougherty, E. R. (2015a). Efficient experimental design for uncertainty reduction in gene regulatory networks. BMC Bioinformatics, 16(Suppl 13), S2.CrossRefGoogle Scholar
  13. Dehghannasiri, R., Yoon, B.-J., & Dougherty, E. R. (2015). Optimal experimental design for gene regulatory networks in the presence of uncertainty. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 12(4), 938–950.CrossRefGoogle Scholar
  14. Dougherty, E. R. (2007). Validation of inference procedures for gene regulatory networks. Current Genomics, 8(6), 351–359.CrossRefGoogle Scholar
  15. Dougherty, E. R. (2016). The evolution of scientific knowledge: From certainty to uncertainty. Bellingham: SPIE Press.CrossRefGoogle Scholar
  16. Dougherty, E. R., & Bittner, M. L. (2011). Epistemology of the cell: A systems perspective on biological knowledge. New York: Wiley.CrossRefGoogle Scholar
  17. Esfahani, M. S., & Dougherty, E. R. (2014). Incorporation of biological pathway knowledge in the construction of priors for optimal Bayesian classification. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 11(1), 202–218.CrossRefGoogle Scholar
  18. Faryabi, B., Vahedi, G., Datta, A., Chamberland, J.-F., & Dougherty, E. R. (2009). Recent advances in intervention in Markovian regulatory networks. Current Genomics, 10(7), 463–477.CrossRefGoogle Scholar
  19. Frazier, P., Powell, W., & Dayanik, S. (2009). The knowledge-gradient policy for correlated normal beliefs. INFORMS Journal on Computing, 21(4), 599–613.MathSciNetzbMATHCrossRefGoogle Scholar
  20. Grigoryan, A. M., & Dougherty, E. R. (1999). Design and analysis of robust binary filters in the context of a prior distribution for the states of nature. Journal of Mathematical Imaging and Vision, 11(3), 239–254.zbMATHCrossRefGoogle Scholar
  21. Hoeting, J. A., Madigan, D., Raftery, A. E., & Volinsky, C. T. (1999). Bayesian model averaging: A tutorial. Statistical Science, 14(4), 382–401.MathSciNetzbMATHCrossRefGoogle Scholar
  22. Huan, X., & Marzouk, Y. M. (2016). Sequential Bayesian optimal experimental design via approximate dynamic programming. arXiv preprint arXiv:1604.08320.
  23. Kaufmann, S. (1993). The origins of order. New York: Oxford University Press.Google Scholar
  24. Madigan, D., & Raftery, A. E. (1994). Model selection and accounting for model uncertainty in graphical models using Occam’s window. Journal of the American Statistical Association, 89(428), 1535–1546.zbMATHCrossRefGoogle Scholar
  25. Mohsenizadeh, D., Dehghannasiri, R., & Dougherty, E. R. (2016). Optimal objective-based experimental design for uncertain dynamical gene networks with experimental error. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 15(1), 218–230.CrossRefGoogle Scholar
  26. Qian, X., & Dougherty, E. R. (2008). Effect of function perturbation on the steady-state distribution of genetic regulatory networks: Optimal structural intervention. IEEE Transactions on Signal Processing, 56(10), 4966–4976.MathSciNetzbMATHCrossRefGoogle Scholar
  27. Raftery, A. E., Madigan, D., & Hoeting, J. A. (1997). Bayesian model averaging for linear regression models. Journal of the American Statistical Association, 92(437), 179–191.MathSciNetzbMATHCrossRefGoogle Scholar
  28. Ryan, E. G., Drovandi, C. C., McGree, J. M., & Pettitt, A. N. (2016). A review of modern computational algorithms for Bayesian optimal design. International Statistical Review, 84(1), 128–154.MathSciNetCrossRefGoogle Scholar
  29. Shmulevich, I., Dougherty, E. R., & Zhang, W. (2002). From Boolean to probabilistic Boolean networks as models of genetic regulatory networks. Proceedings of the IEEE, 90(11), 1778–1792.CrossRefGoogle Scholar
  30. Wasserman, L. (2000). Bayesian model selection and model averaging. Journal of Mathematical Psychology, 44(1), 92–107.MathSciNetzbMATHCrossRefGoogle Scholar
  31. Yoon, B.-J., Qian, X., & Dougherty, E. R. (2013). Quantifying the objective cost of uncertainty in complex dynamical systems. IEEE Transactions on Signal Processing, 61(9), 2256–2266.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Edward R. Dougherty
    • 1
    Email author
  • Lori A. Dalton
    • 2
  • Roozbeh Dehghannasiri
    • 1
  1. 1.Texas A&M UniversityCollege StationUSA
  2. 2.The Ohio State UniversityColumbusUSA

Personalised recommendations