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Articles

Decision-Oriented Two-Parameter Fisher Information Sensitivity Using Symplectic Decomposition

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Pages 28-39 | Received 15 Aug 2022, Accepted 15 May 2023, Published online: 27 Jun 2023

References

  • Arnol’d, V. I. (1989), Mathematical Methods of Classical Mechanics, Graduate Texts in Mathematics (2nd ed.), New York: Springer-Verlag. DOI: 10.1007/978-1-4757-2063-1.
  • Bhatia, R., and Jain, T. (2015), “On Symplectic Eigenvalues of Positive Definite Matrices,” Journal of Mathematical Physics, 56, 112201. DOI: 10.1063/1.4935852.
  • Borgonovo, E. (2007), “A New Uncertainty Importance Measure,” Reliability Engineering & System Safety, 92, 771–784. DOI: 10.1016/j.ress.2006.04.015.
  • Borgonovo, E., and Plischke, E. (2016), “Sensitivity Analysis: A Review of Recent Advances,” European Journal of Operational Research, 248, 869–887. DOI: 10.1016/j.ejor.2015.06.032.
  • Cover, T. M., and Thomas, J. A. (2006), Elements of Information Theory, Hoboken, NJ: Wiley. [Online; accessed 2022-04-20].
  • Critchfield, G. C., and Willard, K. E. (1986), “Probabilistic Analysis of Decision Trees Using Monte Carlo Simulation,” Medical Decision Making, 6, 85–92. DOI: 10.1177/0272989X8600600205.
  • Fisher, R. A., and Russell, E. J. (1922), “On the Mathematical Foundations of Theoretical Statistics,” Philosophical Transactions of the Royal Society of London, Series A, Containing Papers of a Mathematical or Physical Character, 222, 309–368.
  • Gauchy, C., Stenger, J., Sueur, R., and Iooss, B. (2022), “An Information Geometry Approach to Robustness Analysis for the Uncertainty Quantification of Computer Codes,” Technometrics, 64, 80–91. DOI: 10.1080/00401706.2021.1905072.
  • Gosson, d. M. (2006), Symplectic Geometry and Quantum Mechanics / Maurice de Gosson, Operator Theory, Advances and Applications (Vol. 166), Basel: Birkhäuser.
  • Gunawan, R., Cao, Y., Petzold, L., and Doyle, F. J. (2005), “Sensitivity Analysis of Discrete Stochastic Systems,” Biophysical Journal, 88, 2530–2540. DOI: 10.1529/biophysj.104.053405.
  • Jia, G., and Taflanidis, A. A. (2014), “Sample-based Evaluation of Global Probabilistic Sensitivity Measures,” Computers & Structures, 144, 103–118. DOI: 10.1016/j.compstruc.2014.07.019.
  • Komorowski, M., Costa, M. J., Rand, D. A., and Stumpf, M. P. H. (2011), “Sensitivity, Robustness, and Identifiability in Stochastic Chemical Kinetics Models,” Proceedings of the National Academy of Sciences, 108, 8645–8650. DOI: 10.1073/pnas.1015814108.
  • Lee, E. D., Katz, D. M., Bommarito, M. J., and Ginsparg, P. H. (2020), “Sensitivity of Collective Outcomes Identifies Pivotal Components,” Journal of The Royal Society Interface, 17, 20190873. DOI: 10.1098/rsif.2019.0873.
  • Lehmann, E. L., and Casella, G. (1998), Theory of Point Estimation, Springer Texts in Statistics (2nd ed.), New York: Springer.
  • Lemaître, P., Sergienko, E., Arnaud, A., Bousquet, N., Gamboa, F., and Iooss, B. (2015), “Density Modification-based Reliability Sensitivity Analysis,” Journal of Statistical Computation and Simulation, 85, 1200–1223. DOI: 10.1080/00949655.2013.873039.
  • Majda, A. J., and Gershgorin, B. (2010), “Quantifying Uncertainty in Climate Change Science through Empirical Information Theory,” Proceedings of the National Academy of Sciences, 107, 14958–14963. DOI: 10.1073/pnas.1007009107.
  • Nicacio, F. (2021), “Williamson Theorem in Classical, Quantum, and Statistical Physics,” American Journal of Physics, 89, 1139–1151. DOI: 10.1119/10.0005944.
  • Oakley, J. E. (2009), “Decision-Theoretic Sensitivity Analysis for Complex Computer Models,” Technometrics, 51, 121–129. DOI: 10.1198/TECH.2009.0014.
  • Oakley, J. E., and O’Hagan, A. (2004), “Probabilistic Sensitivity Analysis of Complex Models: A Bayesian Approach,” Journal of the Royal Statistical Society, Series B, 66, 751–769. DOI: 10.1111/j.1467-9868.2004.05304.x.
  • Pantazis, Y., Katsoulakis, M. A., and Vlachos, D. G. (2013), “Parametric Sensitivity Analysis for Biochemical Reaction Networks based on Pathwise Information Theory,” BMC Bioinformatics, 14, 311. DOI: 10.1186/1471-2105-14-311.
  • Pereira, J. L., Banchi, L., and Pirandola, S. (2021), “Symplectic Decomposition from Submatrix Determinants,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477, 20210513. DOI: 10.1098/rspa.2021.0513.
  • Rubinstein, R. Y., and Kroese, D. P. (2016), Simulation and the Monte Carlo Method (3rd ed.), New York: Wiley.
  • Saltelli, A., ed. (2008), Global Sensitivity Analysis: The Primer, Chichester, England; Hoboken, NJ: Wiley.
  • Sobol’, I., and Kucherenko, S. (2009), “Derivative based Global Sensitivity Measures and their Link with Global Sensitivity Indices,” Mathematics and Computers in Simulation, 79, 3009–3017. DOI: 10.1016/j.matcom.2009.01.023.
  • Williamson, J. (1936), “On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems,” American Journal of Mathematics, 58, 141–163. DOI: 10.2307/2371062.
  • Yang, J. (2022), “An Information Upper Bound for Probability Sensitivity,” arXiv:2206.02274 [cs, math, stat].
  • Yang, J. (2023), “A General Framework for Probabilistic Sensitivity Analysis with Respect to Distribution Parameters,” Probabilistic Engineering Mechanics, 72, 103433.
  • Yang, J., Langley, R. S., and Andrade, L. (2022), “Digital Twins for Design in the Presence of Uncertainties,” Mechanical Systems and Signal Processing, 179, 109338. DOI: 10.1016/j.ymssp.2022.109338.