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Risk Assessment of Complex Evolving Systems Involving Multiple Inputs

  • A. G. RigasEmail author
  • V. G. Vassiliadis
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 136)

Abstract

When monitoring complex evolving systems a question that often arises is to detect causal chains of events. Do particular inputs force the system to produce new events or prohibits them? This can be also considered as a risk assessment for the systems response. In this work we present two methods of estimating the effect of multiple inputs on a complex neurophysiological system. Both the response and the stimuli are very long binary time series. The first approach is a non-parametric one and describes the linear and the non-linear association of the stationary point processes by estimating the second- and third-order cumulant density functions. The second approach is a parametric one and the association between the inputs and the response of the system is described by a logistic regression model which takes into account the system’s internal processes.

Keywords

Cumulant densities Muscle spindle Penalized likelihood function Periodogram Randomized quantile residuals Stationary point process 

MSC 2010:

60G55 62M15 62F12 62G20 92C55 

References

  1. 1.
    Boyd, I.A.: The isolated mammalian muscle spindle. Trends Neurosci. 3(11), 258–265 (1980)CrossRefGoogle Scholar
  2. 2.
    Brillinger, D.R.: Estimation of product densities. In: Frane, J.W. (ed.) Computer Science and Statistics: 8th Annual Symposium, pp. 431–438. Los Angeles, U.C.L.A. (1975)Google Scholar
  3. 3.
    Brillinger, D.R.: Confidence intervals for the crosscovariance function. Selecta Statistica Canadiana 5, 3–16 (1979)Google Scholar
  4. 4.
    Brillinger, D.R.: Nerve cell spike train data analysis: a progression of technique. JASA 87(418), 260–271 (1992)CrossRefGoogle Scholar
  5. 5.
    Brillinger, D.R.: Time Series: Data Analysis and Theory, vol. 36. SIAM, Philadelphia (2001)CrossRefGoogle Scholar
  6. 6.
    Brillinger, D.R.: Some statistical methods for random process data from seismology and neurophysiology. In: Guttorp, P., Brillinger, D. (eds.) Selected Works of David Brillinger, Selected Works in Probability and Statistics, pp. 89–142. Springer, New York (2012)CrossRefGoogle Scholar
  7. 7.
    Cox, D.R., Lewis, P.A.W.: The Statistical Analysis of Series of Events. Wiley, London (1966)CrossRefzbMATHGoogle Scholar
  8. 8.
    Daley, D.J., Vere-Jones, D.: An Introduction to the Theory of Point Processes: Volume II: General Theory and Structure. Springer, New York (2007)Google Scholar
  9. 9.
    Dobson, A.J., Barnett, A.J.: An Introduction to Generalized Linear Model, 3rd edn. CRC Press, Boca Raton (2008)Google Scholar
  10. 10.
    Dunn, P.K., Smyth, G.K.: Randomized quantile residuals. J. Comput. Graph. Stat. 5(3), 236–244 (1996)Google Scholar
  11. 11.
    Firth, D.: Bias reduction, the Jeffreys prior and GLIM. Advances in GLIM and Statistical Modelling, pp. 91–100. Springer, New York (1992)CrossRefGoogle Scholar
  12. 12.
    Firth, D.: Generalized linear models and Jeffreys priors: an iterative weighted least-squares approach. In: Dodge, Y., Whittaker, J. (eds.) Computational Statistics, vol. 1, pp. 553–557. Physica-Verlag, Heidelberg (1992)CrossRefGoogle Scholar
  13. 13.
    Firth, D.: Bias reduction of maximum likelihood estimates. Biometrika 80(1), 27–38 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Hardin, J.W., Hilbe, J.: Generalized Linear Models and Extensions. Stata Press, College Station (2007)zbMATHGoogle Scholar
  15. 15.
    Heinze, G., Ploner, M.: A SAS macro, S-plus library and r package to perform logistic regression without convergence problems. Technical report 2/2004, Medical University of Vienna, Vienna (2004)Google Scholar
  16. 16.
    Heinze, G., Schemper, M.: A solution to the problem of separation in logistic regression. Stat. Med. 21(16), 2409–2419 (2002)CrossRefGoogle Scholar
  17. 17.
    Holden, A.V.: Models of the Stochastic Activity of Neurones. Springer, Berlin (1976)CrossRefzbMATHGoogle Scholar
  18. 18.
    Jeffreys, H.: An invariant form for the prior probability in estimation problems. Proc. R. Soc. A 186(1007), 453–461 (1946)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Karavasilis, G.J., Kotti, V.K., Tsitsis, D.S., Vassiliadis, V.G., Rigas, A.G.: Statistical methods and software for risk assessment: applications to a neurophysiological data set. Comput. Stat. Data Anal. 49(1), 243–263 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Kotti, V.K., Rigas, A.G.: Identification of a complex neurophysiological system using the maximum likelihood approach. J. Biol. Syst. 11(02), 189–204 (2003)CrossRefzbMATHGoogle Scholar
  21. 21.
    Kotti, V.K., Rigas, A.G.: Logistic regression methods and their implementation. In: Edler, L., Kitsos, C.P. (eds.) Recent Advances in Quantitative Methods in Cancer and Human Health Risk Assessment, pp. 355–369. Wiley, New York (2005)Google Scholar
  22. 22.
    Lindsay, K.A., Rosenberg, J.R.: Linear and quadratic models of point process systems: contributions of patterned input to output. Prog. Biophys. Mol. Biol. 109(3), 76–94 (2012)CrossRefGoogle Scholar
  23. 23.
    MacCullagh, P., Nelder, J.A.: Generalized Linear Models, vol. 37, 2nd edn. CRC Press, Boca Raton (1989)CrossRefGoogle Scholar
  24. 24.
    Marmarelis, V.Z.: Nonlinear Dynamic Modeling of Physiological Systems. Wiley-IEEE Press, New York (2004)CrossRefGoogle Scholar
  25. 25.
    Matthews, P.B.C.: Evolving views on the internal operation and functional role of the muscle spindle. J. Physiol. 320, 1–30 (1981)CrossRefMathSciNetGoogle Scholar
  26. 26.
    Priestley, M.B.: The role of bandwidth in spectral analysis. J. R. Stat. Soc. C 14(1), 33–47 (1965)zbMATHGoogle Scholar
  27. 27.
    Rigas, A.G.: Spectral analysis of stationary point processes using the fast Fourier transform algorithm. J. Time Ser. Anal. 13(5), 441–450 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    Tsitsis, D.S., Karavasilis, G.J., Rigas, A.G.: Measuring the association of stationary point processes using spectral analysis techniques. Stat. Methods Appl. 21(1), 23–47 (2012)CrossRefMathSciNetGoogle Scholar
  29. 29.
    Venzon, D.J., Moolgavkar, S.H.: A method for computing profile-likelihood-based confidence intervals. Appl. Stat. 37, 87–94 (1988)CrossRefGoogle Scholar
  30. 30.
    Windhorst, U.: Muscle proprioceptive feedback and spinal networks. Brain Res. Bull. 73(4), 155–202 (2007)CrossRefGoogle Scholar
  31. 31.
    Zorn, C.: A solution to separation in binary response models. Polit. Anal. 13(2), 157–170 (2005)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringDemocritus University of ThraceXanthiGreece

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