QMC Computation of Confidence Intervals for a Sleep Performance Model

  • Alan Genz
  • Amber Smith
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 23)


A five-dimensional Bayesian forecasting model for cognitive performance impairment during sleep deprivation is used to approximately determine confidence intervals for psychomotor vigilance task (PVT) prediction. Simulation is required to locate the boundary of a confidence region for the model pdf surface. Further simulation is then used to determine PVT lapse confidence intervals as a function of sleep deprivation time. Quasi-Monte Carlo simulation methods are constructed for the two types of simulations. The results from these simulations are compared with results from previous methods, which have used various combinations of grid-search, numerical optimization and simple Monte Carlo methods.


Monte Carlo Sleep Deprivation Circadian Oscillation Numerical Integration Method Psychomotor Vigilance Task 
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  1. 1.
    Borbély, A. A., and Achermann, P., ‘Sleep homeostasis and models of sleep regulation’. J.  Biol. Rhythms 14, pp. 557–568, 1999.Google Scholar
  2. 2.
    Box, G. E. P., and Tiao, G. C., Bayesian Inference in Statistical Analysis, Wiley-Interscience, New York, p. 123, 1992.Google Scholar
  3. 3.
    Dorrian, J., Rogers, N. l., and Dinges, D. F., ‘Psychomotor Vigilance Performance: Neurocognitive Assay Sensitive to Sleep Loss’, pp. 39–70 in Kushida, C. A. (ed.) Sleep Deprivation: Clinical Issues, Pharmacology, and Sleep Loss Effects, Marcel Dekker, New York, 2005.Google Scholar
  4. 4.
    Drmota, M. and Tichy, R. F., Sequences, Discrepancies and Applications, Lecture Notes in Mathematics 1651, Springer-Verlag, New York, 1997.Google Scholar
  5. 5.
    Fang, K.-T., and Wang, Y., Number-Theoretic Methods in Statistics, Chapman and Hall, London, pp. 26–32, 1994.Google Scholar
  6. 6.
    Fishman, G. S., Monte Carlo: Concepts, Algorithms, and Applications, Springer-Verlag, 1996.Google Scholar
  7. 7.
    Fox, B. L, Strategies for Quasi-Monte Carlo (International Series in Operations Research & Management Science, 22), Kluwer Academic Publishers, 1999.Google Scholar
  8. 8.
    Genz, A., and Kass, R., ‘Subregion Adaptive Integration of Functions Having a Dominant Peak’, J. Comp. Graph. Stat. 6, pp. 92–111, 1997.Google Scholar
  9. 9.
    Nuyens, D., and Cools, R., ‘Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces’, Math. Comp 75, pp. 903–920, 2006.Google Scholar
  10. 10.
    Smith, A., Genz, A., Freiberger, D. M., Belenky, G., and Van Dongen, H. P. A., ‘Efficient computation of confidence intervals for Bayesian model predictions based on multidimensional parameter space’, Methods in Enzymology #454: Computer Methods, M. Johnson and L. Brand (Eds), Elsevier, pp. 214–230, 2009.Google Scholar
  11. 11.
    Sloan, I. H., and Joe, S., Lattice Methods for Multiple Integration, Oxford University Press, Oxford, 1994.Google Scholar
  12. 12.
    Tanner, M. A., Tools for Statistical Inference, \({2}^{nd}\) Ed., Springer-Verlag, New York, 1993.Google Scholar
  13. 13.
    Van Dongen, H. P. A., Baynard, M. D., Maislin, G., and Dinges, D. F., ‘Systematic interindividual differences in neurobehavioral impairment from sleep loss: Evidence of trait-like differential vulnerability’, Sleep 27, pp. 423–433, 2004.Google Scholar
  14. 14.
    Van Dongen, H. P. A., and Dinges, D. F., ‘Sleep, Circadian rhythms, and Psychomotor Vigilance’, Clin. Sports Med. 24, pp. 237–249, 2005.Google Scholar
  15. 15.
    Van Dongen, H. P. A., Mott, C. G., Huang, J.-K., Mollicone, D. J., McKenzie, F. D., and Dinges, D. F., ‘Optimization of biomathematical model predictions for cognitive performance impairment in individuals: Accounting for unknown traits and uncertain states in homeostatic and circadian processes’, Sleep 30, pp. 1129–1143, 2007.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Mathematics DepartmentWashington State UniversityPullmanUSA

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