New Applications of Computational Intelligence for Constructing Predictive or Optimal Statistical Decisions under Parametric Uncertainty | Automatic Control and Computer Sciences
Skip to main content
Springer Nature Link
Log in

New Applications of Computational Intelligence for Constructing Predictive or Optimal Statistical Decisions under Parametric Uncertainty

  • Published:
Automatic Control and Computer Sciences Aims and scope Submit manuscript

Abstract

The technique used here emphasizes pivotal quantities and ancillary statistics relevant for obtaining tolerance limits (or confidence intervals) for anticipated outcomes of applied stochastic models under parametric uncertainty and is applicable whenever the statistical problem is invariant under a group of transformations that acts transitively on the parameter space. It does not require the construction of any tables and is applicable whether the experimental data are complete or Type II censored. The exact tolerance limits on order statistics associated with sampling from underlying distributions can be found easily and quickly making tables, simulation, Monte-Carlo estimated percentiles, special computer programs, and approximation unnecessary. The proposed technique is based on a probability transformation and pivotal quantity averaging. It is conceptually simple and easy to use. The discussion is restricted to one-sided tolerance limits. Finally, we give practical numerical examples, where the proposed analytical methodology is illustrated in terms of the exponential distribution. Applications to other log-location-scale distributions could follow directly.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

REFERENCES

  1. Nechval, N.A. and Vasermanis, E.K., Improved Decisions in Statistics, Riga: Izglitibas Soli, 2004.

    Google Scholar 

  2. Nechval, N.A., Berzins, G., and Nechval, K.N., Improved estimation of state of stochastic systems via invariant embedding technique, WSEAS Trans. Math., 2008, vol. 7, no. 4, pp. 141–159.

    MathSciNet  Google Scholar 

  3. Nechval, N.A., Nechval, K.N., Danovich, V., and Liepins, T., Optimization of new-sample and within-sample prediction intervals for order statistics, Proc. 2011 World Congress in Computer Science, Computer Engineering, and Applied Computing, WORLDCOMP’11, Las Vegas: CSREA Press, 2011, pp. 91–97.

  4. Nechval, N.A., Nechval, K.N., and Berzins, G., A new technique for intelligent constructing exact γ-content tolerance limits with expected (1 – α)-confidence on future outcomes in the Weibull case using complete or type II censored data, Autom. Control Comput. Sci., 2018, vol. 52, no. 6, pp. 476–488. https://doi.org/10.3103/s0146411618060081

    Article  Google Scholar 

  5. Nechval, N.A., Berzins, G., and Nechval, K.N., Intelligent technique of constructing exact statistical tolerance limits to predict future outcomes under parametric uncertainty for prognostics and health management of complex systems, Int. J. Adv. Comput. Sci. Its Appl., 2019, vol. 9, pp. 30–47.

    Google Scholar 

  6. Nechval, N.A., Berzins, G., Nechval, K.N., and Krasts, J., A new technique of intelligent constructing unbiased prediction limits on future order statistics coming from an inverse gaussian distribution under parametric uncertainty, Autom. Control Comput. Sci., 2019, vol. 53, no. 3, pp. 223–235. https://doi.org/10.3103/s0146411619030088

    Article  Google Scholar 

  7. Nechval, N.A., Berzins, G., and Nechval, K.N., A novel intelligent technique for product acceptance process optimization on the basis of misclassification probability in the case of log-location-scale distributions, Advances and Trends in Artificial Intelligence: From Theory to Practice. IEA/AIE 2019, Wotawa, F., Friedrich, G., Pill, I., Koitz-Hristov, R., and Ali, M., Eds., Lecture Notes in Computer Science, vol. 11606, Cham: Springer, 2019, pp. 801–818. https://doi.org/10.1007/978-3-030-22999-3_68

  8. Nechval, N.A., Berzins, G., and Nechval, K.N., A novel intelligent technique of invariant statistical embedding and averaging via pivotal quantities for optimization or improvement of statistical decision rules under parametric uncertainty, WSEAS Trans. Math., 2020, vol. 19, pp. 17–38. https://doi.org/10.37394/23206.2020.19.3

    Article  Google Scholar 

  9. Nechval, N.A., Berzins, G., Nechval, K.N., and Danovics, V., A novel technique for optimization of statistical decisions under parametric uncertainty through invariant statistical embedding and averaging in terms of pivotal quantities, J. Phys.: Conf. Ser., 2020, vol. 1603, no. 1, p. 012022. https://doi.org/10.1088/1742-6596/1603/1/012022

    Article  Google Scholar 

  10. Nechval, N.A., Berzins, G., Nechval, K.N., and Danovics, V., Intelligent constructing optimal airline seat protection levels for multiple nested fare classes of single-leg flights, J. Phys.: Conf. Ser., 2020, vol. 1603, no. 1, p. 012023. https://doi.org/10.1088/1742-6596/1603/1/012023

    Article  Google Scholar 

  11. Nechval, N.A., Berzins, G., and Nechval, K.N., A new technique of invariant statistical embedding and averaging via pivotal quantities for intelligent constructing efficient statistical decisions under parametric uncertainty, Autom. Control Comput. Sci., 2020, vol. 54, no. 3, pp. 191–206. https://doi.org/10.3103/s0146411620030049

    Article  Google Scholar 

  12. Nechval, N.A., Berzins, G., Nechval, K.N., and Tsaurkubule, Zh., A new unified computational approach to intelligent constructing shortest-length or equal tails confidence intervals under parametric uncertainty, J. Appl. Math. Comput., 2020, vol. 4, no. 4, pp. 206–223. https://doi.org/10.26855/jamc.2020.12.012

    Article  Google Scholar 

  13. Nechval, N.A., Berzins, G., and Nechval, K.N., Cost-effective planning reliability-based inspections of fatigued structures in the case of log-location-scale distributions of lifetime under parametric uncertainty, Proc. 30th Eur. Safety and Reliability Conf. and 15th Probabilistic Safety Assessment and Management Conf., Baraldi, P., Di Maio, F., and Zio, E., Eds., Venice: Research Publishing Services, 2020, pp. 455–462. https://doi.org/10.3850/978-981-14-8593-0_3664-cd

  14. Nechval, N.A., Intelligent constructing exact tolerance limits for prediction of future outcomes under parametric uncertainty, Encyclopedia of Information Science and Technology, USA: IGI Global, 2020, pp. 701–729. https://doi.org/10.4018/978-1-7998-3479-3.ch049

    Book  Google Scholar 

  15. Nechval, N.A., Berzins, G., Nechval, K.N., and Tsaurkubule, Z., A novel unified computational approach to constructing shortest-length or equal tails confidence intervals in terms of pivotal quantities and quantile functions, Autom. Control Comput. Sci., 2021, vol. 55, no. 1, pp. 66–84. https://doi.org/10.3103/s0146411621010065

    Article  Google Scholar 

  16. Nechval, N.A., Berzinsh, G., and Nechval, K.N., A new technique of invariant statistical embedding and averaging in terms of pivots for improvement of statistical decisions under parametric uncertainty, Advances in Parallel & Distributed Processing, and Applications, Arabnia, H.R. et al., Eds., Transactions on Computational Science and Computational Intelligence, Cham: Springer, 2020, pp. 257–274. https://doi.org/10.1007/978-3-030-69984-0_20

  17. Nechval, N.A., Berzins, G., and Nechval, K.N., A new pivot-based approach to constructing prediction limits and shortest-length or equal tails confidence intervals for future outcomes under parametric uncertainty, Proc. 31st Eur. Safety and Reliability Conf. (ESREL 2021), Angers, France, 2021, Castanier, B., Cepin, M., Bigaud, D., and Berenguer, Ch., Eds., Singapore: Research Publishing Services, 2021, pp. 2886–2893. https://doi.org/10.3850/978-981-18-2016-8_419-cd

  18. Nechval, N.A., Berzins, G., Nechval, K.N., and Tsaurkubule, Zh., Intelligent constructing efficient statistical decisions via pivot-based elimination of unknown (nuisance) parameters from underlying models, Autom. Control Comput. Sci., 2021, vol. 55, no. 5, pp. 469–489. https://doi.org/10.3103/s0146411621050060

    Article  Google Scholar 

  19. Nechval, N.A., Berzins, G., Nechval, K.N., Moldovan, M., Danovics, V., and Bausova, I., Innovative technique for computing shortest length and/or equal tails confidence intervals in reliability and safety under parametric uncertainty, Pattern Recognition and Information Processing (PRIP’2021): Proc. 15th Int. Conf., Minsk, 2021, Minsk: United Inst. of Informatics Problems of the Natl. Acad. of Sci. Belarus, 2021, pp. 206–210.

  20. Nechval, N.A., Berzins, G., and Nechval, K.N., A new unified computational method for finding confidence intervals of shortest length and/or equal tails under parametric uncertainty, 2021 Int. Conf. on Computational Science and Computational Intelligence (CSCI), Las Vegas, 2021, IEEE, 2021, pp. 533–539. https://doi.org/10.1109/csci54926.2021.00046

  21. Nechval, N.A., Berzins, G., and Nechval, K.N., A new simple computational method of simultaneous constructing and comparing confidence intervals of shortest length and equal tails for making efficient decisions under parametric uncertainty, Proceedings of Sixth International Congress on Information and Communication Technology, Yang, X.-S., Sherratt, S., Dey, N., and Joshi, A., Eds., Lecture Notes in Network and Systems, vol. 235, Singapore: Springer, 2021, pp. 473–482. https://doi.org/10.1007/978-981-16-2377-6_44

  22. Nechval, N.A., Berzins, G., Nechval, K.N., Tsaurkubule, Zh., and Moldovan, M., A new intelligent method for eliminating unknown (nuisance) parameters from underlying models as an alternative to the bayesian approach, J. Appl. Math. Comput., 2022, vol. 6, no. 1, pp. 53–65. https://doi.org/10.26855/jamc.2022.03.008

    Article  Google Scholar 

  23. Nechval, N.A., Berzins, G., and Nechval, K.N., Intelligent computational approach to constructing adequate statistical decisions under parametric uncertainty of applied stochastic models, Proc. 2022 Int. Conf. on Computational Science and Computational Intelligence, Las Vegas, 2022, IEEE, 2022, pp. 522–529. https://doi.org/10.1109/CSCI58124.2022.00023

  24. Nechval, N.A., Berzins, G., and Nechval, K.N., Adequate mathematical models of the cumulative distribution function of order statistics to construct accurate tolerance limits and confidence intervals of the shortest length or equal tails, WSEAS Trans. Math., 2023, vol. 22, pp. 154–166. https://doi.org/10.37394/23206.2023.22.20

    Article  Google Scholar 

  25. Nechval, N.A., Berzins, G., and Nechval, K.N., Optimal statistical estimation and dynamic adaptive control of airline seat protection levels for several nested fare classes under parametric uncertainty of customer demand models, WSEAS Trans. Math., 2023, vol. 22, pp. 395–408. https://doi.org/10.37394/23206.2023.22.47

    Article  Google Scholar 

  26. Nechval, N.A., Berzins, G., and Nechval, K.N., A unified technique for prediction and optimization of future outcomes under parametric uncertainty via pivotal quantities and ancillary statistics, Autom. Control Comput. Sci., 2023, vol. 57, no. 3, pp. 234–257. https://doi.org/10.3103/s0146411623030070

    Article  Google Scholar 

  27. Nechval, N.A., Berzins, G., and Nechval, K.N., A novel computational intelligence approach to making efficient decisions under parametric uncertainty of practical models and its applications to industry 4.0, Advanced Signal Processing for Industry, vol. 1: Evolution, Communication Protocols, and Applications in Manufacturing Systems, IOP Publishing, 2023, pp. 1–40. https://doi.org/10.1088/978-0-7503-5247-5ch7

Download references

ACKNOWLEDGMENTS

The authors would like to thank the anonymous reviewers for their valuable comments that helped to improve the presentation of this paper.

Author information

Authors and Affiliations

  1. BVEF Research Institute, University of Latvia, LV-1586, Riga, Latvia

    Nicholas Nechval & Gundars Berzins

  2. Transport and Telecommunication Institute, LV-1019, Riga, Latvia

    Konstantin Nechval

Authors
  1. Nicholas Nechval
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gundars Berzins
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Konstantin Nechval
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nicholas Nechval.

Ethics declarations

The authors declare that they have no conflicts of interest.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nicholas Nechval, Berzins, G. & Nechval, K. New Applications of Computational Intelligence for Constructing Predictive or Optimal Statistical Decisions under Parametric Uncertainty. Aut. Control Comp. Sci. 57, 473–489 (2023). https://doi.org/10.3103/S0146411623050085

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0146411623050085

Keywords:

Search

Navigation