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New Computer Experiment Designs with Area-Interaction Point Processes

Author

Listed:
  • Ahmed Ait Ameur

    (LAMDA-RO Laboratory, Department of Mathematics, Faculty of Sciences, University Saad Dahlab Blida1, Soumâa BP 270, Blida, Algeria
    These authors contributed equally to this work.)

  • Hichem Elmossaoui

    (LAMDA-RO Laboratory, Department of Mathematics, Faculty of Sciences, University Saad Dahlab Blida1, Soumâa BP 270, Blida, Algeria
    These authors contributed equally to this work.)

  • Nadia Oukid

    (LAMDA-RO Laboratory, Department of Mathematics, Faculty of Sciences, University Saad Dahlab Blida1, Soumâa BP 270, Blida, Algeria
    These authors contributed equally to this work.)

Abstract

This article presents a novel method for constructing computer experiment designs based on the theory of area-interaction point processes. This method is essential for capturing the interactions between different elements within a modeled system, offering a more flexible and adaptable approach compared with traditional mathematical modeling. Unlike conventional rough models that rely on simplified equations, our method employs the Markov Chain Monte Carlo (MCMC) method and the Metropolis–Hastings algorithm combined with Voronoi tessellations. It uses a new dynamic called homogeneous birth and death dynamics of a set of points to generate the designs. This approach does not require the development of specific mathematical models for each system under study, making it universally applicable while achieving comparable results. Furthermore, we provide an in-depth analysis of the convergence properties of the Markov Chain to ensure the reliability of the generated designs. An expanded literature review situates our work within the context of existing research, highlighting its unique contributions and advancements. A comparison between our approach and other existing computer experiment designs has been performed.

Suggested Citation

  • Ahmed Ait Ameur & Hichem Elmossaoui & Nadia Oukid, 2024. "New Computer Experiment Designs with Area-Interaction Point Processes," Mathematics, MDPI, vol. 12(15), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:15:p:2397-:d:1447353
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    References listed on IDEAS

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    1. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(3), pages 409-431, August.
    2. ., 1996. "Concepts of Rationality as Foundations of Economic Theory," Chapters, in: Bounded Rationality and Economic Evolution, chapter 2, pages 21-34, Edward Elgar Publishing.
    3. A. Baddeley & M. Lieshout, 1995. "Area-interaction point processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 601-619, December.
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