IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i15p2397-d1447353.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/15/2397/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/15/2397/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. ., 1996. "Concepts of Rationality as Foundations of Economic Theory," Chapters, in: Bounded Rationality and Economic Evolution, chapter 2, pages 21-34, Edward Elgar Publishing.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ferrari, Pablo A. & Fernández, Roberto & Garcia, Nancy L., 2002. "Perfect simulation for interacting point processes, loss networks and Ising models," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 63-88, November.
    2. Liqui-Lung, C., 2023. "Intersectionality in Individual Choice Behavior: Pitfalls and Opportunities," Janeway Institute Working Papers 2321, Faculty of Economics, University of Cambridge.
    3. Glenna F Nightingale & Kevin N Laland & William Hoppitt & Peter Nightingale, 2015. "Bayesian Spatial NBDA for Diffusion Data with Home-Base Coordinates," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-19, July.
    4. Daniel, Jeffrey & Horrocks, Julie & Umphrey, Gary J., 2018. "Penalized composite likelihoods for inhomogeneous Gibbs point process models," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 104-116.
    5. Gregori, P. & van Lieshout, M. N. M. & Mateu, J., 2004. "Mixture formulae for shot noise weighted point processes," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 311-320, May.
    6. Chen, Jiaxun & Micheas, Athanasios C. & Holan, Scott H., 2022. "Hierarchical Bayesian modeling of spatio-temporal area-interaction processes," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    7. Ian W. Renner & David I. Warton, 2013. "Equivalence of MAXENT and Poisson Point Process Models for Species Distribution Modeling in Ecology," Biometrics, The International Biometric Society, vol. 69(1), pages 274-281, March.
    8. Grabarnik, Pavel & Särkkä, Aila, 2009. "Modelling the spatial structure of forest stands by multivariate point processes with hierarchical interactions," Ecological Modelling, Elsevier, vol. 220(9), pages 1232-1240.
    9. Genet, Astrid & Grabarnik, Pavel & Sekretenko, Olga & Pothier, David, 2014. "Incorporating the mechanisms underlying inter-tree competition into a random point process model to improve spatial tree pattern analysis in forestry," Ecological Modelling, Elsevier, vol. 288(C), pages 143-154.
    10. T. Rajala & D. J. Murrell & S. C. Olhede, 2018. "Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1237-1273, November.
    11. Renshaw, Eric & Mateu, Jorge & Saura, Fuensanta, 2007. "Disentangling mark/point interaction in marked-point processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3123-3144, March.
    12. David Dereudre & Frédéric Lavancier & Kateřina Staňková Helisová, 2014. "Estimation of the Intensity Parameter of the Germ-Grain Quermass-Interaction Model when the Number of Germs is not Observed," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 809-829, September.
    13. Nicolas Picard & Avner Bar‐Hen & Frédéric Mortier & Joël Chadœuf, 2009. "The Multi‐scale Marked Area‐interaction Point Process: A Model for the Spatial Pattern of Trees," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 23-41, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:15:p:2397-:d:1447353. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.