New Computer Experiment Designs Using Continuum Random Cluster Point Process

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-21-2023-51
Published: Jun 8, 2023
Cite as:
Hichem Elmossaoui, Nadia Oukid, New Computer Experiment Designs Using Continuum Random Cluster Point Process, Int. J. Anal. Appl., 21 (2023), 51.

Main Article Content

Hichem Elmossaoui, Nadia Oukid

Abstract

In this paper, we propose a new approach for building computer experiment designs using the continuum random cluster point process, also referred to as the connected component Markov point process. Our method involves generating designs through the Markov Chain Monte Carlo method (MCMC) and the Random Walk Metropolis Hastings algorithm (RWMH algorithm), which can be easily scaled to meet various objectives. We have conducted a comprehensive study on the convergence of the Markov chain and compared our approach with existing computer experiment designs. Overall, our approach offers a novel and flexible solution for constructing computer experiment designs.

Article Details

References

  1. D.J. Daley, D. Vere-Jones, An Introduction to the Theory of Point Processes. Volume I: Elementary Theory and Methods, 2nd edn, Springer, Berlin, 1988.
  2. A.J. Baddeley, J. Møller, Nearest Neighbour Markov Point Processes and Random Sets. Int. Stat. Rev. 57 (1989), 89–121. https://doi.org/10.2307/1403381.
  3. A.J. Baddeley, M.N.M. van Lieshout, Area-Interaction Point Processes, Ann. Inst. Stat. Math. 47 (1995), 601–619. https://doi.org/10.1007/bf01856536.
  4. Y.C. Chin, A.J. Baddeley, On Connected Component Markov Point Processes, Adv. Appl. Probab. 31 (1999), 279–282. https://doi.org/10.1239/aap/1029955135.
  5. B.D. Ripley, F.P. Kelly, Markov Point Processes, J. Lond. Math. Soc. s2-15 (1977), 188–192. https://doi.org/10.1112/jlms/s2-15.1.188.
  6. J. Franco, Planification d’Expériences Numériques en Phase Exploratoire pour des Codes de Calculs Simulant des Phénomènes Complexes. Doctoral Thesis, l’Ecole Nationale Supérieure des Mines de SaintEtienne, France, 2008.
  7. H. Elmossaoui, N. Oukid, F. Hannane, Construction of Computer Experiment Designs Using Marked Point Processes, Afr. Mat. 31 (2020), 917–928. https://doi.org/10.1007/s13370-020-00770-9.
  8. H. Elmossaoui, Contribution à la Méthodologie de la Recherche Expérimentale, Doctoral Thesis, University Saad Dahleb, Blida, Algeria, 2020.
  9. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, Equation of State Calculations by Fast Computing Machines, J. Chem. Phys. 21 (1953), 1087–1092. https://doi.org/10.1063/1.1699114.
  10. W.K. Hastings, Monte Carlo Sampling Methods Using Markov Chains and Their Applications, Biometrika. 57 (1970), 97–109. https://doi.org/10.1093/biomet/57.1.97.
  11. A. Baddeley, J. Møller, A.G. Pakes, Properties of Residuals For Spatial Point Processes, Ann. Inst. Stat. Math. 60 (2007), 627–649. https://doi.org/10.1007/s10463-007-0116-6.
  12. S. Chib, E. Greenberg, Understanding the Metropolis-Hastings Algorithm, Amer. Stat. 49 (1995), 327-355. https://doi.org/10.2307/2684568.
  13. S. Chib, E. Greenberg, Markov Chain Monte Carlo Simulation Methods in Econometrics, Econ. Theory. 12 (1996), 409–431. https://doi.org/10.1017/s0266466600006794.
  14. E. Senata, Non-Negative Matrices and Markov Chains, 2nd edition. Springer, New York Heidelberg Berlin, 1981.
  15. G. Winkler, Image Analysis Random Fields and Dynamic Monte Carlo Methods, Springer, Berlin, 1995.
  16. R.L. Dobrushin, Central Limit Theorem for Nonstationary Markov Chains. I, Theory Probab. Appl. 1 (1956), 65–80. https://doi.org/10.1137/1101006.
  17. M. Gunzburger, J. Burkardt, Uniformity Measures for Point Samples in Hypercubes. (2004). https://people.sc.fsu.edu/~jburkardt/publications/gb_2004.pdf.
  18. M.E. Johnson, L.M. Moore, D. Ylvisaker, Minimax and Maximin Distance Designs, J. Stat. Plan. Inference. 26 (1990), 131–148. https://doi.org/10.1016/0378-3758(90)90122-b.
  19. T.T. Warnock, Computational Investigations of Low-Discrepancy Point Sets II. In: Niederreiter H., and Shiue P.JS. (eds) Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing. Lecture Notes in Statistics, 106. Springer, New York, 1995.
  20. J.H. Halton, On the Efficiency of Certain Quasi-Random Sequences of Points in Evaluating Multi-Dimensional Integrals, Numer. Math. 2 (1960), 84–90. https://doi.org/10.1007/bf01386213.
  21. I.M. Sobol, Uniformly Distributed Sequences with an Additional Uniform Property, USSR Comput. Math. Math. Phys. 16 (1976), 236–242. https://doi.org/10.1016/0041-5553(76)90154-3.
  22. H. Faure, Discrépance de Suites Associées à un Système de Numération (en Dimension s), Acta Arith. 41 (1982), 337–351. https://doi.org/10.4064/aa-41-4-337-351.
  23. W.L. Loh, On Latin Hypercube Sampling, Ann. Stat. 24 (1996), 2058-2080. https://doi.org/10.1214/aos/1069362310.
  24. M.D. Morris, T.J. Mitchell, Exploratory Designs for Computational Experiments, J. Stat. Plan. Inference. 43 (1995), 381–402. https://doi.org/10.1016/0378-3758(94)00035-t.
  25. M.C. Shewry, H.P. Wynn, Maximum Entropy Sampling, J. Appl. Stat. 14 (1987), 165–170. https://doi.org/10.1080/02664768700000020.