Article Sidebar

Download
PDF
Statistic
Read Counter : 597 Download : 573

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Main Article Content

Abstract

Kriging is a statistical approach for analyzing computer experiments. Kriging models can be used as fast running surrogate models for computationally expensive computer codes. Kriging models can be built using different methods, the maximum likelihood estimation method and the leave-one-out cross validation method. The objective of this paper is to evaluate and compare these different methods for building kriging models. These evaluation and comparison are achieved via some measures that test the assumptions that are used in building kriging models. We apply kriging models that are built based on the two different methods on a real high dimensional example of a computer code. We demonstrate our evaluation and comparison through some measures on this real computer code.

Keywords

Kriging models Computer codes Maximum likelihood estimation Cross validation Robot Arm function

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following License

CC BY: This license allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.

 

Author Biographies

Younus Hazim Al-Taweel, University of Mosul

Department of Mathematics, College of Education for Pure Science

Najlaa Sadeek, University of Mosul

Department of Mathematics, College of Education for Pure Science
How to Cite
Al-Taweel, Y. H., & Sadeek, N. (2020). A comparison of different methods for building Bayesian kriging models. Pakistan Journal of Statistics and Operation Research, 16(1), 73-82. https://doi.org/10.18187/pjsor.v16i1.2921
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Abdallah, I., Lataniotis, C., and Sudret, B. (2019). Parametric hierarchical kriging for multi-ï¬delity aeroservoelastic simulators application to extreme loads on wind turbines. Probabilistic Engineering Mechanics, 55:67-77.
  2. An, J. and Owen, A. (2001). Quasi-regression. Journal of complexity, 17(4):588-607.
  3. Bastos, L. S. and O'Hagan, A. (2009). Diagnostics for gaussian process emulators. Technometrics, 51(4):425 438.
  4. Drignei, D. (2008). Fast statistical surrogates for dynamical 3d computer models of brain tumors. Journal of Computational and Graphical Statistics, 17(4):844-859.
  5. Fang, K.-T., Li, R., and Sudjianto, A. (2010). Design and modeling for computer experiments. CRC Press.
  6. Fentanes, J. P., Badiee, A., Duckett, T., Evans, J., Pearson, S., and Cielniak, G. (2018). Kriging-based robotic exploration for soil moisture mapping using a cosmic-ray sensor. arXiv preprint arXiv:1811.05384.
  7. Forrester, A. I., Sobester, A., and Keane, A. J. (2007). Multi-ï¬delity optimization via surrogate modelling. Proceedings of the royal society a: mathematical, physical and engineering sciences, 463(2088):3251-3269.
  8. Hung, Y., Joseph, V. R., and Melkote, S. N. (2009). Design and analysis of computer experiments with branching and nested factors. Technometrics, 51(4):354-365.
  9. Karaman, M. R., Susam, T., Er, F., Yaprak, S., and Karkacıer, O. (2009). Simulation of organic matter variability on a sugarbeet ï¬eld using the computer based geostatistical methods. World Academy of Sci, 56:594-598.
  10. Kolachalama, V. B., Bressloff, N. W., and Nair, P. B. (2007). Mining data from hemodynamic simulations via Bayesian emulation. Biomedical engineering online, 6(1):47.
  11. Le Gratiet, L. and Garnier, J. (2014). Recursive co-kriging model for design of computer experiments with multiple levels of ï¬delity. International Journal for Uncertainty Quantiï¬cation, 4(5).
  12. Li, R. and Sudjianto, A. (2005). Analysis of computer experiments using penalized likelihood in gaussian kriging models. Technometrics, 47(2):111-120.
  13. Ly, S., Charles, C., and Degre, A. (2013). Different methods for spatial interpolation of rainfall data for operational hydrology and hydrological modeling at watershed scale: a review. Biotechnologie, Agronomie, Societeet Environnement, 17(2):392-406.
  14. Martin, J. D. and Simpson, T. W. (2005). Use of kriging models to approximate deterministic computer models. AIAA journal, 43(4):853-863.
  15. Overstall, A. M. and Woods, D. C. (2016). Multivariate emulation of computer simulators: model selection and diagnostics with application to a humanitarian relief model. Journal of the Royal Statistical Society: Series C (Applied Statistics).
  16. Rossouw, R., Coetzer, R., and Pretorius, P. (2010). Simulation experiments for maximising the availability of a commercial octene production facility. ORiON, 26(1):53-77.
  17. Roustant, O., Ginsbourger, D., and Deville, Y. (2012). Dicekriging, diceoptim: Two r packages for the analysis of computer experiments by kriging-based metamodeling and optimization.
  18. Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P. (1989). Design and analysis of computer experiments. Statistical Science, 4(4):409-423.
  19. Santner, T. J., Williams, B. J., Notz, W., and Williams, B. J. (2003). The design and analysis of computer experiments, volume 1. Springer.