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Metaheuristic kriging: A new spatial estimation method

Year 2017, Volume: 46 Issue: 3, 483 - 492, 01.06.2017

Abstract

Kriging is one of the most widely used spatial estimation method. In kriging estimation, weights assigned to the neighboring data are determined by minimizing the estimation error variance (EEV). Due to the minimization of the EEV the variability of the estimation result is lower than the original data. This paper presents the metaheuristic kriging (MK) as a new estimation method which has similar structure with kriging. But unlike kriging MK does not minimize the estimation error variance, instead converges to the EEV minimum which provides MK to increase the variability of the estimation. The MK uses the metaheuristic differential evolution algorithm in minimization of the EEV which gives names the MK. As a case study, Ordinary kriging (OK) and MK are applied to the Jura data set to estimate the spatial distribution of the Nickel (Ni) content. Results of the estimations are compared. Results shows that metaheuristic kriging over performed to the ordinary kriging in terms of variability of the estimation. The MK can be used any place where kriging is applied due to the variability of the estimation is higher than OK. The parameters used in MK are case specific so parameter tuning have to be made in the estimations to reach the desired outcomes. This study only exposes the univariate spatial estimation.

References

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Year 2017, Volume: 46 Issue: 3, 483 - 492, 01.06.2017

Abstract

References

  • Aldworth, J., and Noel C. Prediction of nonlinear spatial functionals. Journal of Statistical Planning and Inference 112(1) (2003): 3-41.
  • Chiles, J. and Blanchin, R. Contribution of geostatistics to the control of the geological risk in civil-engineering projects: The example of the Channel Tunnel. Applications of Statistics and Probability-Civil Engineering Reliability and Risk Analysis, M. Lemaire, JL Favre and A. Mebarki (Eds.), AA Balkema, Rotterdam, Netherlands, 1995. 2: p. 1213-1219.
  • Hevesi, J. A., Jonathan D. I., and Alan L. F. Precipitation estimation in mountainous terrain using multivariate geostatistics. Part I: structural analysis." Journal of applied me- teorology 31.7 (1992): 661-676.
  • Journel, A. G., and Huijbregts C. J. Mining geostatistics. Academic press, 1978.
  • Lu, A., Wang, J., Qin, X., Wang, K., Han, P., & Zhang, S. Multivariate and geostatistical analyses of the spatial distribution and origin of heavy metals in the agricultural soils in Shunyi, Beijing, China. Science of the total environment 425 (2012): 66-74.
  • Price, K., Rainer M. S., and Jouni A. L. Differential evolution: a practical approach to global optimization. Springer Science & Business Media, 2006.
  • Rivoirard, J., Simmonds, J., Foote, K. G., Fernandes, P., & Bez, N. Geostatistics for esti- mating fish abundance. John Wiley & Sons, 2008.
  • Storn, R., and Kenneth P. Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces. Vol. 3. Berkeley: ICSI, 1995.
  • Storn, R., and Kenneth P. Differential evolution a simple and efficient heuristic for global optimization over continuous spaces. Journal of global optimization 11(4) (1997): 341-359.
  • Webster, R., and Margaret A. O. Geostatistics for environmental scientists. John Wiley & Sons, 2007.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Statistics
Authors

Fırat Atalay This is me

Güneş Ertunç This is me

Publication Date June 1, 2017
Published in Issue Year 2017 Volume: 46 Issue: 3

Cite

APA Atalay, F., & Ertunç, G. (2017). Metaheuristic kriging: A new spatial estimation method. Hacettepe Journal of Mathematics and Statistics, 46(3), 483-492.
AMA Atalay F, Ertunç G. Metaheuristic kriging: A new spatial estimation method. Hacettepe Journal of Mathematics and Statistics. June 2017;46(3):483-492.
Chicago Atalay, Fırat, and Güneş Ertunç. “Metaheuristic Kriging: A New Spatial Estimation Method”. Hacettepe Journal of Mathematics and Statistics 46, no. 3 (June 2017): 483-92.
EndNote Atalay F, Ertunç G (June 1, 2017) Metaheuristic kriging: A new spatial estimation method. Hacettepe Journal of Mathematics and Statistics 46 3 483–492.
IEEE F. Atalay and G. Ertunç, “Metaheuristic kriging: A new spatial estimation method”, Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 3, pp. 483–492, 2017.
ISNAD Atalay, Fırat - Ertunç, Güneş. “Metaheuristic Kriging: A New Spatial Estimation Method”. Hacettepe Journal of Mathematics and Statistics 46/3 (June 2017), 483-492.
JAMA Atalay F, Ertunç G. Metaheuristic kriging: A new spatial estimation method. Hacettepe Journal of Mathematics and Statistics. 2017;46:483–492.
MLA Atalay, Fırat and Güneş Ertunç. “Metaheuristic Kriging: A New Spatial Estimation Method”. Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 3, 2017, pp. 483-92.
Vancouver Atalay F, Ertunç G. Metaheuristic kriging: A new spatial estimation method. Hacettepe Journal of Mathematics and Statistics. 2017;46(3):483-92.