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Imputing censored data with desirable spatial covariance function properties using simulated annealing

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Abstract

When measurements of values that are less than the limit of detection are reported as not detected, the data are referred to as censored. The non-recording of values below the limit of detection is common in soil science research although modelling data affected by censoring can be problematic. This paper develops and tests a modified version of Spatial Simulated Annealing, called Simulated Annealing by Variogram and Histogram form, for drawing values for censored points given a mixed set of observed and censored data. The algorithm aims to maximise the goodness of fitting between the experimental and theoretical variograms (by allowing variation in its parameters) while the imputed values are constrained to a target histogram form. In practice, the experimental histogram is estimated by transforming the available data (interval and exact observations) to quantiles and fitting a plausible distribution. The theoretical distribution of the data is used to constrain the variogram fitting. The proposed simulated annealing method is designed to find the optimal spatial arrangement of values, given by the lowest errors in variogram and histogram fitting and kriging prediction. The accuracy of the method proposed is assessed on a simulated data set in which the censored point values are known and compared with the Spatial Simulated Annealing algorithm. According to the results obtained, the Simulated Annealing by Variogram and Histogram form (SAVH) approach can be recommended as a useful tool for the analysis of spatially distributed data with censoring.

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Notes

  1. The R project. www.r-project.org.

  2. The Apulia Region. http://bdt.regione.puglia.it/home.html.

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Acknowledgments

This study was supported by a fellowship from the Master and Back program financed by the Regional Sardinia Government, under agreement between the School of Geography, University of Southampton (UK) and the Dipartimento di Economia e Sistemi Arbori, University of Sassari (Italy). Thanks are due to the Apulia Regional Authority for Ecology and the Water Research Institute of the National Research Council for providing the data used in this study. Finally, the authors would like to acknowledge Dr. Edith Cheng at the University of Southampton, for inspiring the analysis and for helpful assistance.

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Authors and Affiliations

  1. Spatial Ecology and Epidemiology Group, University of Oxford, South Park Road, Oxford, OX1 3PS, UK

    L. Sedda

  2. School of Geography, University of Southampton, Highfield, Southampton, S017 1BJ, UK

    P. M. Atkinson

  3. IRSA-CNR, National Research Council, via F. De Blasio 5, 70123, Bari, Italy

    E. Barca & G. Passarella

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  1. L. Sedda
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Correspondence to L. Sedda.

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Sedda, L., Atkinson, P.M., Barca, E. et al. Imputing censored data with desirable spatial covariance function properties using simulated annealing. J Geogr Syst 14, 265–282 (2012). https://doi.org/10.1007/s10109-010-0145-1

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