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

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Imputing censored data with desirable spatial covariance function properties using simulated annealing. / Sedda, L.; Atkinson, P. M.; Barca, E.; Passarella, G.

In: Journal of Geographical Systems, Vol. 14, No. 3, 07.2012, p. 265-282.

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Sedda, L. ; Atkinson, P. M. ; Barca, E. ; Passarella, G. / Imputing censored data with desirable spatial covariance function properties using simulated annealing. In: Journal of Geographical Systems. 2012 ; Vol. 14, No. 3. pp. 265-282.

Bibtex

@article{e75aa09cbf814532946b454132867094,
title = "Imputing censored data with desirable spatial covariance function properties using simulated annealing",
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.",
keywords = "Detection limit, Annealing simulation, Variogram and histogram fitting, Cross-validation, Kriging, MAXIMUM-LIKELIHOOD-ESTIMATION, SOIL PROPERTIES, DATA AUGMENTATION, ASYMMETRIC DATA, MODEL, VARIOGRAMS, REGRESSION, ALGORITHM, INTERPOLATION, DISTRIBUTIONS",
author = "L. Sedda and Atkinson, {P. M.} and E. Barca and G. Passarella",
year = "2012",
month = jul,
doi = "10.1007/s10109-010-0145-1",
language = "English",
volume = "14",
pages = "265--282",
journal = "Journal of Geographical Systems",
issn = "1435-5930",
publisher = "Springer Verlag",
number = "3",

}

RIS

TY - JOUR

T1 - Imputing censored data with desirable spatial covariance function properties using simulated annealing

AU - Sedda, L.

AU - Atkinson, P. M.

AU - Barca, E.

AU - Passarella, G.

PY - 2012/7

Y1 - 2012/7

N2 - 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.

AB - 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.

KW - Detection limit

KW - Annealing simulation

KW - Variogram and histogram fitting

KW - Cross-validation

KW - Kriging

KW - MAXIMUM-LIKELIHOOD-ESTIMATION

KW - SOIL PROPERTIES

KW - DATA AUGMENTATION

KW - ASYMMETRIC DATA

KW - MODEL

KW - VARIOGRAMS

KW - REGRESSION

KW - ALGORITHM

KW - INTERPOLATION

KW - DISTRIBUTIONS

U2 - 10.1007/s10109-010-0145-1

DO - 10.1007/s10109-010-0145-1

M3 - Journal article

VL - 14

SP - 265

EP - 282

JO - Journal of Geographical Systems

JF - Journal of Geographical Systems

SN - 1435-5930

IS - 3

ER -