Conditional Bias in Kriging: Let’s Keep It

Nowak, Marcel; Leuangthong, Oy

doi:10.1007/978-3-319-46819-8_20

Cited by 6 publications

(6 citation statements)

References 5 publications

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“…In long-term mine planning, which is the focus of this work, the challenge is not to find the most accurate value of a specific block, but rather render it possible to estimate some tonnage and grade above some cutoff. The focus on minimizing the conditional bias is not important in this case as argued by Nowak and Leuangthong (2017). Further, Armstrong (1998) warned about using a smoothed block model for long-term mine planning.…”

Section: Mineral Resource Estimation and Classificationmentioning

confidence: 99%

Application of Soft Data in Nodule Resource Estimation

Ellefmo

Kühn

2020

Nat Resour Res

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Minerals and metals are of uttermost importance in our society, and mineral resources on and beneath the deep ocean floor represent a huge potential. Deciding whether mining from the deep ocean floor is financially, environmentally and technologically feasible requires information. Due to great depths and harsh conditions, this information is expensive and time and resource consuming to obtain. It is therefore important to use every piece of data in an optimum way. In this study, data retrieved from images and expert knowledge were used to estimate minimum and maximum nodule abundances at image locations from an area in the Clarion-Clipperton-Zone of the equatorial North East Pacific. From the minimum and maximum values, box cores and the spatial correlation quantified through variogram, a conditional expectation and associated uncertainty were obtained through the Gibbs sampler. The conditional expectation and the uncertainty were used with the assumed certain abundance data from the box cores in a kriging exercise to obtain better informed estimates of the block by block abundance. The quality assessment of the estimations was done based on distance criterion and on kriging quality indicators like the slope of regression and the weight of the mean. From the original image locations, alternative image configurations were tested, and it was shown that such alternatives produce better estimates, without extra costs. Future improvements will focus on improving the estimation of the minimum and the maximum values at image locations.

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Section: Mineral Resource Estimation and Classificationmentioning

confidence: 99%

Application of Soft Data in Nodule Resource Estimation

Ellefmo

Kühn

2020

Nat Resour Res

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“…As long as an estimator may be conditionally unbiased, the block estimates histogram will surely be smoothed and vice versa. Nowak and Leuangthong (2016) warned that both SR and KE should be viewed with caution. As these authors defend the acceptance of conditional bias for resource models, the SR and KE optimisation would defeat this purpose.…”

Section: Key Conceptsmentioning

confidence: 99%

“…The SR is also directly related to the issue of conditional bias in kriging. Nowak and Leuangthong (2016) suggest that it is preferable to have conditionally biased estimates (higher variance) than conditionally unbiased estimates (SR closest to one). Other authors (Deutsch et al 2014) relate the bias-variance trade-off to the objective of the estimate.…”

Section: Introductionmentioning

confidence: 99%

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Kriging parameter optimisation: global versus local search strategies

Fonseca

Costa

Rubio

et al. 2021

Applied Earth Science

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Kriging methods require parameters to define search strategy (kriging neighbourhood). These parameters affect the precision and accuracy of its estimates. Frequently, the choice of these parameters is merely subjective. Some practitioners prioritise estimates that lead to models with a reduced smoothing effect or a regression slope as close as possible to one. However, it is prevalent to use the same kriging neighbourhood or search strategy for all blocks estimated within a stationary domain. This study presents a contribution that challenges this concept by using a block-by-block optimisation approach focused on the localised kriging parameter optimisation (LKPO) methodology. A comparative study is carried out, and some of the metrics analysed include the kriging efficiency and the slope of regression (typical in optimising methodologies in the mining industry). The results indicate that the LKPO methodology provides more accurate and precise estimates than those based on a global kriging neighbourhood.

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“…In its simplest form, practitioners select the interpolant type (OK or ID2-ID3 most of the time), the minimum and maximum number of points (composites) used for the interpolation, and in some cases, the number of points per octant or maximum number of points per drill-hole. Isaaks (2005) A comparison of indirect lognormal and discrete Gaussian change of support methods Rossi and Deutsch (2013), and Nowak and Leuangthong (2017) stated that during prefeasibility and feasibility studies, resource estimates should seek to respect the global recoverable resources (inferred from COS) rather than providing precise local estimates. Doing so, the estimates are necessarily conditionally biased (David, 1977, chapter 11).…”

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confidence: 99%