Applied Bayesian modeling for assessment of interpretation uncertainty in spatial domains. (English) Zbl 1444.62068

Rahman, Azizur (ed.), Statistics for data science and policy analysis. Proceedings of the applied statistics and policy analysis conference 2019, ASPAC2019, Wagga Wagga, Australia, September 5–6, 2019. Singapore: Springer. 3-13 (2020).
Summary: In the mining industry, code compliant reporting standards for public announcements have been developed setting minimum standards for public reporting of exploration results and mineral resources. These include an assessment of the quality and confidence in the data and work carried out since public reporting aims to provide information that is material, transparent and competent to investors.
There are four phases required to estimate an mineral resource (preparation, investigation, model creation and validation), and estimation is highly dependent on the accuracy of the preparation stage which is a result of the quality of the geological interpretation given for the mineralization process and current spatial location. Performance of feasibility studies in mining projects has been poor, with a 50% failure rate, 17% of failures are attributable to issues in geological interpretation. This interpretation seeks to spatially define geologically homogenous areas in the resource (spatial domains), corresponding to a single statistical population with a single orientation, where possible. In the estimation workflow, the creation of the spatial domain presents a challenge in terms of assessing the uncertainty in the geological interpretation often due to the manual and subjective interpretation used to guide its creation as well as in spatial domains with several mineralization overprint events.
The proposed work investigates a Bayesian method using multivariate quantitative data combined with qualitative data to assess the interpretation uncertainty of classification of borehole intervals to a spatial domain defined by a 3D ‘wireframe’ or ‘rock type’ model interpretation using either implicit or explicit modeling techniques.
For the entire collection see [Zbl 1443.62006].


62H11 Directional data; spatial statistics
62R07 Statistical aspects of big data and data science
62P30 Applications of statistics in engineering and industry; control charts


aplore3; brms; R
Full Text: DOI


[1] JORC: The JORC Code 2012 Edition, Joint Ore Reserves Committee of The Australasian Institute of Mining and Metallurgy, Australian Institute of Geoscientists and Minerals Council of Australia (JORC) (2012)
[2] Coombes, J.: The Art and Science of Resource Estimation, Australia (2008)
[3] Coombes, J.: I’D Like to be OK with MIK, UC?, Australia (2016)
[4] McCarthy, P.L.: Managing risk in feasibility studies. In: Edwards, A.C. (ed.) Mineral Resource and Ore Reserve Estimation: The AusIMM Guide to Good Practice. Monograph/Australasian Institute of Mining and Metallurgy 30, pp. 13-18. Australasian Institute of Metallurgy and Australasian Institute of Mining and Metallurgy, Carlton (2014)
[5] Noppé, M.: A framework for presenting and benchmarking resource projects. In: AusIMM Project Evaluation Conference Ausimm, Brisbane (2016)
[6] Caers, J.: Modeling Uncertainty in the Earth Sciences. Wiley, Hoboken (2011) · Zbl 1329.86001
[7] Galli, A., Murillo, E., and Thomann, J.: Dual kriging-its properties and its uses in direct contouring. Verly, G. et al., pp. 621-634 (1984)
[8] Mallet, J.-L.: Discrete smooth interpolation in geometric modelling. Comput. Aided Des. 24(4), 178-191 (1992) · Zbl 0808.65005
[9] Fouedjio, F., Hill, E.J., Laukamp, C.: Geostatistical clustering as an aid for ore body domaining: case study at the Rocklea Dome channel iron ore deposit, Western Australia. Appl. Earth Sci. 127(1), 15-29 (2018)
[10] Lark, R.M., et al.: A statistical assessment of the uncertainty in a 3-D geological framework model. Proc. Geol. Assoc. 124(6), 946-958 (2013)
[11] Arne, D.C., Mackie, R.A., Jones, S.A.: The use of property-scale portable X-ray fluorescence data in gold exploration: advantages and limitations. Geochem. Explor. Environ. Anal. 14(3), 233-244 (2014)
[12] Fisher, L., et al.: Resolution of geochemical and lithostratigraphic complexity: a workflow for application of portable X-ray fluorescence to mineral exploration. Geochem. Explor. Environ. Anal. 14(2), 149-159 (2014)
[13] Bourke, A., Ross, P.-S.: Portable X-ray fluorescence measurements on exploration drill-cores: comparing performance on unprepared cores and powders for ‘whole-rock’ analysis. Geochem. Explor. Environ. Anal. 16, 147-157 (2015)
[14] R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2018)
[15] Gelman, A.: Bayesian Data Analysis, 3rd edn. ed. Chapman & Hall/CRC Texts in Statistical Science, ed. A. Gelman. CRC Press, Boca Raton (2013).
[16] Hosmer, D.W.: Applied Logistic Regression. 3rd edn. ed. Wiley Series in Probability and Statistics, ed. S. Lemeshow and R.X. Sturdivant. Wiley, Hoboken (2013) · Zbl 1276.62050
[17] Rahman, A., et al.: An assessment of the effects of prior distributions on the Bayesian predictive inference. Int. J. Stat. Probab. 5(5), 31 (2016)
[18] Horta, A., et al.: Geostatistical data integration model for contamination assessment. Math. Geosci. 45(5), 575-590 (2013) · Zbl 1321.86022
[19] Buddhachat, K., et al.: Distinguishing real from fake ivory products by elemental analyses: a Bayesian hybrid classification method. Forensic Sci. Int. 272, 142-149 (2017)
[20] Bürkner, P.-C.: brms: an R package for Bayesian multilevel models using Stan. J. Stat. Softw. 80(1), 1-28 (2017)
[21] Neal, R.M.: MCMC using Hamiltonian dynamics. In: Handbook of Markov Chain Monte Carlo (2011) · Zbl 1229.65018
[22] Team, S.D.: Stan Modeling Language: User’s Guide and Reference Manual. Version (2018)
[23] Brooks, S., et al.: Handbook of Markov Chain Monte Carlo. CRC Press, Boca Raton (2011) · Zbl 1218.65001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.