Optimal Thresholding of Predictors in Mineral Prospectivity Analysis
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Original Paper
Optimal Thresholding of Predictors in Mineral Prospectivity Analysis Adrian Baddeley ,1,7 Warick Brown ,2 Robin K. Milne ,3 Gopalan Nair ,3 Suman Rakshit ,4 Tom Lawrence ,6 Aloke Phatak ,5 and Shih Ching Fu 1 Received 19 May 2020; accepted 10 October 2020
Some methods for analysing mineral prospectivity, especially the weights of evidence technique, require the predictor variables to be binary values. When the original evidence data are numerical values, such as geochemical indices, they can be converted to binary values by thresholding. When the evidence layer is a spatial feature such as a geological fault system, it can be converted to a binary predictor by buffering at a suitable cut-off distance. This paper reviews methods for selecting the best threshold or cut-off value and compares their performance. The review covers techniques which are well known in prospectivity analysis as well as unfamiliar techniques borrowed from other literature. Methods include maximisation of the estimated contrast, Studentised contrast, v2 test statistic, Youden criterion, statistical likelihood, Akman–Raftery criterion, and curvature of the capture–efficiency curve. We identify connections between the different methods, and we highlight a common technical error in their application. Simulation experiments indicate that the Youden criterion has the best performance for selection of the threshold or cut-off value, assuming that a simple binary threshold relationship truly holds. If the relationship between predictor and prospectivity is more complicated, then the likelihood method is the most easily adaptable. The weights-of-evidence contrast performs poorly overall. These conclusions are supported by our analysis of data from the Murchison goldfields, Western Australia. We also propose a bootstrap method for calculating standard errors and confidence intervals for the location of the threshold. KEY WORDS: Akman–Raftery criterion, Capture–efficiency curve, Change-point estimation, Likelihood, Weights of evidence, Youden index.
INTRODUCTION 1
School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, GPO Box U1987 Perth, WA 6845, Australia. 2 John de Laeter Centre, Curtin University, Perth, Australia. 3 Department of Mathematics and Statistics, University of Western Australia, Perth, Australia. 4 SAGI-West, School of Molecular and Life Sciences, Curtin University, Perth, Australia. 5 Centre for Transforming Maintenance through Data Science, Curtin University, Perth, Australia. 6 Canberra, Australia. 7 To whom correspondence should be addressed; e-mail: [email protected]
In many techniques for mineral prospectivity analysis, especially weights of evidence (WofE), the predictor variables are required to be binary (0 or 1) values (Agterberg 1992; Agterberg et al. 1993; Bonham-Carter et al. 1990). Geological survey data of other kinds can be used, provided they are first converted to binary values by thresholding (Goodacre et al. 1993). If the original evidence layer is a g
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