A Comparative Analysis of Favorability Mappings by Weights of Evidence, Probabilistic Neural Networks, Discriminant Analysis, and Logistic Regression

This study compares the performance of favorability mappings by weights of evidence (WOE), probabilistic neural networks (PNN), logistic regression (LR), and discriminant analysis (DA). Comparisons are made by an objective measure of performance that is based on statistical decision theory. The study further emphasizes out-of-sample inference, and quantifies the extent to which outcome is influenced by optimum variable discretization with classification and regression trees (CARTS). Favorability mapping methodologies are evaluated systematically across three case studies with contrasting scale and geologic information: $$\begin{gathered} Case{\text{}}Study{\text{}}Carlin{\text{}}Alamos{\text{}}Nevada \hfill \\ {\text{}}Se\dim ent - Hosted{\text{ }}Intrusion - \operatorname{Re} lated{\text{}}Intrusion - \operatorname{Re} leted \hfill \\ {\text{ }}gold{\text{}}copper{\text{}}copper \hfill \\ Scale{\text{}}deposit{\text{}}district{\text{}}regional \hfill \\ Cell{\text{}}Size{\text{}}small{\text{}}(0.01{\text{}}km^2 ){\text{}}medium{\text{}}(1{\text{}}km^2 ){\text{}}l\arg e{\text{}}(7{\text{}}km^2 ) \hfill \\ Information{\text{}}Level{\text{}}high{\text{}}\bmod erate{\text{}}low \hfill \\ Geo\operatorname{var} iables{\text{}}complex{\text{}}simple{\text{}}simple \hfill \\ Variable{\text{}}\operatorname{int} erdependency{\text{}}\bmod erate{\text{}}low{\text{ }}high \hfill \\ Asymmetry{\text{}}in{\text{}}frequency{\text{}}of{\text{}}\bmod est{\text{ }}considerable{\text{}}severe{\text{}} \hfill \\ barren{\text{}}and{\text{}}\min eralized{\text{}}cells{\text{ }} \hfill \\ \end{gathered} $$ Estimated favorabilities for all cells then are represented by computed percent correct classification, and expected loss of optimum decision. The deposit-scale Carlin study reveals that the performances of the various methods from lowest to highest expected decision loss are: PNN, nonparametric DA, binary PNN (WOE variables), LR, and WOE. Moreover, the study indicates that approximately 40% of the increase in expected decision loss using WOE instead of PNN is the result of information loss from variable discretization. The remaining increases in losses using WOE are the result of its lesser inferential power than PNN. The district-scale Alamos study shows that the lowest expected decision loss is not by PNN, but by canonical DA. CARTS discretization improves greatly the performance of WOE. However, PNN and DA perform better than WOE. Unlike findings from the Alamos and Carlin studies, results from the regional-scale Nevada study indicate that decision losses by LR and DA are lower than those by WOE or PNN. Moreover, decision losses by CARTS-based canonical DA are noticeably the lowest of all, including those by LR and DA using the original variables.