2. Probabilistic Mineral Resource Potential Mapping

1. 2. Probabilistic Mineral Resource Potential Mapping • The processing of geo-scientific information for the purpose of estimating probabilities of occurrence for various types of mineral deposits was made easier when Geographic Information Systems became available. Weights-of-Evidence modeling and logistic regression are examples of GIS implementations.

15. Weights of Evidence (WofE)

16. BAYES’ RULE P(D on A) = P(D and A)/P(A) P(A on D) = P(A and D)/P(D) P(D on A) = P(A on D) * P(D)/P(A)

17. ODDS & LOGITS O = P/(1-P); P = O/(1+O); logit = ln O ln O(D on A) = W+(A) + ln O(D) W+(A) = ln {P(A on D)/P(A not on D)}

18. VARIANCE OF WEIGHT s2 = n-1(A and D) + n-1(A and not D)

19. Negative Weight & Contrast W-(A) = W+(not A) Contrast: C = W+(A) - W-(A)

20. PRESENT, ABSENT or MISSING add W+, W- or 0 to prior logit

21. TWO or MORE LAYERS Add Weight(s) assuming Conditional Independence P(<A and B> on D) = P(A on D) * P(B on D)

25. UNCERTAINTY DUE TO MISSING DATA P(D) = EX{P(D on X)} = S P(D on Ai) * P(Ai) or S P(D on <Ai and Bk>) * P(<Ai and Bk>) etc.

26. VARIANCE (MISSING DATA) s2{P(D)} = S {P(D on Ai) - P(D)}2 * P(Ai) or S {P(D on <Ai and Bk>) - P(D)}2 * P(<Ai and Bk>) etc.

27. TOTAL UNCERTAINTY Var (Posterior Logit) = Var (Prior Logit) + + S Var (Weights) + Var (Missing Data)

28. Uncertainty inLogits and Probabilities D {Logit (P)} = 1/P(1-P) s(P) ~ P(1-P) s{Logit (P)}

29. Meguma Terrain Example

36. Table 1. Number of gold deposits, area in km2, weights, contrast (C) with standard deviations (s). In total: 68 deposits on 2945 km2

39. Logistic Regression Logit (i) = b0 + xi1b1 + xi2b2 + … + xim bm

40. Newton-Raphson Iteration b(t+1) = b(t) + {XTV(t)X)}-1XTr(t), t = 1, 2, … r(t) = y(t) - p(t)

43. Seafloor Example