Improvement of Weighted Weights of Evidence and Its Applications in Sn-Cu Mineral Potential Mapping in Gejiu, Yunnan Province, China
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摘要: 为了探讨新的加权系数估计方法对于消除或减弱证据层不满足条件独立性假设时对预测结果的影响, 对加权证据权模型的加权系数估计方法进行了新的探讨，尝试用顺序估计法估计加权系数.加权系数的顺序估计法是将加权证据权模型与基于模糊预测对象的证据权模型相结合，将证据层按照一定顺序逐步加入到加权证据权模型中，在加入到模型的过程中依次用已经获得的后验概率作为模糊训练层对证据层加入到模型的顺序进行修正，并通过条件相关系数的方法估计加权系数.分别以1组多元正态分布模拟数据和个旧锡铜多金属矿产资源预测为例，比较了多种模型的后验概率，结果表明加权证据权模型对减弱证据层不满足条件独立性假设所产生的影响是有效的.Abstract: This paper proposes a new method to estimate weighting coefficients in weighted weights of evidence (WWofE) in order to reduce the influence of correlation among evidence layers when hypothesis of conditional independence is not true. Sequential estimation method in WWofE combines WWofE and dual weights of evidence (DWofE) to gradually add evidence layers with specific sequence to WWofE model. In the process, the posterior probability obtained by former evidence layers is considered as fuzzy training layer in DWofE to correct the sequence of layers. The weighting coefficients are estimated by using conditional correlation coefficient. As a case study, a group data generated by four variable normal distribution and Sn-Cu mineral resources assessment in Gejiu, Yunan, southwestern China are used. The results show that WWofE model is effective to reduce the influence of correlations among evidence layers.
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图 1 4个证据图层二态图层(张生元等, 2009)
a.构造交汇点距离6 km.白色点表示构造交汇点；b.采用S-A方法分解得到的地球化学综合异常图；c.采用局部奇异性方法得到的局部地球化学异常图；d.个旧组地层.黑色三角形表示Sn矿床
Fig. 1. Binary maps of four evidence maps
图 2 3种证据权模型后验概率分级图
a.模型Ⅰ后验概率异常分级图；b.模型Ⅱ后验概率异常分级图；c.模型Ⅲ后验概率异常分级图.黑色三角形表示Sn矿床
Fig. 2. Anomaly classification of posteriori probabilities obtained by three models
表 1 各种方法计算的后验概率及排序
Table 1. Four posterior probability and their ranks in unique condition
类型 $ \overline{\mathrm{ABC}}$ $ \mathrm{A} \overline{\mathrm{BC}}$ $ \overline{\mathrm{A}} \mathrm{B} \overline{\mathrm{C}}$ $\mathrm{AB} \overline{\mathrm{C}} $ $ \overline {{\rm{AB}}} {\rm{C}}$ ${\rm{A}}\overline {\rm{B}} {\rm{C}} $ $ \overline{\mathrm{A}} \mathrm{BC}$ ABC 误差 后验概率理论值 0.034 0.409 0.249 0.765 0.235 0.752 0.590 0.966 后验概率理论值排序 8 5 6 2 7 3 4 1 普通证据权后验概率 0.010 0.269 0.176 0.891 0.117 0.835 0.746 0.991 55.100 普通证据权后验概率排序 8 5 6 2 7 3 4 1 加权证据权后验概率 0.013 0.300 0.169 0.885 0.122 0.841 0.716 0.989 45.600 加权证据权后验概率排序 8 5 6 2 7 3 4 1 
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表 2 基于各个子区域3种证据权模型后验概率从大到小排序
Table 2. The rank of posterior probabilities obtained by using three models in unique condition
子区域 面积单元数 所含矿床数 Ⅰ Ⅱ Ⅲ ABCD 31.6 1 1 1 1 ${\rm{ABC}}\overline {\rm{D}} $ 19.4 2 3 3 2 ${\rm{AB}}\overline {\rm{C}} {\rm{D}} $ 22.0 3 5 4 5 ${\rm{AB}}\overline {{\rm{CD}}} $ 10.3 0 8 8 6 ${\rm{A}}\overline {\rm{B}} {\rm{CD}} $ 23.6 0 7 6 8 ${\rm{A}}\overline {\rm{B}} {\rm{C}}\overline {\rm{D}} $ 20.7 0 11 10 10 ${\rm{A}}\overline {{\rm{BC}}} {\rm{D}} $ 158.6 0 13 13 13 ${\rm{A}}\overline {{\rm{BCD}}} $ 207.1 1 15 14 14 $\overline {\rm{A}} {\rm{BCD}} $ 42.6 3 2 2 3 $\overline {\rm{A}} {\rm{BC}}\overline {\rm{D}} $ 17.3 0 4 5 4 $ \overline {\rm{A}} {\rm{B}}\overline {\rm{C}} {\rm{D}}$ 36.3 0 6 7 7 $\overline {\rm{A}} {\rm{B}}\overline {{\rm{CD}}} $ 5.2 0 10 11 9 $\overline {{\rm{AB}}} {\rm{CD}} $ 13.9 0 9 9 11 $\overline {{\rm{AB}}} {\rm{C}}\overline {\rm{D}} $ 61.9 0 12 12 12 $\overline {{\rm{ABC}}} {\rm{D}} $ 171.7 0 14 15 15 $\overline {{\rm{ABCD}}} $ 429.7 1 16 16 16
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