一种非累乘型联合条件概率计算的新证据权方法及其在矿产资源定量评价中的应用研究

The poor conditional independence of evidence variables causing large error of calculation has long been a difficult point in the quantitative assessment of the mineral resource and other fields with the evidence weight model. This is because that the joint conditional probability is computed to get the posterior probability by the form of cascade multiplicative form computing conditional probability of each evidence variables in existing evidence weight model. Therefore all the evidence variables are required to be conditionally independent each other. But this condition is hard to be meet for the multi-variables in the prediction of mineral resources are related, resulting in large error between it and the true joint condition probability. If the joint conditional probability of all variables is directly calculates instead of by the form of cascade multiplicative of conditional probability of each evidence variables, then the error caused by poor conditional independence of the evidence variables should be eliminate. Therefore, this project want to study a new weights of evidence model of non cascade multiplicative form computing joint conditional probability, in which the joint conditional probability of original variables or their principal components' joint conditional probability density can be calculated directly, and then use this to compute posterior probability or odd containing ore prospect of each sample unit. Because of the new method don’t using cascade multiplicative form computing joint conditional probability, the variable is not required to satisfy the condition of conditional independence, which can avoid the loss of important information, and can avoid the error caused by the poor condition. It not only can improve the forecasting accuracy, but also can make the model of the mixed model of the continuous variable and the discrete variables directly.

证据变量条件独立性差导致计算误差大的问题一直是证据权模型进行矿产资源定量评价研究的难点。其根源就在于现有证据权模型在计算后验概率时采用各证据变量条件概率累乘积计算证据变量联合条件概率。故其要求各证据变量间条件独立。但是矿产资源预测评价中的变量多为相关，由此导致其各证据变量条件概率累乘积与联合条件概率值之间产生较大误差。如果不采用条件概率累乘积形式而是直接计算全部变量联合条件概率，就没有因证据变量条件独立性差所产生的误差。因此本项目拟研究出非累乘型联合条件概率计算的新证据权方法及其矿产资源定量评价方法，通过直接计算原始变量的联合条件概率或者原始变量的主成分的联合条件概率密度，由于不采用累乘式计算证据变量的联合条件概率，不需要变量满足条件独立性的苛刻条件，既可以避免变量被删除丢失重要找矿信息，又可以避免由于相关变量之间条件独立性差而导致的计算误差。不但可以提高预测精度，而且还可以让连续型变量直接与离散变量混合计算证据权模型，解决了证据权模型矿产资源定量评价方法的另一个难题。

传统累乘式定性证据权模型是基于贝叶斯后验概率最大原则的二类离散变量后验奇比对数分类模型，在随机变量相互条件独立假设下建立了基于累乘式类联合概率的后验奇比对数形式证据权模型，需要检验变量独立性，因变量独立性无法满足而产生分类误差；只能用定性数据，定量数据无法直接使用，需要人为设置阈值转换为二态离散型定性数据，增加工作而且代入转换误差。.本项目研究建立了基于定量数据非累乘式类联合概率的后验奇比对数形式证据权模型，以正反二类样本概率密度之比对数作为连续型证据函数代替证据权，样本概率密度函数采用混合高斯核密度估计方法直接计算。.本项目研究还建立了可以使用定量数据的非累乘式证据权模型后验奇比对数模型分类方法及其矿产资源评价方法，通过主成分分析降低维数，把主成分代入定量数据非累乘式类联合概率的后验奇比对数形式证据权分类模型，成功地解决了累乘式二态定性证据权模型的两个问题，无需检验样本独立性，也不用人工把连续型变量数据转换为离散型数据。据此建立了定量非累乘式证据权模型矿产资源评价方法。采用该方法对广西丹池锡矿成矿带进行矿产资源评价取得了满意的成果，证明其可行性。.本研究解决了长期以来定量数据不能直接进行证据权分类的问题，减少了数据处理工作，提高矿产资源评价自动化，提高评价工作精度；也解决了目前贝叶斯简单分类法要求变量间条件独立的问题，具有较好的推广价值。

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