Geo-information identification for exploring non-stationary relationships between volcanic sedimentary Fe mineralization and controlling factors in an area with overburden in eastern Tianshan region, China

GIS-based spatial analysis has been a common practice in mineral exploration, by which mineral potentials can be delineated to support following sequences of exploration. Mineral potential mapping is generally composed of geo-information extraction and integration. Geological anomalies frequently indicate mineralization. Volcanic sedimentary Fe deposits in eastern Tianshan mineral district, China provide an example of such an indication. However, mineral exploration in this area has been impeded by the desert coverage and geo-anomalies indicative to the presence of mineralization are often weak and may not be efficiently identified by traditional exploring methods. Furthermore, geological guidance regarding to spatially non-stationary relationships between Fe mineralization and its controlling factors were not sufficiently concerned in former studies, which limited the application of proper statistics in mineral exploration. In this dissertation, geochemical distributions associated with controlling factors of the Fe mineralization are characterized by various GIS-based spatial analysis methods. The singularity index mapping technique is attempted to separate geochemical anomalies from background, especially in the desert covered areas. Principal component analysis is further used in integrating the geochemical anomalies to identify geo-information of geological bodies or geological activities associated with Fe mineralization. In order to delineate mineral potentials, spatially weighted principal component analysis with more geological guidance is tried to integrate these identified controlling factors. At the end, as the first time been introduced to mineral exploration, a geographically weighted regression method is currently attempted investigate spatially non-stationary interrelationships presented across the space. Based on the results, superimposition of these controlling factors can be qualitatively and quantitatively summarized that provides a constructive geo-information to Fe mineral exploration in this area. From the practices in this dissertation, GIS-based mineral exploration will not only be efficient in mapping mineral potentials but also be supportive to strategies making of following mineral exploration. All of these experiences can be suggested to future mineral exploration in the other regions

Principal component analysis in high dimensional data: application for genomewide association studies

In genomewide association studies (GWAS), population stratification (PS) is a major confounding factor which causes spurious associations by inflating test statistics. PS refers to differences in allele frequencies by disease status due to systematic differences in ancestry, rather than causal association of genes with disease. PCA is commonly used to infer population structure by computing PC scores, which are subsequently used for control of population stratification. Even though PCA is now widely used for PS adjustment, there are still challenges for PCA based effective PS control. One common feature of the genomic data is the strong local correlation among adjacent loci/markers caused by linkage disequilibrium (LD). It is known that this local correlation can have a negative effect on estimated PC scores and produce spurious PCs which do not truly reflect underlying population structure. To address this problem, we have employed a shrinkage PCA approach where coefficients are used to down-weight the contribution of highly correlated SNPs in PCA. Another challenge in PC analysis is choosing which PCs to include as covariates to adjust population stratification. While searching for a reasonable measure for PC selection, we have found the precise relationship between genotype principal components and inflation of association test statistics. Based on this fact, We propose a new approach, called EigenCorr, which selects principal components based on both their eigenvalues and their correlation with the (disease) phenotype. Our approach tends to select fewer principal components for stratification control than does testing of eigenvalues alone, providing substantial computational savings and improvements in power. Under many circumstances, it is of interest to predict PC scores. Although PC score prediction is commonly used in practice, characteristics of the predicted PC scores have not been systematically studied. Under high dimensional settings we have found that the naive predicted PC scores are systematically biased toward 0, and this phenomenon is largely due to the inconsistency of the sample eigenvalues and eigenvectors. We have extended existing convergence results of sample eigenvalues and eigenvectors and derived asymptotic shrinkage factors. Based on these asymptotic results, we propose the bias-adjusted PC score prediction