Mixture copulas are popular and essential tools for studying complex dependencies among variables. However, selecting the correct mixture models often involves repeated testing and estimations using criteria such as AIC, which could require effort and time. In this paper, we propose a method that would enable us to select and estimate the correct mixture copulas simultaneously. This is accomplished by first overfitting the model and then conducting the Bayesian estimations. We verify the correctness of our approach by numerical simulations. Finally, the real data analysis is performed by studying the dependencies among three major financial markets.

Spatial clustering is dependent on spatial scales. With the widespread use of web maps, a fast clustering method for multi-scale spatial elements has become a new requirement. Therefore, to cluster and display elements rapidly at different spatial scales, we propose a method called Multi-Scale Massive Points Fast Clustering based on Hierarchical Density Spanning Tree. This study refers to the basic principle of Clustering by Fast Search and Find of Density Peaks aggregation algorithm and introduces the concept of a hierarchical density-based spanning tree, combining the spatial scale with the tree links of elements to propose the corresponding pruning strategy, and finally realizes the fast multi-scale clustering of elements. The first experiment proved the time efficiency of the method in obtaining clustering results by the distance-scale adjustment of parameters. Accurate clustering results were also achieved. The second experiment demonstrated the feasibility of the method at the aggregation point element and showed its visual effect. This provides a further explanation for the application of tree-link structures.