基于单细胞测序的超高维数据的统计方法研究

单细胞测序技术已经逐渐成为基因遗传和疾病分析，特别是癌症早期的诊断、追踪以及个体化治疗的重要手段。对单细胞测序超高维数据统计分析的难点在于样本数据测序深度严重不够，但数据量十分巨大且观测信号离散。本项目将重点研究统计方法解决如下难题：（1）在单细胞测序数据的分类判别过程中寻找影响分类的特征基因，从而提高癌症诊断的准确率；（2）单细胞测序数据分析中，如何在已知的癌症亚型基础上探索新的亚型的统计方法，并研究理论性质；（3）研究结合单细胞测序和重亚硫酸盐技术的scBS-seq数据寻找影响癌症的甲基化区域的统计方法；（4）研究scBS-seq数据进行癌症诊断的统计方法。为解决上述难题，本项目将利用单细胞测序数据的特点来筛选特征基因，利用离散分布等来拟合新数据，提出符合离散分布的模型来构建检验和分类判别等统计框架，并给出理论收敛性质。进一步，本项目也将新提出的统计方法应用到癌症的临床数据分析。

Single-cell sequencing technology has gradually become an important means of gene inheritance and disease analysis, especially for the early diagnosis, tracking and individualized treatment of cancer. One major challenge in analyzing the ultra-high dimensional single-cell sequencing data is that the sample data sequencing depth is seriously insufficient, whereas the volume of data is huge and the observation signal is discrete. This project will focus on statistical aspects to solve several important problems as follows: (1) In the process of the classification of single-cell sequencing data, the characteristic genes affecting the classification were searched so as to improve the accuracy of cancer diagnosis; (2) In the analysis of single cell sequencing data, how to explore the statistical methods of new cancer subtypes based on the known subtypes and study the theoretical properties; (3) To study scBS-seq data combined with single cell sequencing and heavy sulfite technology to find statistical methods affecting the methylation region of cancer; (4) To study the statistical methods of scBS-seq data for cancer diagnosis. Specifically to solve the above problems, this project will use the characteristics of single-cell sequencing data to screen feature genes, use the discrete distributions to fit the new data, propose the model conforming to the discrete distribution to build the statistical framework for hypothesis testing and classification, and derive the theoretical convergence. Furthermore, the project will also apply the newly proposed statistical methods to analyze some clinical data of cancer.