基于基金委数学学科青年科学基金项目申请和资助数据的统计分析

Statistical Analysis Based on the Application and Funding Data of the National Natural Science Foundation of China for Youth Science Fund Projects in Mathematics

国家自然科学基金委员会是资助数学研究的重要部门之一,自成立以来已资助中国数学学科项目超过22000项,其中青年科学基金项目超过8600项.研究数学学科青年科学基金项目的申请和资助情况,有助于了解我国数学青年人才发展规模.论文利用数据科学的技术,首先对青年科学基金项目的申请资助情况进行整体分析,并按照学科、年龄、院校、性别等因素对项目资助率进行分层透视.针对近些年青年科学基金整体“量增率减”的现象,论文第三部分利用统计学的方法从申请人的维度分析资助比例的变化规律.针对已获青年项目立项者继续申请面上项目的情况,论文通过引入删失数据机制和Kaplan-Meier生存曲线方法,推断出青年项目立项距面上项目获批的间隔时长分布,得到了间隔时长的更准确的均值和分位数估计,有效解决了只考虑已获批面上项目者将导致的“抽样偏差”问题.

The National Natural Science Foundation of China(NSFC)is one of the fundamental departments funding mathematical research.Since its establishment,it has supported over 22,000 mathematical projects in China,with more than 8,600 being Youth Science Fund projects.Examining the application and funding status of the Youth program in mathematical disciplines is beneficial for understanding the scale of young mathematical talent development in China,assessing the quality of fund reviews,and planning fund support strategies.Utilizing data science techniques,the paper initially conducts an overall analysis of the application and funding status of Youth Science Fund projects.We then conduct hierarchical statistics analysis on project funding rates based on factors such as discipline,age,institution,and gender.Addressing the recent phenomenon of an overall"decreasing growth rate"in the Youth program,we further conduct statistical analysis from the applicants'perspective,including analyzing the changing patterns of funding proportions and comparing the funding rates of different applicants.Regarding the situation where recipients of Youth projects continue to apply for General projects,the paper utilizes the censored data mechanism and Kaplan—Meier estimation to infer the distribution of the time intervals between the approval of Youth and General programs.This approach provides more accurate estimates of the mean and quantiles of the time interval,effectively addressing the"sampling bias"problem that arises when considering only those who have obtained general project approvals.