In a previous paper [CSIAM Trans. Appl. Math. 2 (2021), 1-55], the authors proposed a theoretical framework for the analysis of RNA velocity, which is a promising concept in scRNA-seq data analysis to reveal the cell state-transition dynamical processes underlying snapshot data. The current paper is devoted to the algorithmic study of some key components in RNA velocity workflow. Four important points are addressed in this paper: (1) We construct a rational time-scale fixation method which can determine the global gene-shared latent time for cells. (2) We present an uncertainty quantification strategy for the inferred parameters obtained through the EM algorithm. (3) We establish the optimal criterion for the choice of velocity kernel bandwidth with respect to the sample size in the downstream analysis and discuss its implications. (4) We propose a temporal distance estimation approach between two cell clusters along the cellular development path. Some illustrative numerical tests are also carried out to verify our analysis. These results are intended to provide tools and insights in further development of RNA velocity type methods in the future.

翻译：在前期论文[CSIAM Trans. Appl. Math. 2 (2021), 1-55]中，作者提出了用于分析RNA速度的理论框架。RNA速度是单细胞RNA测序数据分析中的重要概念，旨在揭示快照数据背后的细胞状态转变动力学过程。本文致力于RNA速度工作流程中若干关键组件的算法研究，重点解决了四个关键问题：（1）构建了理性时间尺度固定方法，可确定细胞全局共享的基因潜变量时间；（2）提出了针对EM算法推断参数的不确定性量化策略；（3）建立了下游分析中基于样本量的速度核带宽最优选择准则，并探讨其理论意义；（4）提出了沿细胞发育路径的两细胞簇间时间距离估算方法。文中还通过数值实验验证了理论分析，相关成果旨在为后续RNA速度类方法的研发提供工具与洞见。