标题： 从单细胞转录组快照中加速基因表达模型的贝叶斯推断 显示英文标题

标题： Accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts

摘要： 理解如何利用单细胞转录组的快照来研究生物系统中随机基因表达的调控，需要最先进的计算分析和统计推断方法。 基于贝叶斯的方法是模型选择和从单细胞数据中量化参数不确定性的最全面的方法。 这种方法不切实际，因为当前的数值算法太慢，无法处理典型的基因表达模型。 为了解决这个问题，我们首先证明了离散状态基因表达模型的时间依赖性mRNA分布是动态泊松混合分布，其混合核由分段确定性马尔可夫过程表征。 我们将这一分析结果与动力学蒙特卡洛算法结合，创建了一种混合数值方法，与当前方法相比，将时间依赖性mRNA分布的计算速度提高了1000倍。 然后，我们将该混合算法集成到现有的蒙特卡洛采样器中，以在合理的时间内估计许多不同竞争模型的贝叶斯后验分布。 我们在几个合成数据集上验证了我们的加速贝叶斯推断方法。 我们的结果表明，如果已知模型，对于中等采样的数据集，可以合理地约束动力学参数\textit{事前}。 如果模型未知，贝叶斯证据可以用来严格量化模型相对于其他模型的数据可能性。 我们证明贝叶斯证据能够选择真实模型，并且优于常用的近似指标，例如贝叶斯信息准则（BIC）或赤池信息准则（AIC），这些指标常用于模型选择。 显示英文摘要

摘要： Understanding how stochastic gene expression is regulated in biological systems using snapshots of single-cell transcripts requires state-of-the-art methods of computational analysis and statistical inference. A Bayesian approach to statistical inference is the most complete method for model selection and uncertainty quantification of kinetic parameters from single-cell data. This approach is impractical because current numerical algorithms are too slow to handle typical models of gene expression. To solve this problem, we first show that time-dependent mRNA distributions of discrete-state models of gene expression are dynamic Poisson mixtures, whose mixing kernels are characterized by a piece-wise deterministic Markov process. We combined this analytical result with a kinetic Monte Carlo algorithm to create a hybrid numerical method that accelerates the calculation of time-dependent mRNA distributions by 1000-fold compared to current methods. We then integrated the hybrid algorithm into an existing Monte Carlo sampler to estimate the Bayesian posterior distribution of many different, competing models in a reasonable amount of time. We validated our method of accelerated Bayesian inference on several synthetic data sets. Our results show that kinetic parameters can be reasonably constrained for modestly sampled data sets, if the model is known \textit{a priori}. If the model is unknown,the Bayesian evidence can be used to rigorously quantify the likelihood of a model relative to other models from the data. We demonstrate that Bayesian evidence selects the true model and outperforms approximate metrics, e.g., Bayesian Information Criterion (BIC) or Akaike Information Criterion (AIC), often used for model selection.