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Understanding how stochastic gene expression is regulated in biologicalsystems using snapshots of single-cell transcripts requires state-of-the-artmethods of computational analysis and statistical inference. A Bayesianapproach to statistical inference is the most complete method for modelselection and uncertainty quantification of kinetic parameters from single-celldata. This approach is impractical because current numerical algorithms are tooslow to handle typical models of gene expression. To solve this problem, wefirst show that time-dependent mRNA distributions of discrete-state models ofgene expression are dynamic Poisson mixtures, whose mixing kernels arecharacterized by a piece-wise deterministic Markov process. We combined thisanalytical result with a kinetic Monte Carlo algorithm to create a hybridnumerical method that accelerates the calculation of time-dependent mRNAdistributions by 1000-fold compared to current methods. We then integrated thehybrid algorithm into an existing Monte Carlo sampler to estimate the Bayesianposterior distribution of many different, competing models in a reasonableamount of time. We validated our method of accelerated Bayesian inference onseveral synthetic data sets. Our results show that kinetic parameters can bereasonably 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 torigorously quantify the likelihood of a model relative to other models from thedata. We demonstrate that Bayesian evidence selects the true model andoutperforms approximate metrics, e.g., Bayesian Information Criterion (BIC) orAkaike Information Criterion (AIC), often used for model selection.

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