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

## TL;DR

This paper introduces a fast Bayesian inference method for gene expression models from single-cell transcript data, enabling efficient model selection and parameter estimation with a 1000-fold speedup over existing techniques.

## Contribution

The authors developed a hybrid numerical algorithm combining analytical results and kinetic Monte Carlo to accelerate Bayesian inference for gene expression models.

## Key findings

- Accelerated inference enables practical Bayesian model comparison.
- Bayesian evidence outperforms BIC and AIC in model selection.
- Parameters can be reasonably constrained with modest data samples.

## Abstract

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.