Systematic comparison and optimization of parameter estimation methods for stochastic gene expression kinetics

Accurately estimating kinetic parameters of stochastic gene expression is a key challenge in quantitative single-cell transcriptomics. Building on the strengths of traditional methods, such as the method of moments and maximum likelihood estimation (MLE), we propose a novel framework: moment-reduced MLE (MR-MLE). We combined these three parameter estimation methods with four steady-state mRNA distribution computation strategies (exact distribution expression, Laplace approximation, finite state projection (FSP), and Gauss–Jacobi quadrature) to form nine distinct inference methods. These methods were systematically compared on both synthetic and real experimental data across two core dimensions: computational efficiency and parameter estimation accuracy. Results show that the Laplace approximation yields unreliable parameter estimates; the method of moments is computationally efficient but suffers from small-sample bias; the exact distribution solution is the least computationally efficient; and the FSP method exhibits fluctuating efficiency with varying gene expression levels. Notably, MR-MLE integrated with Gauss–Jacobi quadrature achieves the optimal balance between computational speed and inference robustness. Thus, we recommend this method as the preferred choice for fitting experimental data, providing a reliable and efficient computational solution for large-scale single-cell gene expression data analysis.