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

Liang Chen; Ying Sheng; Zhihui Xie; Feng Jiao; Liang Chen; Ying Sheng; Zhihui Xie; Feng Jiao

doi:10.3934/era.2026102

Electronic Research Archive

2026, Volume 34, Issue 4: 2261-2278. doi: 10.3934/era.2026102

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Research article Special Issues

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

Liang Chen ^1,2,
Ying Sheng ^{1,2
,
,},
Zhihui Xie ^{2
,
,},
Feng Jiao ^{1,2
,
,}

1.
Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
2.
College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China

Received: 10 January 2026 Revised: 23 February 2026 Accepted: 05 March 2026 Published: 12 March 2026

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.
- stochastic gene expression,
- parameter estimation method,
- steady-state distribution,
- computational efficiency,
- estimation accuracy
Citation: Liang Chen, Ying Sheng, Zhihui Xie, Feng Jiao. Systematic comparison and optimization of parameter estimation methods for stochastic gene expression kinetics[J]. Electronic Research Archive, 2026, 34(4): 2261-2278. doi: 10.3934/era.2026102

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Abstract

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.

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