In the modelling of stochastic phenomena, such as quasi-reaction systems, parameter estimation of kinetic rates can be challenging, particularly when the time gap between consecutive measurements is large. Local linear approximation approaches account for the stochasticity in the system but fail to capture the nonlinear nature of the underlying process. At the mean level, the dynamics of the system can be described by a system of ODEs, which have an explicit solution only for simple unitary systems. An analytical solution for generic quasi-reaction systems is proposed via a first order Taylor approximation of the hazard rate. This allows a nonlinear forward prediction of the future dynamics given the current state of the system. Predictions and corresponding observations are embedded in a nonlinear least-squares approach for parameter estimation. The performance of the algorithm is compared to existing SDE and ODE-based methods via a simulation study. Besides the increased computational efficiency of the approach, the results show an improvement in the kinetic rate estimation, particularly for data observed at large time intervals. Additionally, the availability of an explicit solution makes the method robust to stiffness, which is often present in biological systems. An illustration on Rhesus Macaque data shows the applicability of the approach to the study of cell differentiation.

翻译：在随机现象（如准反应系统）的建模中，动力学速率的参数估计可能具有挑战性，特别是在连续测量之间的时间间隔较大时。局部线性近似方法考虑了系统中的随机性，但未能捕捉底层过程的非线性本质。在平均水平上，系统的动力学可以通过一个常微分方程组来描述，该方程组仅对简单的单一系统具有显式解。本文通过对风险率进行一阶泰勒近似，提出了适用于一般准反应系统的解析解。这使得在给定系统当前状态的情况下，能够对未来动力学进行非线性前向预测。预测结果与相应观测值被嵌入非线性最小二乘法中进行参数估计。通过模拟研究，将该算法的性能与现有的基于随机微分方程和常微分方程的方法进行了比较。结果表明，除了该方法计算效率的提高外，特别是在观测数据时间间隔较大的情况下，动力学速率估计的精度也有所提升。此外，显式解的存在使得该方法对刚性（这在生物系统中经常出现）具有鲁棒性。对恒河猴数据的示例说明了该方法在细胞分化研究中的适用性。