Latent event history models for quasi-reaction systems
针对准反应系统，提出一种潜在事件历史模型，结合扩展卡尔曼滤波的期望最大化算法，解决现有方法在密集观测下的数值不稳定问题，并在COVID-19传播数据中展示应用。
Various processes, such as cell differentiation and disease spreading, can be modelled as quasi-reaction systems of particles using stochastic differential equations. The existing Local Linear Approximation (LLA) method infers the parameters driving these systems from measurements of particle abundances over time. While dense observations of the process in time should in theory improve parameter estimation, LLA fails in these situations due to numerical instability. Defining a latent event history model of the underlying quasi-reaction system resolves this problem. A computationally efficient Expectation-Maximization algorithm is proposed for parameter estimation, incorporating an extended Kalman filter for evaluating the latent reactions. A simulation study demonstrates the method's performance and highlights the settings where it is particularly advantageous compared to the existing LLA approaches. An illustration of the method applied to the diffusion of COVID-19 in Italy is presented.