The inherent complexity of biological agents often leads to motility behavior that appears to have random components. Robust stochastic inference methods are therefore required to understand and predict the motion patterns from time-discrete trajectory data provided by experiments. In many cases, second-order Langevin models are needed to adequately capture the motility. Additionally, population heterogeneity needs to be taken into account when analyzing data from several individual organisms. In this work, we describe a maximum likelihood approach to infer dynamical, stochastic models and, simultaneously, estimate the heterogeneity in a population of motile active particles from discretely sampled, stochastic trajectories. To this end, we propose a method to approximate the likelihood for non-linear second-order Langevin models. We show that this maximum likelihood ansatz outperforms alternative approaches, especially for short trajectories. Additionally, we demonstrate how a measure of uncertainty for the heterogeneity estimate can be derived. We thereby pave the way for the systematic, data-driven inference of dynamical models for actively driven entities based on trajectory data, deciphering temporal fluctuations and inter-particle variability.

翻译：生物主体的内在复杂性常导致其运动行为呈现随机成分。因此需要稳健的随机推断方法，从实验提供的离散时间轨迹数据中理解和预测运动模式。在许多情况下，需要二阶朗之万模型才能充分描述运动特征。此外，在分析多个独立生物体的数据时，必须考虑群体异质性。本研究提出一种极大似然方法，用于推断动力学随机模型，同时根据离散采样的随机轨迹估计运动活性粒子系综中的异质性。为此，我们提出一种近似非线性二阶朗之万模型似然函数的方法。研究表明，该极大似然假设方法优于其他替代方法，尤其适用于短时轨迹。我们还展示了如何推导异质性估计的不确定性度量。通过上述工作，我们为基于轨迹数据对活性驱动实体进行系统性、数据驱动的动力学模型推断铺平了道路，从而揭示时间涨落与粒子间变异性。