Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across a range of scales, including count data collected across a series of fixed sampling regions to characterize population-level dispersal, as well as individual trajectory data to examine at the motion of individuals within a diffusive population. In this work we consider a lattice-based random walk model and examine the extent to which model parameters can be determined by collecting count data and/or trajectory data. Our analysis combines agent-based stochastic simulations, mean-field partial differential equation approximations, likelihood-based estimation, identifiability analysis, and model-based prediction. These combined tools reveal that working with count data alone can sometimes lead to challenges involving structural non-identifiability that can be alleviated by collecting trajectory data. Furthermore, these tools allow us to explore how different experimental designs impact inferential precision by comparing how different trajectory data collection protocols affects practical identifiability. Open source implementations of all algorithms used in this work are available on GitHub.

翻译：扩散的随机模型被常规用于研究种群扩散，包括动物、植物、种子和细胞群体。成像与实地测量技术的进步意味着数据通常可以在不同尺度上收集，包括在固定采样区域收集的计数数据以表征群体层面的扩散，以及个体轨迹数据以观察扩散种群内个体的运动。本研究考虑基于晶格的随机游走模型，探讨通过收集计数数据和/或轨迹数据能在多大程度上确定模型参数。我们的分析结合了基于智能体的随机模拟、平均场偏微分方程近似、基于似然的估计、可识别性分析以及基于模型的预测。这些综合工具表明，仅使用计数数据有时会面临结构性不可识别性的挑战，而收集轨迹数据可缓解这一问题。此外，这些工具使我们能够通过比较不同轨迹数据收集方案对实际可识别性的影响，探索不同实验设计如何影响推断精度。本研究中使用的所有算法的开源实现均可在GitHub上获取。