The mean squared displacement (MSD) of particles or probes is commonly estimated from microscopy videos using particle tracking approaches, which rely on tuning parameters manually, and are often unstable over the entire lag time range, especially in dense or low-contrast situations. In this work, we propose model-free ab initio uncertainty quantification (MF-AIUQ), a model-free method for scattering analysis of microscopy video based on a probabilistic framework, which estimates MSD without isolating particles and linking their trajectories. Based on the relationship between the intermediate scattering function (ISF) and the MSD derived from the cumulant theorem, MF-AIUQ estimates the MSD values by the marginal maximum likelihood estimator. To reduce the computational cost, the likelihood function is approximated by a subset of Fourier-transformed intensities. These intensities are equally spaced at the logarithmic values of Fourier basis functions and lag time points. We found that the ISF is smooth in this logarithmic input space, and the information of the ISF can be captured by this subset of inputs. We examine the method through simulation studies covering several representative stochastic processes and three experimental systems: a Newtonian fluid for evaluating performance in optically dense and bright-field settings, a gelation system with an evolving MSD shape, and snail mucin, a viscoelastic biopolymer, for modulus estimation. Across these studies, MF-AIUQ provides smooth and stable MSD estimates over the full lag time range and serves as a useful complementary approach in settings where particle tracking is unreliable or a parametric model of MSD is unavailable or unverifiable.

翻译：粒子或探针的均方位移（MSD）通常通过粒子追踪方法从显微镜视频中估算，这类方法依赖于手动调整参数，且在整个时滞范围内常不稳定，尤其在密集或低对比度场景中。本研究提出无模型先验不确定性量化（MF-AIUQ），这是一种基于概率框架的无模型方法，用于显微镜视频的散射分析，无需分离粒子或追踪其轨迹即可估算MSD。基于累积量定理推导出的中间散射函数（ISF）与MSD之间的关系，MF-AIUQ通过边际最大似然估计器估算MSD值。为降低计算成本，似然函数通过傅里叶变换强度的子集进行近似，这些强度在傅里叶基函数和时滞点的对数值上等间距分布。研究发现，ISF在此对数输入空间中具有平滑性，且其信息可通过该输入子集捕获。我们通过涵盖多个代表性随机过程的模拟研究及三个实验系统对方法进行了验证：用于评估光学致密明场环境下性能的牛顿流体、具有动态演化MSD形状的凝胶体系，以及黏弹性生物聚合物蜗牛黏液（用于模量估算）。在全部研究中，MF-AIUQ在整个时滞范围内提供了平滑稳定的MSD估算结果，在粒子追踪不可靠或MSD参数模型不可用/不可验证的场景中，可作为有效的补充方法。