Ab initio uncertainty quantification in scattering analysis of microscopy
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显微成像散射分析中的从源头不确定性量化
- 研究问题
- 显微成像散射分析如何从数据处理起点传播参数估计的不确定性，并减少依赖研究者经验选择波矢分析范围的做法？
- 方法与思路
- 作者构建概率生成模型，将传统差分动态显微估计联系到潜在因子变差函数拟合，再以最大边际似然整合全部波矢信息并加速计算。
- 材料陈述的贡献
- 摘要称，该方法无需预先选择波矢范围，利用 Toeplitz 协方差结构降低计算成本，并在模拟及三类物理实验中展示估计与模型选择用途。
- 阅读关注点
- 应核对生成模型和噪声设定、不同波矢的信息权重、不确定性传播方式，以及广义 Schur 算法的计算性质和实验比较条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收均未核实；摘要未给出模型成立条件、误差量化或具体性能结果，也未说明经济数据适用性。
原文摘要
Estimating parameters from data is a fundamental problem, customarily done by minimizing a loss function between a model and observed statistics. In scattering-based analysis, researchers often employ their domain expertise to select a specific range of wave vectors for analysis, a choice that can vary depending on the specific case. We introduce another paradigm that defines a probabilistic generative model from the beginning of data processing and propagates the uncertainty for parameter estimation, termed the ab initio uncertainty quantification (AIUQ). As an illustrative example, we demonstrate this approach with differential dynamic microscopy (DDM) that extracts dynamical information through Fourier analysis at a selected range of wave vectors. We first show that the conventional way of estimation in DDM is equivalent to fitting a temporal variogram in the reciprocal space using a latent factor model. Then we derive the maximum marginal likelihood estimator, which optimally weighs the information at all wave vectors, therefore eliminating the need to select the range of wave vectors. Furthermore, we substantially reduce the computational cost by utilizing the generalized Schur algorithm for Toeplitz covariances without approximation. Simulated studies validate that AIUQ improves estimation accuracy and enables model selection with automated analysis. The utility of AIUQ is also demonstrated by three distinct sets of experiments: first in an isotropic Newtonian fluid, pushing limits of optically dense systems compared to multiple particle tracking; next in a system undergoing a sol-gel transition, automating the determination of gelling points and critical exponent; and lastly, in discerning anisotropic diffusive behavior of colloids in a liquid crystal. These outcomes collectively underscore AIUQ's versatility to capture system dynamics in an efficient and automated manner.