Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany.
Phys Chem Chem Phys. 2018 Nov 28;20(46):29018-29037. doi: 10.1039/c8cp04043e.
We employ Bayesian statistics using the nested-sampling algorithm to compare and rank multiple models of ergodic diffusion (including anomalous diffusion) as well as to assess their optimal parameters for in silico-generated and real time-series. We focus on the recently-introduced model of Brownian motion with "diffusing diffusivity"-giving rise to widely-observed non-Gaussian displacement statistics-and its comparison to Brownian and fractional Brownian motion, also for the time-series with some measurement noise. We conduct this model-assessment analysis using Bayesian statistics and the nested-sampling algorithm on the level of individual particle trajectories. We evaluate relative model probabilities and compute best-parameter sets for each diffusion model, comparing the estimated parameters to the true ones. We test the performance of the nested-sampling algorithm and its predictive power both for computer-generated (idealised) trajectories as well as for real single-particle-tracking trajectories. Our approach delivers new important insight into the objective selection of the most suitable stochastic model for a given time-series. We also present first model-ranking results in application to experimental data of tracer diffusion in polymer-based hydrogels.
我们采用贝叶斯统计方法和嵌套抽样算法，比较和排序多种遍历性扩散模型（包括异常扩散），并评估它们在计算机生成和真实时间序列中的最佳参数。我们专注于最近引入的扩散率扩散布朗运动模型，该模型产生了广泛观察到的非高斯位移统计，并将其与布朗运动和分数布朗运动进行比较，也包括具有一些测量噪声的时间序列。我们使用贝叶斯统计和嵌套抽样算法在单个粒子轨迹层面上进行模型评估分析。我们评估了各个扩散模型的相对模型概率，并计算了每个模型的最佳参数集，将估计的参数与真实参数进行比较。我们测试了嵌套抽样算法的性能及其对计算机生成（理想化）轨迹和真实单粒子跟踪轨迹的预测能力。我们的方法为给定时间序列选择最合适的随机模型提供了新的重要见解。我们还首次在应用于聚合物水凝胶中示踪扩散的实验数据的模型排名结果中展示了这一方法。
