Journal
PHYSICAL CHEMISTRY CHEMICAL PHYSICS
Volume 20, Issue 46, Pages 29018-29037Publisher
ROYAL SOC CHEMISTRY
DOI: 10.1039/c8cp04043e
Keywords
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Funding
- Danish Council for Independent Research Natural Sciences (FNU) [4002-00428B]
- Deutsche Forschungsgemeinschaft (DFG) [ME 1535/6-1, ME 1535/7-1]
- Humboldt Polish Honorary Research Scholarship (Foundation for Polish Science)
- Deutscher Akademischer Austauschdienst [57214224]
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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.
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