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Bayesian analysis of single-particle tracking data using the nested-sampling algorithm: maximum-likelihood model

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Summary
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We use Bayesian statistics and nested sampling to rank diffusion models and find optimal parameters for time-series data. This method objectively selects the best stochastic model for analyzing particle movement, even with noise.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Computational Science

Background:

  • Diffusion processes are fundamental in various scientific fields, but selecting appropriate models for complex time-series data remains challenging.
  • Anomalous diffusion, characterized by non-Gaussian displacement statistics, is frequently observed in biological and material systems.
  • Existing methods often struggle to objectively compare and parameterize diverse diffusion models.

Purpose of the Study:

  • To develop and validate a robust Bayesian framework for comparing and ranking various ergodic diffusion models, including anomalous diffusion.
  • To assess the optimal parameters for different diffusion models using both simulated and real-world time-series data.
  • To evaluate the performance and predictive power of the nested-sampling algorithm for individual particle trajectory analysis.

Main Methods:

  • Employing Bayesian statistics with the nested-sampling algorithm for model comparison and parameter estimation.
  • Analyzing individual particle trajectories from both in silico-generated and experimental single-particle-tracking data.
  • Focusing on the 'diffusing diffusivity' model and comparing it against Brownian motion and fractional Brownian motion models.

Main Results:

  • The nested-sampling algorithm effectively evaluates relative model probabilities and computes optimal parameter sets for each diffusion model.
  • Accurate estimation of model parameters was achieved by comparing estimated values against known true parameters in simulated data.
  • Demonstrated the algorithm's performance and predictive capabilities on both idealized and noisy experimental time-series.

Conclusions:

  • The proposed Bayesian approach provides a powerful tool for the objective selection of the most suitable stochastic diffusion model for a given time-series.
  • The study offers new insights into understanding diffusion dynamics, particularly for systems exhibiting non-Gaussian behavior.
  • Initial applications to experimental data of tracer diffusion in hydrogels highlight the practical utility of this model-ranking approach.