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An accurate probabilistic step finder for time-series analysis.

Alex Rojewski1, Max Schweiger1, Ioannis Sgouralis2

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A new Bayesian nonparametric (BNP) method, BNP-Step, accurately identifies transitions in noisy time-series data. This approach overcomes limitations of existing models by not assuming holding times and rigorously handling uncertainty, improving analysis of sparse and noisy experimental data.

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Area of Science:

  • Biophysics
  • Statistical Mechanics
  • Data Science

Background:

  • Analysis of noisy time-series data from experiments like Förster resonance energy transfer, patch clamp, and force spectroscopy commonly uses hidden Markov models or step-finding algorithms.
  • Hidden Markov models assume geometric holding times, potentially biasing step location detection in sparse or noisy data.
  • Existing step-finding algorithms often use ad hoc metrics and approximate methods, lacking robustness and rigorous uncertainty propagation.

Purpose of the Study:

  • To develop a robust, general, and probabilistic (Bayesian) step-finding tool for analyzing noisy time-series data.
  • To overcome the limitations of existing methods by avoiding assumptions on holding time distributions and ad hoc step penalization.
  • To accurately determine the number and location of transitions between discrete states without a predefined kinetic model.

Main Methods:

  • Developed a Bayesian nonparametric (BNP) approach, termed BNP Step (BNP-Step), to analyze time-series data.
  • Treated the unknown number of steps within a Bayesian nonparametric framework.
  • Learned the emission distribution characteristic of each state without assuming a kinetic model.

Main Results:

  • BNP-Step accurately determines the number and location of transitions between discrete states.
  • The method successfully analyzes sparser data with higher noise and more closely spaced states compared to current methods.
  • BNP-Step rigorously propagates measurement uncertainty into posterior estimates of transition locations, numbers, and emission levels.

Conclusions:

  • BNP-Step offers a superior alternative for analyzing noisy time-series data, particularly in biophysical experiments.
  • The method's ability to handle uncertainty and avoid restrictive assumptions makes it highly versatile.
  • Demonstrated performance on synthetic and force spectroscopy data validates its effectiveness and robustness.