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Trajectory inference and parameter estimation in stochastic models with temporally aggregated data.

Maria Myrto Folia1, Magnus Rattray1

  • 1Division of Informatics, Imaging and Data Sciences, Faculty of Biology, Medicine and Health, University of Manchester, Manchester, UK.

Statistics and Computing
|August 28, 2018
PubMed
Summary

This study presents a Kalman filter (KF) algorithm to accurately infer system parameters and trajectories from temporally aggregated data in stochastic models. The method enhances inference for molecular biology applications, addressing challenges with noisy, aggregated measurements.

Keywords:
Kalman filterLinear noise approximationStochastic systems biologyTime aggregation

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Area of Science:

  • * Computational Biology
  • * Systems Biology
  • * Biophysics

Background:

  • * Stochastic models are crucial for understanding cellular heterogeneity and fluctuations in molecular biology.
  • * The chemical master equation models intracellular stochasticity, but solutions are often computationally intensive.
  • * Inferring system dynamics and parameters from observed data is challenging, especially with aggregated measurements.

Purpose of the Study:

  • * To generalize existing inference methods for stochastic models to handle temporally aggregated data.
  • * To develop a Kalman filter (KF) algorithm combined with the linear noise approximation (LNA) for improved inference.
  • * To accurately estimate model parameters and infer system trajectories from aggregated time-series data.

Main Methods:

  • * Generalization of the linear noise approximation (LNA) for inference with temporally aggregated data.
  • * Development and application of a Kalman filter (KF) algorithm integrated with the LNA.
  • * Validation using both synthetic and real-world single-cell gene expression data.

Main Results:

  • * The proposed KF-LNA method accurately infers the posterior distribution of model parameters from aggregated data.
  • * Accurate inference of system variable trajectories is achieved even with aggregated measurements.
  • * Standard KF inference on aggregated data without accounting for aggregation leads to underestimation of process noise and biased parameter estimates.

Conclusions:

  • * The developed KF-LNA approach provides a robust method for parameter estimation and trajectory inference in stochastic systems with aggregated data.
  • * This method is particularly relevant for applications like single-cell gene expression studies using reporters like luciferase.
  • * Accounting for temporal aggregation is critical to avoid biased parameter estimates and inaccurate noise quantification in stochastic modeling.