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

Statistics and Computing
Maria Myrto Folia, Magnus Rattray

Abstract

Stochastic models are of fundamental importance in many scientific and engineering applications. For example, stochastic models provide valuable insights into the causes and consequences of intra-cellular fluctuations and inter-cellular heterogeneity in molecular biology. The chemical master equation can be used to model intra-cellular stochasticity in living cells, but analytical solutions are rare and numerical simulations are computationally expensive. Inference of system trajectories and estimation of model parameters from observed data are important tasks and are even more challenging. Here, we consider the case where the observed data are aggregated over time. Aggregation of data over time is required in studies of single cell gene expression using a luciferase reporter, where the emitted light can be very faint and is therefore collected for several minutes for each observation. We show how an existing approach to inference based on the linear noise approximation (LNA) can be generalised to the case of temporally aggregated data. We provide a Kalman filter (KF) algorithm which can be combined with the LNA to carry out inference of system variable trajectories and estimation of model parameters. We apply and evaluate our ...Continue Reading

References

Aug 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·D T Gillespie
Oct 21, 2009·BMC Bioinformatics·Michał KomorowskiDavid A Rand
Jun 11, 2010·Nature·David G SpillerMichael R H White
May 3, 2011·PLoS Biology·Claire V HarperMichael R H White
Jan 29, 2014·Biometrics·Paul FearnheadChris Sherlock

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Citations

Jul 2, 2019·Frontiers in Genetics·Pavel LoskotLyudmila Mihaylova

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Software Mentioned

Spyder
Python
Anaconda
Numpy
KF2

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