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Developing a Kalman Filter-Based Method to Estimate the Probability Distribution of Stochastic Systems in Biology


A. Hjartarson

Master Thesis, FS 12 (10150)

A numerical method is proposed in order to approximate the solution of the chemical master equation (CME) for chemical reaction networks on an arbitrary set of states. The method can be seen as a modification or a closure extension of the finite state projection (FSP) method, in the sense that stochastic simulations are used to close the system dynamics. A Kalman filter is constructed in order to further optimize the state estimate using noise covariance matrices computed based on the simulations. The proposed method can be used to approximate the solution of the CME on a time varying set of states, which can for instance be useful in cases where the probability distribution does not reach stationarity (e.g. due to time-varying inputs). Examples are shown in which the proposed method is implemented and is shown to be more accurate than an FSP equivalent and the Gillespie algorithm. Additionally, a Kalman filter is used to estimate the complete probability distribution of a system from observations of marginal distributions of species that can be measured experimentally. Finally, the closure method is utilized in parameter inference, presenting preliminary results on a simple gene expression model.


Type of Publication:

(12)Diploma/Master Thesis

J. Ruess

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2012:IFA_4254
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