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Title: Inference for Reaction Networks Using the Linear Noise Approximation
Contributor(s): Fearnhead, Paul (author); Giagos, Vasileios (author); Sherlock, Chris (author)
Publication Date: 2014
Open Access: Yes
DOI: 10.1111/biom.12152Open Access Link
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Abstract: We consider inference for the reaction rates in discretely observed networks such as those found in models for systems biology, population ecology, and epidemics. Most such networks are neither slow enough nor small enough for inference via the true state-dependent Markov jump process to be feasible. Typically, inference is conducted by approximating the dynamics through an ordinary differential equation (ODE) or a stochastic differential equation (SDE). The former ignores the stochasticity in the true model and can lead to inaccurate inferences. The latter is more accurate but is harder to implement as the transition density of the SDE model is generally unknown. The linear noise approximation (LNA) arises from a first-order Taylor expansion of the approximating SDE about a deterministic solution and can be viewed as a compromise between the ODE and SDE models. It is a stochastic model, but discrete time transition probabilities for the LNA are available through the solution of a series of ordinary differential equations. We describe how a restarting LNA can be efficiently used to perform inference for a general class of reaction networks; evaluate the accuracy of such an approach; and show how and when this approach is either statistically or computationally more efficient than ODE or SDE methods. We apply the LNA to analyze Google Flu Trends data from the North and South Islands of New Zealand, and are able to obtain more accurate short-term forecasts of new flu cases than another recently proposed method, although at a greater computational cost.
Publication Type: Journal Article
Source of Publication: Biometrics, 70(2), p. 457-466
Publisher: Wiley-Blackwell Publishing Ltd
Place of Publication: United Kingdom
ISSN: 1541-0420
Field of Research (FOR): 060114 Systems Biology
010405 Statistical Theory
010406 Stochastic Analysis and Modelling
Socio-Economic Outcome Codes: 920404 Disease Distribution and Transmission (incl. Surveillance and Response)
970101 Expanding Knowledge in the Mathematical Sciences
970106 Expanding Knowledge in the Biological Sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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