The forward-reverse algorithm for stochastic reaction networks with applications to statistical inference

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In this work, we present an extension of the forward-reverse algorithm by Bayer and Schoenmakers [Annals of Applied Probability, 24(5):1994--2032, October 2014] to the context of stochastic reaction networks (SRNs). It makes the approximation of expected values of functionals of bridges for this type of process computationally feasible. We then apply this bridge-generation technique to the statistical inference problem of approximating the reaction coefficients based on discretely observed data. To this end, we introduce a two-phase iterative inference method in which, during the first phase, we solve a set of deterministic optimization problems where the SRNs are replaced by their reaction-rate ODE approximation; then, during the second phase, the Monte Carlo version of the Expectation-Maximization (EM) algorithm is applied to start from the output of the previous phase.

By selecting a set of over-dispersed seeds as initial points for the phase I, the output of parallel runs of our two-phase method is a cluster of maximum likelihood estimates. For convergence assessment, we use techniques from the theory of Markov chain Monte Carlo. Our results are illustrated by numerical examples.

Collaborators

• ​Alvaro Moraes (KAUST)
• Christian Bayer (WIAS)
• Raul Tempone  (KAUST)
• Pedro Vilanova  (KAUST)

Publications

• C. Bayer, A. Moraes, R. Temone, P. Vilanova, The forward-reverse algorithm for stochastic reaction networks with applications to statistical inference​, Stochastic Analysis and Applications, Volume 34, Issue 2, 2016.