TY - JOUR

T1 - An efficient forward–reverse expectation-maximization algorithm for statistical inference in stochastic reaction networks

AU - Bayer, Christian

AU - Moraes, Alvaro

AU - Tempone, Raul

AU - Vilanova, Pedro

N1 - Funding Information:
Thework described in this paperwas supported byKingAbdullahUniversity of Science andTechnology (KAUST). A. Moraes, R. Tempone and P. Vilanova are members of the KAUST SRI Center for Uncertainty Quantification at the Computer, Electrical andMathematical Science and Engineering Division, KAUST.

PY - 2016/3/3

Y1 - 2016/3/3

N2 - ABSTRACT: In this work, we present an extension of the forward–reverse representation introduced by Bayer and Schoenmakers (Annals of Applied Probability, 24(5):1994–2032, 2014) to the context of stochastic reaction networks (SRNs). We apply this stochastic representation to the computation of efficient approximations of expected values of functionals of SRN bridges, that is, SRNs conditional on their values in the extremes of given time intervals. We then employ this SRN bridge-generation technique to the statistical inference problem of approximating reaction propensities based on discretely observed data. To this end, we introduce a two-phase iterative inference method in which, during phase I, we solve a set of deterministic optimization problems where the SRNs are replaced by their reaction-rate ordinary differential equations approximation; then, during phase II, we apply the Monte Carlo version of the expectation-maximization algorithm to the phase I output. By selecting a set of overdispersed seeds as initial points in phase I, the output of parallel runs from our two-phase method is a cluster of approximate maximum likelihood estimates. Our results are supported by numerical examples.

AB - ABSTRACT: In this work, we present an extension of the forward–reverse representation introduced by Bayer and Schoenmakers (Annals of Applied Probability, 24(5):1994–2032, 2014) to the context of stochastic reaction networks (SRNs). We apply this stochastic representation to the computation of efficient approximations of expected values of functionals of SRN bridges, that is, SRNs conditional on their values in the extremes of given time intervals. We then employ this SRN bridge-generation technique to the statistical inference problem of approximating reaction propensities based on discretely observed data. To this end, we introduce a two-phase iterative inference method in which, during phase I, we solve a set of deterministic optimization problems where the SRNs are replaced by their reaction-rate ordinary differential equations approximation; then, during phase II, we apply the Monte Carlo version of the expectation-maximization algorithm to the phase I output. By selecting a set of overdispersed seeds as initial points in phase I, the output of parallel runs from our two-phase method is a cluster of approximate maximum likelihood estimates. Our results are supported by numerical examples.

KW - Forward–reverse algorithm

KW - Monte Carlo expectation-maximization algorithm

KW - bridges for continuous-time Markov chains

KW - inference for stochastic reaction networks

UR - http://www.scopus.com/inward/record.url?scp=84959118707&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959118707&partnerID=8YFLogxK

U2 - 10.1080/07362994.2015.1116396

DO - 10.1080/07362994.2015.1116396

M3 - Article

AN - SCOPUS:84959118707

VL - 34

SP - 193

EP - 231

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

SN - 0736-2994

IS - 2

ER -