2015/04/16 by Christian Bayer, Bayer, Christian, Alvaro Moraes +6
Biochemistry, Genetics and Molecular Biology · Decision Sciences · Engineering · Materials Science · #60J22 #60J27 #60J75 #62M05 #65C05 #65C60 #92C42 #92C60 #FOS: Mathematics #Gene Regulatory Network Analysis #Machine Learning in Materials Science #Numerical Analysis (math.NA) #Optimal Experimental Design Methods #Probabilistic and Robust Engineering Design #Process Optimization and Integration
paper · pdf · doi:10.48550/arxiv.1504.04155
openalex publication_date 2015/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we present an extension to the context of Stochastic Reaction\nNetworks (SRNs) of the forward-reverse representation introduced in "Simulation\nof forward-reverse stochastic representations for conditional diffusions", a\n2014 paper by Bayer and Schoenmakers. We apply this stochastic representation\nin the computation of efficient approximations of expected values of\nfunctionals of SNR bridges, i.e., SRNs conditioned to its values in the\nextremes of given time-intervals. We then employ this SNR bridge-generation\ntechnique to the statistical inference problem of approximating the reaction\npropensities based on discretely observed data. To this end, we introduce a\ntwo-phase iterative inference method in which, during phase I, we solve a set\nof deterministic optimization problems where the SRNs are replaced by their\nreaction-rate Ordinary Differential Equations (ODEs) approximation; then,\nduring phase II, we apply the Monte Carlo version of the\nExpectation-Maximization (EM) algorithm starting from the phase I output. By\nselecting a set of over dispersed seeds as initial points for phase I, the\noutput of parallel runs from our two-phase method is a cluster of approximate\nmaximum likelihood estimates. Our results are illustrated by numerical\nexamples.\n