Abstract

Co-authors: CHRISTIAN BAYER (WIAS, BERLIN ), CHIHEB BEN HAMMOUDA (KAUST, THUWAL ), ALVARO MORAES (ARAMCO, DAMMAM ), FABRIZIO RUGGERI (IMATI, MILAN ), PEDRO VILANOVA (KAUST, THUWAL ) 

Stochastic Reaction Networks (SRNs), that are intended to describe the time evolution of interacting particle systems where one particle interacts with the others through a finite set of reaction channels. SRNs have been mainly developed to model biochemical reactions but they also have applications in neural networks, virus kinetics, and dynamics of social networks, among others. 

This talk is focused on novel fast simulation algorithms and statistical inference methods for SRNs. 

Regarding simulation, our novel Multi-level Monte Carlo (MLMC) hybrid methods provide accurate estimates of expected values of a given observable at a prescribed final time. They control the global approximation error up to a user-selected accuracy and up to a certain confidence level, with near optimal computational work. 

With respect to statistical inference, we first present a multi-scale approach, where we introduce a deterministic systematic way of using up-scaled likelihoods for parameter estimation. In a second approach, we derive a new forward-reverse representation for simulating stochastic bridges between consecutive observations. This allows us to use the well-known EM Algorithm to infer the reaction rates.