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In this work, we consider the problem of estimating summary statistics tocharacterise biochemical reaction networks of interest. Such networks are oftendescribed using the framework of the Chemical Master Equation (CME). Forphysically-realistic models, the CME is widely considered to be analyticallyintractable. A variety of Monte Carlo algorithms have therefore been developedto explore the dynamics of such networks empirically. Amongst them is themulti-level method, which uses estimates from multiple ensembles of samplepaths of different accuracies to estimate a summary statistic of interest. {Inthis work, we develop the multi-level method in two directions: (1) to increasethe robustness, reliability and performance of the multi-level method, weimplement an improved variance reduction method for generating the sample pathsof each ensemble; and (2) to improve computational performance, we demonstratethe successful use of a different mechanism for choosing which ensembles shouldbe included in the multi-level algorithm.

Robustly simulating biochemical reaction kinetics using multi-level Monte Carlo approaches