Discrete-state\, continuo us-time Markov models are widely used to model bi ochemical reaction networks. Their complexity gene rally precludes analytic solution\, and so we rel y on Monte Carlo simulation to estimate system sta tistics of interest. The most widely used method is the Gillespie algorithm. This algorithm is exa ct but computationally complex. As such\, approxim ate stochastic simulation algorithms such as the tau-leap algorithm are often used. Sample paths a re generated by taking leaps of length tau through time and using an approximate method to generate reactions within leaps. However\, tau must be re latively small to avoid significant estimator bias and this significantly impacts on potential comp utational advantages of the method.

The m ulti-level method of Anderson and Higham tackles t his problem by employing a variance reduction app roach that involves generating sample paths with different accuracies in order to estimate statisti cs. A base estimator is computed using many (chea p) paths at low accuracy. The bias inherent in thi s estimator is then reduced using a number of cor rection estimators. Each correction term is estim ated using a collection of (increasingly expensive ) paired sample paths where one path of each pair is generated at a higher accuracy compared to th e other. By sharing randomness between these paire d sample paths a relatively small number of paire d paths are required to calculate each correction term.

This talk will outline two m ain extensions to the multi-level method. First\, I will discuss how to extend the multi-level meth od to use an adaptive time-stepping approach. Thi s enables use of the method to explore systems whe re the reaction activity changes significantly ov er the timescale of interest. Second\, I will dis cuss how to harness the multi-level approach to es timate probability distributions of species of in terest\, giving examples of the utility of this a pproach by applying it to systems that exhibit bis table behaviour. \; LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR