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SUMMARY:Multi-level Monte Carlo: adaptive algorithms and distribution esti
 mation - Ruth Baker ()
DTSTART:20160121T133000Z
DTEND:20160121T141500Z
UID:TALK64666@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span> <span>Co-authors: Christopher Lester (University of  Ox
 ford)\, Christian Yates (University of Bath)\, Daniel Wilson  (University 
 of Oxford) <br></span></span><span><br>Discrete-state\, continuous-time Ma
 rkov models are widely used to model  biochemical reaction networks. Their
  complexity generally precludes analytic  solution\, and so we rely on Mon
 te Carlo simulation to estimate system statistics  of interest. The most w
 idely used method is the Gillespie algorithm. This  algorithm is exact but
  computationally complex. As such\, approximate stochastic  simulation alg
 orithms such as the tau-leap algorithm are often used. Sample  paths are g
 enerated by taking leaps of length tau through time and using an  approxim
 ate method to generate reactions within leaps. However\, tau must be  rela
 tively small to avoid significant estimator bias and this significantly  i
 mpacts on potential computational advantages of the method. <br> <br>The m
 ulti-level method of Anderson and Higham tackles this problem by  employin
 g a variance reduction approach that involves generating sample paths  wit
 h different accuracies in order to estimate statistics. A base estimator i
 s  computed using many (cheap) paths at low accuracy. The bias inherent in
  this  estimator is then reduced using a number of correction estimators. 
 Each  correction term is estimated using a collection of (increasingly exp
 ensive)  paired sample paths where one path of each pair is generated at a
  higher  accuracy compared to the other. By sharing randomness between the
 se paired  sample paths a relatively small number of paired paths are requ
 ired to calculate  each correction term. <br> <span><br>This talk will out
 line two main extensions to the multi-level method. First\,  I will discus
 s how to extend the multi-level method to use an adaptive  time-stepping a
 pproach. This enables use of the method to explore systems where  the reac
 tion activity changes significantly over the timescale of interest.  Secon
 d\, I will discuss how to harness the multi-level approach to estimate  pr
 obability distributions of species of interest\, giving examples of the ut
 ility  of this approach by applying it to systems that exhibit bistable be
 haviour. &nbsp\;</span></span>
LOCATION:Seminar Room 1\, Newton Institute
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