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Statistics and Computing

, Volume 28, Issue 1, pp 131–144 | Cite as

Inference and rare event simulation for stopped Markov processes via reverse-time sequential Monte Carlo

  • Jere KoskelaEmail author
  • Dario Spanò
  • Paul A. Jenkins
Article
  • 195 Downloads

Abstract

We present a sequential Monte Carlo algorithm for Markov chain trajectories with proposals constructed in reverse time, which is advantageous when paths are conditioned to end in a rare set. The reverse time proposal distribution is constructed by approximating the ratio of Green’s functions in Nagasawa’s formula. Conditioning arguments can be used to interpret these ratios as low-dimensional conditional sampling distributions of some coordinates of the process given the others. Hence, the difficulty in designing SMC proposals in high dimension is greatly reduced. Empirically, our method outperforms an adaptive multilevel splitting algorithm in three examples: estimating an overflow probability in a queueing model, the probability that a diffusion follows a narrowing corridor, and the initial location of an infection in an epidemic model on a network.

Keywords

Intractable likelihood Rare event simulation Sequential Monte Carlo Stopped Markov process Time reversal 

Mathematics Subject Classification

62M05 60J20 60J22 

Notes

Acknowledgements

The authors are grateful to Adam Johansen and Murray Pollock for fruitful conversations on rare event simulation and to Ayalvadi Ganesh for pointing out the problem of inferring initial locations on networks.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany
  2. 2.Department of StatisticsUniversity of WarwickCoventryUK
  3. 3.Departments of Statistics and Computer ScienceUniversity of WarwickCoventryUK

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