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A first step to implement Gillespie’s algorithm with rejection sampling

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  • Qihong Duan
  • Junrong Liu

Abstract

It is well known that firings of a well-stirred chemically reacting system can be described by a continuous-time Markov chain. The currently-used exact implementations of Gillespie’s algorithm simulate every reaction event individually and thus the computational cost is inevitably high. In this paper, we present an exact implementation of a continuous-time Markov chain with bounded intensity which can simulate the process at given time points. The implementation involves rejection sampling, with a trajectory either accepted or rejected based on just a few reaction events. A simulation study on the Schlögl model is presented and supplementary materials for this article are available online. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Qihong Duan & Junrong Liu, 2015. "A first step to implement Gillespie’s algorithm with rejection sampling," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 85-95, March.
    • Handle: RePEc:spr:stmapp:v:24:y:2015:i:1:p:85-95
    DOI: 10.1007/s10260-014-0283-6
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    1. Alexandros Beskos & Omiros Papaspiliopoulos & Gareth O. Roberts & Paul Fearnhead, 2006. "Exact and computationally efficient likelihood‐based estimation for discretely observed diffusion processes (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 333-382, June.
    2. Elliott, Robert J. & Chen, Zhiping & Duan, Qihong, 2009. "Insurance claims modulated by a hidden Brownian marked point process," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 163-172, October.
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