Computing Poisson probabilities
Communications of the ACM
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Inexact Uniformization Method for Computing Transient Distributions of Markov Chains
SIAM Journal on Scientific Computing
Brief Communication: Discrete-time stochastic modeling and simulation of biochemical networks
Computational Biology and Chemistry
Computational Probability for Systems Biology
FMSB '08 Proceedings of the 1st international workshop on Formal Methods in Systems Biology
Fokker–Planck approximation of the master equation in molecular biology
Computing and Visualization in Science
Approximation of Event Probabilities in Noisy Cellular Processes
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
SABRE: A Tool for Stochastic Analysis of Biochemical Reaction Networks
QEST '10 Proceedings of the 2010 Seventh International Conference on the Quantitative Evaluation of Systems
Review: Stochastic approaches for modelling in vivo reactions
Computational Biology and Chemistry
A hybrid factored frontier algorithm for dynamic Bayesian network models of biopathways
Proceedings of the 9th International Conference on Computational Methods in Systems Biology
Symmetry-Based model reduction for approximate stochastic analysis
CMSB'12 Proceedings of the 10th international conference on Computational Methods in Systems Biology
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Molecular noise, which arises from the randomness of the discrete events in the cell, significantly influences fundamental biological processes. Discrete-state continuous-time stochastic models (CTMC) can be used to describe such effects, but the calculation of the probabilities of certain events is computationally expensive. We present a comparison of two analysis approaches for CTMC. On one hand, we estimate the probabilities of interest using repeated Gillespie simulation and determine the statistical accuracy that we obtain. On the other hand, we apply a numerical reachability analysis that approximates the probability distributions of the system at several time instances. We use examples of cellular processes to demonstrate the superiority of the reachability analysis if accurate results are required.