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
Computational Probability for Systems Biology
FMSB '08 Proceedings of the 1st international workshop on Formal Methods in Systems Biology
Sliding Window Abstraction for Infinite Markov Chains
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Review: Stochastic approaches for modelling in vivo reactions
Computational Biology and Chemistry
Formalisms for Specifying Markovian Population Models
RP '09 Proceedings of the 3rd International Workshop on Reachability Problems
Hybrid numerical solution of the chemical master equation
Proceedings of the 8th International Conference on Computational Methods in Systems Biology
Approximation of event probabilities in noisy cellular processes
Theoretical Computer Science
Communications of the ACM
A Hybrid Factored Frontier Algorithm for Dynamic Bayesian Networks with a Biopathways Application
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Delayed continuous-time markov chains for genetic regulatory circuits
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
The Propagation Approach for Computing Biochemical Reaction Networks
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Quantitative reactive modeling and verification
Computer Science - Research and Development
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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.