Approximation of Event Probabilities in Noisy Cellular Processes
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
Hybrid numerical solution of the chemical master equation
Proceedings of the 8th International Conference on Computational Methods in Systems Biology
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Approximation of event probabilities in noisy cellular processes
Theoretical Computer Science
Parameter identification for Markov models of biochemical reactions
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
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IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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The uniformization method (also known as randomization) is a numerically stable algorithm for computing transient distributions of a continuous time Markov chain. When the solution is needed after a long run or when the convergence is slow, the uniformization method involves a large number of matrix-vector products. Despite this, the method remains very popular due to its ease of implementation and its reliability in many practical circumstances. Because calculating the matrix-vector product is the most time-consuming part of the method, overall efficiency in solving large-scale problems can be significantly enhanced if the matrix-vector product is made more economical. In this paper, we incorporate a new relaxation strategy into the uniformization method to compute the matrix-vector products only approximately. We analyze the error introduced by these inexact matrix-vector products and discuss strategies for refining the accuracy of the relaxation while reducing the execution cost. Numerical experiments drawn from computer systems and biological systems are given to show that significant computational savings are achieved in practical applications.