AI Article Synopsis
- The method of moments offers a way to simplify the chemical master equation used in stochastic chemical kinetics, but it often leads to the closure problem, which leaves approximations without error estimates.
- Various moment closure schemes have been proposed to address this issue, yet they still lack reliable bounds for the approximations made.
- This paper introduces a new approach that uses semidefinite programming to determine rigorous bounds on key quantities like mean molecular counts and their variances, providing a more reliable check on moment closure approximations.
Article Abstract
The method of moments has been proposed as a potential means to reduce the dimensionality of the chemical master equation (CME) appearing in stochastic chemical kinetics. However, attempts to apply the method of moments to the CME usually result in the so-called closure problem. Several authors have proposed moment closure schemes, which allow them to obtain approximations of quantities of interest, such as the mean molecular count for each species. However, these approximations have the dissatisfying feature that they come with no error bounds. This paper presents a fundamentally different approach to the closure problem in stochastic chemical kinetics. Instead of making an approximation to compute a single number for the quantity of interest, we calculate mathematically rigorous bounds on this quantity by solving semidefinite programs. These bounds provide a check on the validity of the moment closure approximations and are in some cases so tight that they effectively provide the desired quantity. In this paper, the bounded quantities of interest are the mean molecular count for each species, the variance in this count, and the probability that the count lies in an arbitrary interval. At present, we consider only steady-state probability distributions, intending to discuss the dynamic problem in a future publication.
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| http://dx.doi.org/10.1063/1.5009950 | DOI Listing |
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