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# A finite state projection method for steady-state sensitivity analysis of stochastic reaction networks

Dürrenberger, Patrik; Gupta, Ankit; Khammash, Mustafa

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"description": "<p><strong>Abstract</strong></p>\n\n<p>Consider the standard stochastic reaction network model where the dynamics is given by a continuous-time Markov chain over a discrete lattice. For such models, estimation of parameter sensitivities is an important problem, but the existing computational approaches to solve this problem usually require time-consuming Monte Carlo simulations of the reaction dynamics. Therefore, these simulation-based approaches can only be expected to work over finite time-intervals, while it is often of interest in applications to examine the sensitivity values at the steady-state after the Markov chain has relaxed to its stationary distribution. The aim of this paper is to present a computational method for the estimation of steady-state parameter sensitivities, which instead of using simulations relies on the recently developed&nbsp;<em>stationary finite state projection</em>algorithm [Gupta&nbsp;<em>et al.</em>, J. Chem. Phys.&nbsp;<strong>147</strong>, 154101 (2017)] that provides an accurate estimate of the stationary distribution at a fixed set of parameters. We show that sensitivity values at these parameters can be estimated from the solution of a Poisson equation associated with the infinitesimal generator of the Markov chain. We develop an approach to numerically solve the Poisson equation, and this yields an efficient estimator for steady-state parameter sensitivities. We illustrate this method using several examples.</p>",
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