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

## TL;DR

This paper introduces a new computational method for estimating steady-state sensitivities in stochastic reaction networks, avoiding time-consuming simulations by leveraging the stationary Finite State Projection algorithm and solving a Poisson equation.

## Contribution

It presents a novel approach combining the stationary FSP and Poisson equation solutions to efficiently compute steady-state sensitivities without simulations.

## Key findings

- Accurately estimates steady-state sensitivities
- Reduces computational time compared to simulation-based methods
- Validated on multiple example networks

## Abstract

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 stationary Finite State Projection (sFSP) algorithm [J. Chem. Phys. 147, 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.