  Stochastic modeling and simulation provide powerful predictive methods for
the intrinsic understanding of fundamental mechanisms in complex biochemical
networks. Typically, such mathematical models involve networks of coupled jump
stochastic processes with a large number of parameters that need to be suitably
calibrated against experimental data. In this direction, the parameter
sensitivity analysis of reaction networks is an essential mathematical and
computational tool, yielding information regarding the robustness and the
identifiability of model parameters. However, existing sensitivity analysis
approaches such as variants of the finite difference method can have an
overwhelming computational cost in models with a high-dimensional parameter
space. We develop a sensitivity analysis methodology suitable for complex
stochastic reaction networks with a large number of parameters. The proposed
approach is based on Information Theory methods and relies on the
quantification of information loss due to parameter perturbations between
time-series distributions. For this reason, we need to work on path-space,
i.e., the set consisting of all stochastic trajectories, hence the proposed
approach is referred to as "pathwise". The pathwise sensitivity analysis method
is realized by employing the rigorously-derived Relative Entropy Rate (RER),
which is directly computable from the propensity functions. A key aspect of the
method is that an associated pathwise Fisher Information Matrix (FIM) is
defined, which in turn constitutes a gradient-free approach to quantifying
parameter sensitivities. The structure of the FIM turns out to be
block-diagonal, revealing hidden parameter dependencies and sensitivities in
reaction networks.
