David F. Anderson, Jingyi Ma
Stochastic reaction networks are continuous-time Markov chain models for interacting populations, with applications in biochemistry, epidemiology, ecology, and related areas. We study finite-difference sensitivity estimation when a single estimator requires several nearby parameterized paths. Existing variance-reducing couplings are typically pairwise, so that repeated use is either inefficient or requires application-specific choices in multi-path settings. We introduce the multi-path stacked coupling (MSC), a space-time Poisson construction that jointly generates any finite collection of parameterized paths. Each pairwise marginal of MSC has the same law as the corresponding split coupling pair, allowing existing variance bounds to transfer directly; in finite-state settings, we also obtain first-order expansions for the mean and second moment of finite-difference numerators. We apply MSC in three settings of practical importance: estimating many first derivatives simultaneously, estimating a single first derivative using a wider finite-difference stencil, and estimating higher-order derivatives. Numerical experiments on a processive phosphorylation network demonstrate strong performance in each of the three application areas considered, consistent with the theoretical advantages of MSC: across all three applications, MSC achieves the smallest root mean square error (RMSE) among the methods considered over the tested computational budgets.