Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics
Provides efficient sensitivity analysis for practitioners modeling complex stochastic systems with high-dimensional parameters or disparate timescales.
The paper introduces centered likelihood ratio estimators for sensitivity indices of complex stochastic dynamics, achieving low, constant-in-time variance, making them suitable for long-time and steady-state regimes. The method is broadly applicable to chemical reaction networks, Langevin equations, and financial models.
We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher Information Matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systems with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithms without additional modifications.