Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics

TL;DR

This paper introduces highly efficient centered likelihood ratio estimators for sensitivity indices in complex stochastic dynamics, suitable for long-term and steady-state analysis, with broad applicability and easy implementation.

Contribution

It proposes a new covariance-based likelihood ratio estimator that is low-variance, scalable to high dimensions, and applicable across various stochastic models.

Findings

Estimators have low, constant-in-time variance.

Applicable to diverse stochastic systems including chemical, Langevin, and financial models.

Easy to implement without modifying existing simulation algorithms.

Abstract

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.