Variance-based sensitivity analysis and orthogonal approximations for stochastic models

TL;DR

This paper introduces new unbiased estimators for sensitivity analysis and approximation errors in stochastic models, improving accuracy and efficiency in Monte Carlo simulations of chemical reaction networks.

Contribution

It develops novel estimators for conditional moments and sensitivity indices, with performance analysis and numerical validation in chemical reaction network simulations.

Findings

New estimators outperform previous methods in some cases

Estimator variances depend on the simulation method used

Numerical simulations demonstrate improved sensitivity analysis accuracy

Abstract

We develop new unbiased estimators of a number of quantities defined for functions of conditional moments, like conditional expectations and variances, of functions of two independent random variables given the first variable, including certain outputs of stochastic models given the models parameters. These quantities include variance-based sensitivity indices, mean squared error of approximation with functions of the first variable, orthogonal projection coefficients, and newly defined nonlinearity coefficients. We define the above estimators and analyze their performance in Monte Carlo procedures using generalized concept of an estimation scheme and its inefficiency constant. In numerical simulations of chemical reaction networks, using the Gillespie's direct and random time change methods, the new schemes for sensitivity indices of conditional expectations in some cases outperformed the ones proposed previously, and variances of some estimators significantly depended on the simulation method being applied.