Variance decomposition in stochastic simulators

Abstract

Articles you may be interested inThis work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models. C 2015 AIP Publishing LLC. [http://dx

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

“…Hence, in the MNRM, the randomness is encapsulated in the Poisson processes describing the channels' dynamics. This crucial point was exploited in our previous paper, 16 where control of the realizations of the Poisson processes was exploited to perform a variance decomposition and analyze the variability induced by different reaction channels.…”

“…For the purpose of decomposing the variance, as pursued below, a fine distinction and control of the individual channels' dynamics is required. 16 The standard SSA is not suitable for the purpose of performing the variance decomposition because the algorithm combines all channels' dynamics to determine the next reaction time and the first firing channel. For this reason, we consider the Modified Next Reaction Method 24 (MNRM) (see Algorithm 1) which is a slightly modified version of the original Next Reaction Method (NRM).…”

“…17 Adopting this definition, we were able, in Ref. 16, to perform an analysis of the relative influences of different reaction channels on the total variability of some model outputs of a stochastic simulator.…”

“…16, where it has been proposed to identify a particular realization of the inherent stochasticity with the corresponding realization of the standard Poisson processes appearing the so-called randomtime-change representation of the dynamics. 17 Adopting this definition, we were able, in Ref.…”

“…16 to propose a GSA method for stochastic simulators having additionally uncertain parameters. In doing so, we aim to preserve the ability to perform a global variance decomposition, namely, one that is not simply based on the SA of statistical moments.…”