  Sensitivity analysis is a process of computing sensitivity indices, which are
certain measures of importance of parameters in influencing the outputs of
mathematical models. Sensitivity indices computed in variance-based sensitivity
analysis yield quantitative answers to questions like how much on average the
variance of model output, measuring its uncertainty, decreases, if exact values
of certain unknown parameters are determined, e. g. in an experiment. We
propose new schemes for estimation of variance-based sensitivity indices of
outputs of stochastic models, their conditional expectations, and histograms
given the parameters. Unbiased estimators obtained in these schemes can be used
in a Monte Carlo (MC) procedure approximating sensitivity indices. We derive
relations between variances of final estimators of MC procedures making the
same number of evaluations of given function, but using different schemes, both
for the newly introduced schemes and for some used before in the literature.
Numerical experiment for a discrete state stochastic Markov model of a chemical
reaction network (DM) shows that our method can lead to much lower error than
method analogous to the one offered by Degasperi et al. Further numerical
experiments demonstrate that the application of random time change (RTC)
algorithm due to Rathinam et al. for simulation of DM can lead to over 30 times
lower variance of estimators of certain sensitivity indices than when
Gillespie's direct (GD) method is used, and that this variance may
significantly depend on the order of reactions in GD method. We provide some
intuitions explaining these effects. We generalize measures used for comparing
dispersion of different distributions, such as coefficient of variation and
Fano factor to the random parameters case, in a way that they can be computed
along with variance-based sensitivity indices.
