  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.
