  We explain in detail how to estimate mean values and assess statistical
errors for arbitrary functions of elementary observables in Monte Carlo
simulations. The method is to estimate and sum the relevant autocorrelation
functions, which is argued to produce more certain error estimates than binning
techniques and hence to help toward a better exploitation of expensive
simulations. An effective integrated autocorrelation time is computed which is
suitable to benchmark efficiencies of simulation algorithms with regard to
specific observables of interest. A Matlab code is offered for download that
implements the method. It can also combine independent runs (replica) allowing
to judge their consistency.
