We perform a thorough analysis on the choice of estimators for random series
path integral methods. In particular, we show that both the thermodynamic
(T-method) and the direct (H-method) energy estimators have finite variances
and are straightforward to implement. It is demonstrated that the agreement
between the T-method and the H-method estimators provides an important
consistency check on the quality of the path integral simulations. We
illustrate the behavior of the various estimators by computing the total,
kinetic, and potential energies of a molecular hydrogen cluster using three
different path integral techniques. Statistical tests are employed to validate
the sampling strategy adopted as well as to measure the performance of the
parallel random number generator utilized in the Monte Carlo simulation. Some
issues raised by previous simulations of the hydrogen cluster are clarified.Comment: 15 pages, 1 figure, 3 table