  In Monte Carlo simulations, proposed configurations are accepted or rejected
according to an acceptance ratio, which depends on an underlying probability
distribution and an a priori sampling probability. By carefully selecting the
probability distribution from which random variates are sampled, simulations
can be made more efficient, by virtue of an autocorrelation time reduction. In
this paper, we illustrate how to directly sample random variates from a two
dimensional truncated exponential distribution. We show that our direct
sampling approach converges faster to the target distribution compared to
rejection sampling. The direct sampling of one and two dimensional truncated
exponential distributions is then applied to a recent Path Integral Monte Carlo
(PIMC) algorithm for the simulation of Bose-Hubbard lattice models at zero
temperature. The new sampling method results in improved acceptance ratios and
reduced autocorrelation times of estimators, providing an effective speed up of
the simulation.
