  We calculate the pair correlation function of an interacting Bose gas in a
harmonic trap directly via Path Integral Quantum Monte Carlo simulation for
various temperatures and compare the numerical result with simple approximative
treatments. Around the critical temperature of Bose-Einstein condensation, a
description based on the Hartree-Fock approximation is found to be accurate. At
low temperatures the Hartree-Fock approach fails and we use a local density
approximation based on the Bogoliubov description for a homogeneous gas. This
approximation agrees with the simulation results at low temperatures, where the
contribution of the phonon-like modes affects the long range behavior of the
correlation function. Further we discuss the relation between the pair
correlation and quantities measured in recent experiments.
