Ab initio quantum trajectory simulations of a cavity QED system comprising an atomic beam traversing a coherently driven standing-wave cavity are carried out. The intensity correlation function in transmission is computed and compared with the experimental measurements of Rempe et al [Phys. Rev. Lett. 67, 1727 (1991)] and Foster et al. [Phys. Rev. A 61, 053821 (2000)]. It is shown that atomic beam density fluctuations induced by the motion of the atoms can account for the reported disagreement of the experimental results with theory (by an overall scale factor of 2 to 4). Moderate misalignments of the atomic beam produce large intracavity photon number fluctuations which significantly degrade the quantum correlations. One parameter fits to the experimental data are made in the weak-field limit with the adjustable parameter being the atomic beam tilt. Departures of the experimental conditions from the weak-field limit are discussed.