  HI intensity mapping data traces the large-scale structure matter
distribution using the integrated emission of neutral hydrogen gas (HI). The
cross-correlation of the intensity maps with optical galaxy surveys can
mitigate foreground and systematic effects, but has been shown to significantly
depend on galaxy evolution parameters of the HI and the optical sample.
Previously, we have shown that the shot noise of the cross-correlation scales
with the HI content of the optical samples, such that the shot noise estimation
infers the average HI masses of these samples. In this article, we present an
adaptive framework for the cross-correlation of HI intensity maps with galaxy
samples using our implementation of the halo model formalism (Murray et al
2018, in prep) which utilises the halo occupation distribution of galaxies to
predict their power spectra. We compare two HI population models, tracing the
spatial halo and the galaxy distribution respectively, and present their auto-
and cross-power spectra with an associated galaxy sample. We find that the
choice of the HI model and the distribution of the HI within the galaxy sample
have minor significance for the shape of the auto- and cross-correlations, but
highly impact the measured shot noise amplitude of the estimators, a finding we
confirm with simulations. We demonstrate parameter estimation of the HI halo
occupation models and advocate this framework for the interpretation of future
experimental data, with the prospect of determining the HI masses of optical
galaxy samples via the cross-correlation shot noise.
