  The Milky Way is thought to host a huge population of interstellar objects
(ISOs), numbering approximately $10^{15}\mathrm{pc}^{-3}$ around the Sun, which
are formed and shaped by a diverse set of processes ranging from planet
formation to galactic dynamics. We define a novel framework: firstly to predict
the properties of this Galactic ISO population by combining models of processes
across planetary and galactic scales, and secondly to make inferences about the
processes modelled, by comparing the predicted population to what is observed.
We predict the spatial and compositional distribution of the Galaxy's
population of ISOs by modelling the Galactic stellar population with data from
the APOGEE survey and combining this with a protoplanetary disk chemistry
model. Selecting ISO water mass fraction as an example observable quantity, we
evaluate its distribution both at the position of the Sun and averaged over the
Galactic disk; our prediction for the Solar neighbourhood is compatible with
the inferred water mass fraction of 2I/Borisov. We show that the well-studied
Galactic stellar metallicity gradient has a corresponding ISO compositional
gradient. We also demonstrate the inference part of the framework by using the
current observed ISO composition distribution to constrain the parent star
metallicity dependence of the ISO production rate. This constraint, and other
inferences made with this framework, will improve dramatically as the Vera C.
Rubin Observatory Legacy Survey of Space and Time (LSST) progresses and more
ISOs are observed. Finally, we explore generalisations of this framework to
other Galactic populations, such as that of exoplanets.
