  Observations of exoplanetary systems provide clues about the intrinsic
distribution of planetary systems, their architectures, and how they formed. We
develop a forward modelling framework for generating populations of planetary
systems and "observed" catalogues by simulating the Kepler detection pipeline
(SysSim). We compare our simulated catalogues to the Kepler DR25 catalogue of
planet candidates, updated to include revised stellar radii from Gaia DR2. We
constrain our model based on the observed 1D marginal distributions of orbital
periods, period ratios, transit depths, transit depth ratios, transit
durations, transit duration ratios, and transit multiplicities. Models assuming
planets with independent periods and sizes do not adequately account for the
properties of the multiplanet systems. Instead, a clustered point process model
for exoplanet periods and sizes provides a significantly better description of
the Kepler population, particularly the observed multiplicity and period ratio
distributions. We find that $0.56^{+0.18}_{-0.15}$ of FGK stars have at least
one planet larger than $0.5 R_\oplus$ between 3 and 300 d. Most of these
planetary systems ($\sim 98\%$) consist of one or two clusters with a median of
three planets per cluster. We find that the Kepler dichotomy is evidence for a
population of highly inclined planetary systems and is unlikely to be solely
due to a population of intrinsically single planet systems. We provide a large
ensemble of simulated physical and observed catalogues of planetary systems
from our models, as well as publicly available code for generating similar
catalogues given user-defined parameters.
