  The XENONnT experiment searches for weakly-interacting massive particle
(WIMP) dark matter scattering off a xenon nucleus. In particular, XENONnT uses
a dual-phase time projection chamber with a 5.9-tonne liquid xenon target,
detecting both scintillation and ionization signals to reconstruct the energy,
position, and type of recoil. A blind search for nuclear recoil WIMPs with an
exposure of 1.1 tonne-years yielded no signal excess over background
expectations, from which competitive exclusion limits were derived on
WIMP-nucleon elastic scatter cross sections, for WIMP masses ranging from 6
GeV/$c^2$ up to the TeV/$c^2$ scale. This work details the modeling and
statistical methods employed in this search. By means of calibration data, we
model the detector response, which is then used to derive background and signal
models. The construction and validation of these models is discussed, alongside
additional purely data-driven backgrounds. We also describe the statistical
inference framework, including the definition of the likelihood function and
the construction of confidence intervals.
