A great number of astrophysical observations suggests that of the matter in our universe, only a sixth is made up of known matter. The rest, named dark matter, has not been successfully identified. This thesis presents the analysis and statistical inference that was used by the XENON1T collaboration to conduct a search for a particular dark matter candidate; weakly interacting massive particles (WIMPs).

XENON1T is a dual-phase time projection chamber that can detect particles scattering in a 2 tonne target of liquid xenon with deposited recoil energies above ~3 keV. This is low enough to observe the elastic recoil between a WIMP and a xenon nucleus for WIMP masses >5 GeV c-2. The results presented in this thesis use 278.8 days of data, with an analysis mass of 1.3 tonne.

XENON1T uses models for backgrounds and signals within this volume to construct a combined likelihood for two science data-taking periods as well as calibration data-sets. Fits to simulated data-sets were used to calibrate and validate the confidence interval construction. In addition, analysis choices were evaluated both to optimize the discovery power and expected sensitivity of the search, and to improve the robustness of the analysis.

No significant excess was observed in the search for a spin-independent WIMP-nucleon interaction for any WIMP masses between 6 GeV c-2 and 104 GeV c-2 for the 1 ton-year exposure. This analysis produced the strongest constraint on the spin-independent WIMP-nucleon cross-section so far, with a minimum of 4.1 10-47 cm2 for a 30 GeV c-2 WIMP.

Keywords: Dark matter, direct detection, statistical analysis.