The theoretical description of nature, within the standard model framework of particle physics, gives rise to a manifold of different symmetries. The most fundamental one is the combined symmetry of charge conjugation, parity transformation, and time reversal (CPT symmetry). Currently all experimental evidence opposes the idea of a broken CPT symmetry. The ASACUSA collaboration, at the "Antiproton Decelerator", at the European Organisation for Nuclear Research (CERN), tries to measure the ground state hyperfine splitting of antihydrogen. By comparing this splitting with the similar signal in ordinary hydrogen, the CPT symmetry can be directly tested. During the course of this thesis, a detector system for detecting annihilations from antihydrogen at the end of the experimental setup was developed. In this work the construction of the detector will be described in detail, including control and data acquisition of the setup. A special focus will be on the electronic components, the inner working of the data acquisition, and the structure of the measured data. The recorded data was analysed using Bayesian methods. Both, the identification of annihilation events and their consequent distinction from background signals, and the statistical analysis of the data are covered in detail. Finally, based on the statistical analysis, the data significance is presented.