Thermoelectric inorganic clathrates of type I are under intense experimental and theoretical study. Partly due to its embodiment of the phonon glass electron crystal property but also because the diversity of elements which can make up the structure. This allows for a fine tuning of thermoelectrical properties, producing high zT values. Density functional theory calculations and experimental work sample only a small subset of materials and compositions. In this thesis, cluster expansions based on the compressive sensing algorithm is developed and used together with Monte Carlo simulations. This method allow the investigation of configurational dependency on temperature and composition. The clathrates Ba8Ga16Ge30, Ba8Ga16Si30, Ba8Al16Ge30 and Ba8Al16Si30 are studied as well as their non-stoichiometric versions. Calculated site occupancy factors are in good agreement with experimental work. The experimental works can be understood with stoichiometry and vacancies. Secondly, it is found that the band gap decreases as the disorder increases for all clathrates. Finally the cluster expansion in conjunction with the Monte Carlo method produces ground state structures that accurately predicts the energy which is confirmed with density functional theory calculations.