Knowledge about the interior density distribution of a planetary body can constrain geophysical processes and reveal information about the origin and evolution of the body. Properties of this interior distribution can be inferred by analyzing gravity acceleration data sampled by orbiting satellites. Usually, the gravity data is complemented with additional laser ranging or seismic data in order to reduce the range of possible density models of the interior. However, additional data might not be available and tight prior constraints on model parameters might not be justified. In this case, the flexibility of using non-informative priors and the ability to quantify the non-uniqueness of the gravity inversions are of even greater importance. In this work, we present a gravity inversion algorithm, THeBOOGIe, that samples the posterior distribution of density in the interior of a planet or moon according to Bayes theorem, following a Metropolis-Hastings iterative algorithm. It uses non-informative priors on the number, location, shape and magnitude of density anomalies. Different samples of the posterior show different density models of the interior consistent with the observed gravity data. Inversions of synthetic gravity data are ran using point masses, spherical caps and Voronoi regions (VRs) to parametrize density anomalies. THeBOOGIe is able to retrieve the lateral location of shallow density anomalies and the shape, depth and magnitude of a mid-mantle anomaly. The uncertainty of the model parameters increases with depth, as expected. Bouguer gravity data of the Moon obtained by the GRAIL mission was inverted using a VR parametrization. Shallow anomalies related to the SPA basin, crustal dichotomy and near side basins were found in the correct latitude and longitude and a trade-off in their thickness and magnitude. Positive and negative density anomalies were found in the depth range 500-1141 km. The location of deep moonquakes do not have a clear relation to the location of these density anomalies. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]