The presence of missing data in polarization measurements from radio telescopes negatively affects both the rotation measure (RM) transfer function and the Fara- day depth spectra from these data. Such gaps in polarization data are mostly caused by flagging of radio frequency interference and their effects worsen as the percentage of missing data increases. In this thesis, I present a novel method for reconstructing missing polarization data based on Gaussian processes (GPs). Gaussian processes are stochastic processes that enable us to encode prior knowl- edge in our models. They also provide a comprehensive way of incorporating and quantifying uncertainties in regression modelling. In addition to imputing miss- ing values, I also demonstrate that Gaussian process modelling can be used for recovering rotation measure values directly. Since standard Gaussian processes are computationally prohibitive, I implement and test a model that is based on a scalable Gaussian implementation called celerite. To train and test these GP models, I use simulated data based on the specifications of the MeerKAT, a precursor instrument to the Square Kilometre Array (SKA). I evaluate the GP- based models by comparing their performance with that of well-tested methods. As the results show, reconstructing missing polarization data using this proba- bilistic method increases the Î» 2 -coverage and improves the appearance and the resolution of the Faraday depth spectra.