Recommender systems are designed to provide recommendations to users by means of an analysis of past preferences. To achieve this, recommender systems use information filtering techniques, these can be: Collaborative Filtering, Content-based Filtering, Demographic Filtering, and Hybrid. Collaborative Filtering computes the recommendations based on the ratings that the community of users have made over a set of items. There are two collaborative filtering approaches: memory-based, which usually provides inaccurate but explainable recommendations; and model-based, whose recommendations are more precise but hard to understand.Today's has increased the development of sophisticated machine learning algorithms which can be used in recommendation systems context. In this doctoral thesis, firts is presented a comprehensive review the literature on modelbased approaches for recommender systems of collaborative filtering, highlighting strengths and weaknesses they provide. Then, based on the advantages offered by the approaches based on probabilistic models, a Bayesian model is proposed, that combines the space of users and items, and that provides as good results as the matrix factorization models, but unlike these, generates an easily interpretable representation, therefore, the recommendations are easy to explain.The proposed modelit predicts new ratings of a user based on the existing ratings in the dataset, and it allows to easily compute a measure of reliability associate to the predictions. Reliability can be defined as the certainty of the recommendation system in the calculation of predictions. Some experiments were performed in order to compare the proposed approach with several baseline models, which were selected both from the family of approaches based on matrix factorization and from those that use a probabilistic approach to explain their results. The experiments were carried out using four public datasets of collaborative filtering, these were: MovieLens, FilmTrust, Yahoo,