We propose a new method to program robots based on Bayesian inference and learning. It is called BRP for Bayesian Robot Programming. The capacities of this programming method are demonstrated through a succession of increasingly complex experiments. Starting from the learning of simple reactive behaviors, we present instances of behavior combination, sensor fusion, hierarchical behavior composition, situation recognition and temporal sequencing. This series of experiments comprises the steps in the incremental development of a complex robot program. The advantages and drawbacks of BRP are discussed along with these different experiments and summed up as a conclusion. These different robotics programs may be seen as an illustration of probabilistic programming applicable whenever one must deal with problems based on uncertain or incomplete knowledge. The scope of possible applications is obviously much broader than robotics.