The main purpose of this thesis is to disclose the potential of exploiting the synergies between Statistical Science and Machine Learning. In particular, we propose a specific feed-forward Bayesian Neural Network (BNN) as a parametric statistical model able to both yield better punctual predictions than linear models and handle uncertainty through more grounded intervals than the ones offered by bootstrapping conventional Neural Networks. On top of proposing a complete methodology (based on DoE for architecture selection and MCMC to conduct inference) to apply BNNs in real cases, we analyze, using theoretical arguments from Microeconomics, the positive effect on society that it would have to use BNNs as pricing model for peer-to-peer online marketplaces and, moreover, we implement them for the case of Airbnb in Barcelona