Inferenza Bayesiana per famiglie esponenziali in un contesto di privacy differenziale

Differential Privacy has established itself as the leading framework to privacy. The goal of this dissertation is to explain how Bayesian Inference can provide an interesting solution for making inference using perturbed data coming from a differentially private mechanism. In particular, we will study the case of the exponential families and we will consider a Laplace mechanism as a differentially private mechanism. Furthermore, we will implement the inference algorithm for the multinomial case and we will discuss about its performance.