Vaccines have greatly reduced the burden of infectious disease, ranking in their impact on global health second only after clean water. Most vaccines confer protection by the production of antibodies with binding affinity for the antigen, which is the main effector function of B cells. This results in short term changes in the B Cell receptor (BCR) repertoire when an immune response is launched, and long term changes when immunity is conferred. Analysis of antibodies in the serum is usually used to evaluate vaccine response, however this is limited and therefore the investigation of the BCR repertoire provides far more detail for the analysis of vaccine response. Here, we introduce a novel Bayesian model to describe the observed distribution of BCR sequences and the pattern of sharing across time and between individuals, with the goal to identify vaccine-specific BCR sequences. We use data from two studies to assess the model and estimate that we can identify vaccine-specific sequences with 69% sensitivity.