It is poorly known whether musical training leads to improvements in general cognitive abilities, such as statistical learning (SL). In standard SL paradigms, musicians have better performances than non-musicians. However, these better performances could be due to an improved ability to process sensory information, as opposed to an improved ability to learn sequence statistics. Unfortunately, these very different explanations make similar predictions on the performances averaged over multiple trials. To solve this controversy, we developed a Bayesian model and recorded electroencephalography (EEG) to study trial-by-trial responses. Our results confirm that musicians perform~15% better than non-musicians at predicting items in auditory sequences that embed either simple or complex statistics. This higher performance is explained in the Bayesian model by parameters governing SL, as opposed to parameters governing sensory information processing. EEG recordings reveal a neural underpinning of the musician's advantage: the P300 amplitude correlates with the Bayesian model surprise elicited by each item, and so, more strongly for musicians than non-musicians. Finally, early EEG components correlate with the Bayesian model surprise elicited by simple statistics, as opposed to late EEG components that correlate with Bayesian model surprise elicited by complex statistics surprise, and so more strongly for musicians than non-musicians. Overall, our results prove that musical expertise is associated with improved neural SL, and support music-based intervention to fine tune general cognitive abilities.Keywords: statistical learning, musical expertise, P300, Bayesian model, EEG explored the temporal structure of the EEG response by correlating three Bayesian models computing statistics at three levels of complexity with the EEG response amplitude at each time point.