Summary: We create the first computationally tractable Bayesian statistical model for learning unknown correlation structures in fully sequential simulation selection. Correlations represent similarities or differences between various design alternatives and can be exploited to extract much more information from each individual simulation. However, in most applications, the correlation structure is unknown, thus creating the additional challenge of simultaneously learning unknown mean performance values and unknown correlations. Based on our new statistical model, we derive a Bayesian procedure that seeks to optimize the expected opportunity cost of the final selection based on the value of information, thus anticipating future changes to our beliefs about the correlations. Our approach outperforms existing methods for known correlation structures in numerical experiments, including one motivated by the problem of optimal wind farm placement, where real data are used to calibrate the simulation model.