I would suggest, actually, not the Bayesian approach, but statistical prediction rule or trained neural network.
Given the asymptotic efficiency of the Bayes decision rule in a broad range of settings, those alternatives would give equivalent or less accurate classifications if enough training data (and computational power) were available. If this argument is not familiar, you might want to consult Chapter 2 of The Elements of Statistical Learning.
Given the asymptotic efficiency of the Bayes decision rule in a broad range of settings, those alternatives would give equivalent or less accurate classifications if enough training data (and computational power) were available. If this argument is not familiar, you might want to consult Chapter 2 of The Elements of Statistical Learning.