Currently, many Brain Computer Interfaces (BCI) classifiers output point estimates of user intent which make it difficult to incorporate context prior information or assign a principled confidence measurement to a decision. We propose a Bayesian framework to extend current Steady State Visually Evoked Potential (SSVEP) classifiers to a maximum a posteriori (MAP) classifiers by using a Kernel Density Estimate (KDE) to learn the distribution of features conditioned on stimulation class. To demonstrate our framework we extend Canonical Correlation Analysis (CCA) and Power Spectral Density (PSD) style methods. Traditionally, in either example, the class is estimated as the class associated with the maximum feature. Our framework increases performance by relaxing the assumption that a stimulation class's sample often maximizes its class-associated feature. Further, by leveraging the KDE, we present a method which estimates the performance of a classifier under different stimulation frequency sets. Using this, we optimize the selection of stimulation frequencies from those present in a training set.