We propose a new method for the detection of evoked potentials that combines a generative model and a discriminative classifier. The method is a variant of the support vector machine (SVM), which uses the Fisher kernel. The kernel function is derived from a generative statistical model known as mixed effects model (MEM). Instead of arbitrarily selecting the Gaussian kernel for the SVM, we exploit the Fisher kernel derived from the MEM for the SVM. The strength of this approach is that it combines the rich information encoded in the generative model, the MEM, with the discriminative power of the SVM algorithm. Our results show that the new method of combining the two complementary approaches - the generative model (MEM) and the discriminative model (SVM) via the Fisher kernel - achieves substantial improvement over the generative model (MEM) and provides better performance than the discriminative model (Gaussian kernel SVM) on the detection of evoked potentials in neural signals.