I am reviewing my lectures in Machine Learning and my current topic is Bayesian Classifier. The context is the classification of two classes C1 and C2.
My book (neural networks and learning machines by haykin) states that the Bayesian classifier, under the assumption that the two classes have a multivariate Gaussian distribution and we are basing our decision on the log likelyhood ratio the classifier acts as a linear classifier.
However, looking on wikipedia it states that the Bayes classifier acts as a linear classifier only when classes have multinomial distribution.
I know that the multinomial distribution is similar to the multivariate gaussian for a high number of samples but I don't understand why wikipedia is not specifying the case described in my book. Am I missing something?