Name of classification algorithm based on gaussian distributions estimated from data?

Question

Can you help me find the name of this classification method:

Assume we have $n$ dimensional feature vectors we want to classify in two classes.

1. We model the classes as two $n$ dimensional gaussian distributions estimated from the data.
2. We classify a new vector to the class that maximizes the PDF (probability density function) at that point.

Answer 1

Probably Quadratic Discriminant Analysis.

There are also names for different constraints you could make:

1. Covariance matrices of both classes are equal - Linear Discriminant Analysis.

2. Only diagonal elements of the covariance matrix are non-zero - Naive Bayes Classifier

3. Covariance matrix is identity (diagonals = 1, non-diagonals = 0) - Nearest Centroid Classifier