Data Mining, 4th Edition

(9.1)

Once the model parameters have been estimated, the mean of the posterior for a new example can be calculated, which can then serve as a reduced dimensional representation for it. The mathematics (though still perhaps daunting) is greatly simplified by the fact that marginalizing, multiplying and dividing Gaussians distributions produces other Gaussian distributions that are functions of observed values, mean vectors, and covariance matrices. In fact, many more sophisticated methods and models for data analysis rely on the ease with which key quantities can be computed when the underlying model is based on linear Gaussian forms.

Marginal ...