## ABSTRACT

Multivariate general linear models (MGLM) [9, 355, 396] generalize widely used univariate general linear models [394] by incorporating vector valued responses and explanatory variables. For instance, the surface coordinates or displacement vector ﬁelds can be taken as the response variable P (Figure 7.4). The displacement vector ﬁelds are mainly obtained from the deformationbased morphometry (DBM) [81]. This chapter is mainly based on [80]. For this chapter, it is necessary to review multivariate normal distributions,

7.1 Multivariate Normal Distributions The multivariate normal distribution is a generalization of the univariate normal distribution to higher dimensions. So it can be deﬁned from 1D normal distributions as follows.