ABSTRACT

Gaussian tree models. It turns out that this model has all the basic features of other models introduced earlier.

8.1 Gaussian models

Denote by PDm the set of symmetricm×mmatrices that are positive definite. We say that a random vector Y with values y in Rm has multivariate Gaussian distribution with the mean parameter µ ∈ Rm and the covariance matrix Σ ∈ PDm, which we denote by Y ∼ N(µ,Σ), if it has density with respect to the Lebesgue measure on Rm of the form:

fµ,Σ(y) = 1

(2pi)m/2 (det Σ)−1/2 exp(−1

2 (y − µ)TΣ−1(y − µ)).