TMB Documentation
v1.7.22

Multivariate normal distribution with unstructered correlation matrix. More...
#include <density.hpp>
Additional Inherited Members  
Public Member Functions inherited from MVNORM_t< scalartype_ >  
matrixtype  cov () 
Covariance matrix extractor. More...  
scalartype  operator() (vectortype x) 
Evaluate the negative log density.  
scalartype  operator() (vectortype x, vectortype keep) 
Evaluate projected negative log density. More...  
Multivariate normal distribution with unstructered correlation matrix.
Class to evaluate the negative log density of a multivariate Gaussian variable with unstructured symmetric positive definite correlation matrix (Sigma). The typical application of this is that you want to estimate all the elements of Sigma, in such a way that the symmetry and positive definiteness constraint is respected. We parameterize S via a lower triangular matrix L with unit diagonal i.e. we need (n*nn)/2 parameters to describe an n dimensional correlation matrix.
For instance in the case n=4 the correlation matrix is given by
\[\Sigma = D^{\frac{1}{2}}LL'D^{\frac{1}{2}}\]
where
\[ L=\begin{pmatrix} 1 \\ \theta_0 & 1 \\ \theta_1 & \theta_2 & 1 \\ \theta_3 & \theta_4 & \theta_5 & 1 \end{pmatrix} \]
(lower triangle filled rowwise) and
\[ D=diag(LL') \]
Example:
Definition at line 253 of file density.hpp.