Example 11
Case-Study XI: d-dimensional multivariate student T distribution
To test the performance of DREAM for distributions with a tail, the eleventh case study involves a d = 25-dimensional student T distribution with 60 degrees of freedom. The target distribution can be written as
|
(11.01) |
where 
is the d-variate student distribution with v degrees of freedom (v > 1) centered at the 
vector 
and with 
scale (correlation) matrix 
. The probability density function of 
is given by
|
(11.02) |
where 
denotes the Gamma function, and T denotes transpose. In the special case of v = 1, Equation (11.02) reduces to the multivariate Cauchy distribution.
The values of 
are set to zero and all-pairwise correlations in the matrix 
are set to 0.5, respectively. The initial states of each of the 
Markov chains are generated with Latin hypercube sampling by drawing randomly from 
, the 
-variate uniform distribution with lower bound values of 
and upper ranges equal to 
. Default values of the algorithmic variables are used.
Implementation of plugin functions
The complete source code can be found in DREAM SDK - Examples\D3\Drm_Example11\Plugin\Src_Cpp
