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