On optimal direction gibbs sampling

Generalized Gibbs kernels are those that may take any direction not necessarily bounded to each axis along the parameters of the objective function. We study how to optimally choose such directions in a Directional, random scan, Gibbs sampler setting. The optimal direction is chosen by minimizing to the mutual information (Kullback-Leibler divergence) of two steps of the MCMC for a truncated Normal objective function. The result is generalized to be used when a Multivariate Normal (local) approximation is available for the objective function. Three Gibbs direction distributions are tested in highly skewed non-normal objective functions.