Generalized Gibbs samplers simulate from any direction, not necessarily limited to the coordinate directions of the parameters of the objective function. We study how to optimally choose such directions in a random scan Gibbs sampler setting. We consider that optimal directions will be those that minimize the Kullback-Leibler divergence of two Markov chain Monte Carlo steps. Two distributions over direction are proposed for the multivariate Normal objective function. The resulting algorithms

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... used to simulate from a truncated multivariate Normal distribution, and the performance of our algorithms is compared with the performance of two algorithms based on the Gibbs sampler.