In this paper, we discuss an efficient Bayesian computational method when observed data are incomplete in discrete graphical models. The data augmentation (DA) algorithm of Tanner and Wong [8] is applied to finding the posterior distribution. Utilizing the idea of local computation, it is possible to improve the DA algorithm. We propose a local computation DA (LC-DA) algorithm and evaluate its computational efficiency.
{Graphical models provide an undirected graph representation of relations between the components of a random vector. In the Gaussian case such an undirected graph is used to describe conditional independence relations among such components. In this paper, we consider a continuous-time Gaussian model which is accessible to observations only at time T. We introduce the concept of infinitesimal conditional independence for such a model. Then, we address the corresponding graphical model selection problem, i. e. the problem to estimate the graphical model from data. Finally, simulation studies are proposed to test the effectiveness of the graphical model selection procedure.}