Problem statement: Until recently, many addition chain techniques constructed to support scalar multiplication operation have been proposed tailored to limited computational resources. In securing the efficiency of ECC point operation, the combinations of the two basic operations, point addition and doubling are mostly implemented. Using binary method, the operation of doubling depends solely o...

In graphical modelling, the existence of substantive background knowledge on block ordering of variables is used to perform structural learning within the family of chain graphs (CGs) in which every block corresponds to an undirected graph and edges joining vertices in different blocks are directed in accordance with the ordering.We show that this practice may lead to an inappropriate restricti...

When a Bayesian version of the general linear mixed model is created by adopting a conditionally conjugate prior distribution, a simple block Gibbs sampler can be employed to explore the resulting intractable posterior density. In this article it is shown that, under mild conditions that nearly always hold in practice, the block Gibbs Markov chain is geometrically ergodic.