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We represent switching activity in VLSI circuits using a graphical probabilistic model based on cascaded Bayesian networks (CBNs). We develop an elegant method for maintaining probabilistic consistency in the interfacing boundaries across the CBNs during the inference process using a tree-dependent (TD) probability distribution function. A tree-dependent (TD) distribution is an approximation of the true joint probability function over the switching variables, with the constraint that the underlying Bayesian network representation is a tree. The tree approximation of the true joint probability function can be arrived at using a maximum weight spanning tree (MWST) built using pairwise mutual information between switchings at two signal lines. Further we also develop a TD distribution based method to model correlations among the primary inputs which is critical for accuracy in Bayesian modeling of switching activity. Experimental results for ISCAS circuits are presented to illustrate the efficacy of the proposed methods.