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Switching activity estimation is an important aspect of power estimation at circuit level. Switching activity in a node is temporally correlated with its previous value and is spatially correlated with other nodes in the circuit. It is important to capture the effects of such correlations while estimating the switching activity of a circuit. In this paper, we propose a new switching probability model for combinational circuits that uses a logic-induced directed-acyclic graph (LIDAG) and prove that such a graph corresponds to a Bayesian network (BN), which is guaranteed to map all the dependencies inherent in the circuit. BNs can be used to effectively model complex conditional dependencies over a set of random variables. The BN inference schemes serve as a computational mechanism that transforms the LIDAG into a junction tree of cliques to allow for probability propagation by local message passing. The proposed approach is accurate and fast. Switching activity estimation of ISCAS and MCNC circuits with random and biased input streams yield high accuracy (average mean error=0.002) and low computational time (average elapsed time including CPU, memory access and I/O time for the benchmark circuits=3.93 s).