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This paper considers the problem of distributed inferencing in a sensor network. It particularly explores the probabilistic inferencing problem in the context of a distributed Boltzmann machine-based framework for monitoring the network. The paper offers a variational mean-field approach to develop communication-efficient local algorithm for variational inferencing in distributed environments (VIDE). It compares the performance of the proposed approximate variational technique with respect to the exact and centralized techniques. It shows that the VIDE offers a much more communication-efficient solution at very little cost in terms of the accuracy. It also offers experimental results in order to substantiate the scalability of the proposed algorithm.