We consider sensor transmission power control for state estimation, using a Bayesian inference approach. A sensor node sends its local state estimate to a remote estimator over an unreliable wireless communication channel with random data packet drops. As related to packet dropout rate, transmission power is chosen by the sensor based on the relative importance of the local state estimate. The proposed power controller is proved to preserve Gaussianity of local estimate innovation, which enables us to obtain a closed-form solution of the expected state estimation error covariance. Comparisons with alternative non-data-driven controllers demonstrate performance improvement using our approach. (C) 2015 Elsevier Ltd. All rights reserved.