Decision making in a noisy and dynamically changing environment is a fundamental task for a cell. To choose appropriate decisions over time, a cell must be equipped with intracellular kinetics that can conduct dynamic and efficient decision making. By using the theory of sequential inference, I demonstrate that dynamic Bayesian decision making can be implemented by an intracellular kinetics with a dual positive feedback structure. I also show that the combination of linear instantaneous and nonlinear stationary sensitivities to the input dominantly contributes to decision making efficiency, and that the state-dependent sensitivity change further suppresses noisy response. The statistical principles underlying these two factors are further clarified to be a log-likelihood-dependent quantification of the input information and uncertainty-dependent sensitivity control.