Burst suppression is an electroencephalogram pattern observed in states of severely reduced brain activity, such as general anesthesia, hypothermia and anoxic brain injuries. The burst suppression ratio (BSR), defined as the fraction of EEG spent in suppression per epoch, is the standard quantitative measure used to characterize burst suppression. We present a state space model to compute a dynamic estimate of the BSR as the instantaneous probability of suppression. We estimate the model using an approximate EM algorithm and illustrate its application in the analysis of rodent burst suppression recordings under general anesthesia. Our approach removes the need to artificially average the ratio over long epochs and allows us to make formal statistical comparisons of burst activity at different time points. Our state-space model suggests a more principled way to analyze this key EEG feature that may offer more informative assessments of its associated brain state.