We propose a novel, robust estimator for the probability of speech presence at each time-frequency point in the short-time discrete Fourier domain. While existing estimators perform quite reliably in stationary noise environments, they usually exhibit a large falsealarm rate in nonstationary noise that results in a great deal of noise leakage when applied to a speech enhancement task. The proposed estimator overcomes this problem by temporally smoothing the cepstrum of the a posteriori signal-to-noise ratio (SNR), and yields considerably less noise leakage and low speech distortions in both, stationary and nonstationary noise as compared to state-of-the-art estimators. Especially in babble noise, this results in large SNR improvements.