In this paper, a new approach to sequential estimation of the time-varying prior parameters of nonstationary noise is presented using the log-spectral or cepstral data of the corrupted noisy speech. Incremental Bayes learning is developed to provide a basis for noise prior evolution, recursively updating the noise prior statistics (mean and variance) using the approximate Gaussian posterior computed at the preceding time step. The algorithm for noise prior evolution is derived in detail, and is evaluated using the Aurora2 database with the root-mean-square (RMS) error measure. Experimental results show that when the time-varying variance and mean of the nonstationary noise prior are estimated and exploited, superior performance is achieved compared with using either no noise prior information or using the time-invariant, fixed mean and variance in the noise prior distribution.