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In this paper we propose a method to determine the active speaker for each time-frequency point in the noisy signals of a microphone array. This detection is based on a statistical model where the speech signals as well as noise signals are assumed to be multivariate Gaussian random variables in the Fourier domain. Based on this model we derive a maximum-likelihood detector for the active speaker. The decision is based on the a posteriori signal to noise ratio (SNR) of a speaker dependent max-SNR beamformer.