A hearing device, e.g. a hearing aid, comprises an input unit; an output unit; an adaptive beamformer filtering unit configured to provide a spatially filtered signal based on a multitude of electric input signals from the input unit and an adaptively updated adaptation factor β; a memory, wherein A) a reference value REF, equal to or dependent on a value, βov, of said adaptation factor β determined when a voice of the user is present, or B) a set of parameters for classification based on logistic regression or a neural network, is stored; and an own voice detector configured to provide an estimate of whether or not, or with what probability, a given input sound originates from the voice of the user, and wherein said estimate is dependent on a) a current value of said adaptation factor β and said reference value REF, or on b) said set of parameters for classification based on logistic regression or a neural network, respectively.