1. A voice activity detection apparatus comprising: an acoustic signal analyzer that receives a digital acoustic signal containing a speech signal and a noise signal; generates a non-speech Gaussian mixture model, a Gaussian mixture model being hereafter referred to as a GMM, and a speech GMM both adapted to a noise environment, by using a silence GMM and a clean-speech GMM both generated beforehand for each frame of the digital acoustic signal; and calculates non-speech probabilities and speech probabilities of Gaussian distributions left after one or more Gaussian distributions having the smallest output probability are pruned from the GMMs; and a speech detection information generator that calculates a speech state probability to non-speech state probability ratio based on a state transition model of a speech state and a non-speech state, by using the non-speech probabilities and the speech probabilities, generates information about a speech period based on the calculated probability ratio, and outputs the information as speech detection information.