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, wherein the acoustic signal analyzer comprises: an initial noise probabilistic model estimation processor that estimates initial noise probabilistic model parameters; a parameter prediction processor that predicts noise probabilistic model parameters of the current frame from estimated noise probabilistic model parameters of a preceding frame by a random walk process; a parameter update processor that receives the noise probabilistic model parameters of the current frame and updates parameters of all Gaussian distributions contained in the silence GMM and the clean-speech GMM; a probabilistic model parameter generation and estimation processor that generates a non-speech GMM and a speech GMM adapted to the noise environment in the current frame by using the updated parameters of the Gaussian distributions and parameters of various Gaussian distributions of the silence GMM and the clean-speech GMM; an output probability calculation processor that calculates the output probability of each Gaussian distribution contained in the generated GMMs; a probability weight calculation processor that calculates probability weights used for weighting the output probabilities of the Gaussian distributions in the non-speech state and the speech state, by parameterizing the distribution of the output probabilities of the Gaussian distributions with a higher-order statistic; a dominant distribution determination processor that prunes Gaussian distributions having an extremely small output probability and extracts only Gaussian distributions having a sufficiently large output probability; a first weighted average processor that obtains a weighted average of the noise probabilistic model parameters of the current frame predicted by the parameter prediction processor, by using the probability weights calculated by the probability weight calculation processor; and a second weighted average processor that obtains a weighted average of noise probabilistic model parameters subjected to weighted averaging by the first weighted average processor, only for the Gaussian distributions extracted by the dominant distribution determination processor.